text:
Confusion between various formulas of Gibbs free energy
According to the assumptions of Constant P and T and no non mechanical work, we get
ΔG=ΔH-TΔS
But there is another form of the Gibbs free energy equation which takes Reversible process and no non mechanical work as assumption
dG=Vdp-SdT
If I Use the assumptions constant Pressure and Temperature, according to the above equation we get dG=0,which contradicts the first equation.
What is the mistake I am making? Also, when ΔGsystem=-TΔStotal

For T const, p const, zero nonmechanical work and for  reversible system, Delta H = Q = T Delta S, so delta G = 0.

You omitted the effect on G of changes in the number of moles of the reacting chemical species.

@Chet Miller, Can u elaborate a bit

See my answer at  https://chemistry.stackexchange.com/questions/138563/entropy-paradox-and-confusion-with-gibbs-energy/138607#138607  for the restrictions on $dG=Vdp-SdT$.

The differential you took as formula for Gibbs free energy is merely that for a compression/expansion, there is no reaction involved. A compression at constant T and P is a non-process.

The Gibbs free energy of a multicomponent mixture is a function not only of temperature and pressure, but also of the number of moles of the various species in the mixture:  $$G=G(T, P, n_1, n_2. m_3. ...)$$So, $$dG=\frac{\partial G}{\partial T}dT+\frac{\partial G}{\partial P}dP+\frac{\partial G}{\partial n_1}dn_1+\frac{\partial G}{\partial n_2}dn_2+\frac{\partial G}{\partial n_3}dn_3+...$$or
$$dG=-SdT+VdP+\mu_1dn_1+\mu_2dn_2+\mu_3dn_3+...$$ where the $\mu's$ are the partial derivatives of the Gibbs free energy with respect to the number of moles of each of the species, and are referred to as the so-called Chemical Potentials of the various species in the solution.  The numbers of moles of the species in the mixture change as the reaction proceeds, and that causes the Gibbs free energy to change.

Im sorry, the chemical potential is not yet introduced to us (Im just a high school student). Is it a part of non PV Work?

It is contribution to the system G by chemical compounds, describing how much G increases by addition of the unit amount of compound. It is kind of measure of compound energy usable potentially for work. Note that the value changes with concentration, i.e. is incremental ( differential )

E.g., the same galvanic cell,but with different concentration of electrolytes, is able to provide different maximal electromotoric work per the same amount of spent active components.

What I'm saying is that, in addition to temperature and pressure, the Gibbs free energy of a solution/mixture depends on the proportions of the chemical species that make up the solution (or gas mixture)..  Is that so hard to accept?


text:
Free on-line dissociation constants
Is there a decent on-line source for dissociation constants for acids and bases as CRC alternative?
This chemistry stackexchange old answer no longer has valid links:
Is there an online database of acid and basic dissociation constants?
I can only find abrupt and and possibly non-reliable links with often missed temperature like these:

https://www2.chemistry.msu.edu/faculty/reusch/VirtTxtJml/acidity.htm
https://courses.lumenlearning.com/boundless-chemistry/chapter/strength-of-acids/
https://infotables.com/chemical-tables/87-dissociation-constants-of-acids-and-bases-inorganic.html
https://chem.libretexts.org/Ancillary_Materials/Reference/Reference_Tables/Equilibrium_Constants/E1%3A_Acid_Dissociation_Constants_at_25C
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Acids_and_Bases/Monoprotic_Versus_Polyprotic_Acids_And_Bases/Polyprotic_Acids_and_Bases_1
https://depts.washington.edu/eooptic/links/acidstrength.html
https://clas.sa.ucsb.edu/staff/Resource%20Folder/Chem109ABC/Acid,%20Base%20Strength/Table%20of%20Acids%20w%20Kas%20and%20pKas.pdf

Thank you.

source: Stack Exchange

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text:
How efficient is Zinc Acetate as an Oxygen absorber?
I used to work in a microbiology lab and they used zinc acetate as O2 absorber for the anaerobic chamber. Was this an efficient way to scrub O2 from the air? I am asking because I want to make an N2 gas source by removing the oxygen from airflow. I only need to be able to produce at most 500 ccm of 99% N2. Is there something else I should consider?

I don't see any way for this compound to absorb oxygen, at all...

Just look up commercial O2 scrubbers, e.g. https://www.chromres.com/blog/the-fundamentals-of-oxygen-scrubbing  BTW, it is probably more economical to use compressed N2 or liquid N2, only using a scrubber to remove the last fraction of a percent of O2 that enters the system.

@Mithoron That was what they told me it was, they said it was zinc acetate dissolved in mineral oil, and the air was bubbled through it using an air pump and stone for a fish tank. The O2 in the chamber stayed below 0.5% at all times.

@DrMoishe Pippik I am trying to avoid using compressed sources and I do not have easy access to liquid N2. Thank you for the link though.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Significant figures in a calculation of atomic mass from isotopic abundance
I had this question:

Naturally occurring europium consists of two isotopes with a mass of 151 and 153. Europium-151 has an abundance of 48.030 and, and europium-153 has a natural abundance of 51.970. What is the atomic mass of europium? Do not include units. Be sure to round to the correct number of significant figures.

So I do the math for the calculation:
$(151 \times 0.48030)+(153 \times 0.51970) = 152.0394$
I submit 152.0 because, as I understand it, the products of the math in the parentheses should be considered to have 3 sig figs each - ending in the tenths place. So when I add those two sums up, it should end in the tenths place too given addition/subtraction sig figs rules. This is marked as incorrect, and I worry I am misunderstanding something.
I emailed the professor, and he said it was a word question and I needed only to select the fewest sig figs of the ones provided (151 and 153 have 3), so my answer should have been 152 without the 0 in the tenths place. Is this usually the case? What confuses me is I don't think I was allowed to do this for other word problems, but I could be wrong. Is there a difference between word problems and other problems, and is 3 really the amount of sig figs I should have had?

Teachers should not be torturing students with significant figure rules. They should rather teach common sense and critical reasoning in science rather than impose significant figure rules as heavenly rules. No wonder chemistry doesn't attract the brightest rather than repels them. Nobody does research with atomic mass measurements like this. I have Linus Pauling' General Chemistry Textbook (Two Nobel Prizes), and it does not even mention these these type of calculations.

Anyway, use significant figures as "common sense". These are approximate rules and the idea is that do not use unnecessary numbers once you quote the answer. Rounding off should be done at  end of all calculations. There is nothing such as sig fig rules for word problems etc.

"Do not include units" in a question with all quantities being dimensionless as well as omitted percent sign at the natural abundance value are troubling signs. As for the sig figs, your professor pretty much explained it all right and I'm not sure what kind of answer you expect on top of that. The thing is, significant figures are supposed to be studied in a math class prior to chemistry and physics (because they belong to numerical analysis) so that the questions like "do sig figs depend on the type of question" don't even arise.

Don't use an asterisk for multiplication in displayed formulas and don't omit leading zeros. Try to make title that is concise and reflects what's exactly being asked for. Never use pointless "question about".

IMHO, this case is a typical example of a task made up for a sake of the task, with rather weird up to ridiculous formulation. They should use rather real life example with meaningful numbers and approach. E.g. volumetry with uncertainties of mass, volume and concentration.

@andselisk The issue is I feel like I'm getting mixed messages from the professor, and I don't feel like pressing him for an explaination I can apply more easily will serve me. Hence why I was looking for advice from people more familiar with this. YouTube videos didn't answer my specific questions. If I had to do a calculation to solve the problem, would I not normally have to use the multi-step solution (explained) he taught previously? I definitely would have been great to have previous knowledge before the class, but I didn't know what I didn't know. Thanks for the advice on formatting.

This is somewhat of a trick question by not giving the atomic masses correctly but abundances to great precision with no indication that this has been done. The correct way according to 'What is the atomic mass of europium? ' would be to look up accurate masses and use error propagation to work out summed values of then truncate error depending on number of decimal places used in masses and percentages. etc.

Also, I'm not sure what clumsily missing the per signs is actually a troubling sign for, but feel free to go into more detail about that, about what students should ideally be taught before chemistry, about formatting, or whatever. Or just answer my question. To reiterate: when calculating the atomic mass of europium, using the specific numbers provided in the question, how many significant figures is appropriate? Since my professor specifically mentioned this is a 'word question,' I'm trying to figure out if there are special rules that make the logic in my initial conclusion (152.0) faulty.

Because I don't see how, as long as the word problem involved me doing calculations, I wouldn't go with the significant figures from my calculation. These were his exact words: all you needed to do was look at the significant figures of the given (least). 151 and 153 were both listed as 3 significant figures.

So is this a matter of academic rules regarding word problems or how you're normally supposed to handle significant figures? Or am I actually calculating things wrong. If it's the latter, a more thorough explanation would be appreciated. Circumstances mean I don't feel comfortable nagging at my professor for explainations.

Putting the task ridiculousness aside, IMHO the expected procedure is this:  isotope masses have 3 sig figs. Multiplied by numbers with more sig figs keeps these 3 sig figs. So does the summation. The result with 3 sig figs is 152. ( as said, ridiculousness aside ). Round up just the final result not to cummulate rounding errors.

Are we intended to treat the 151 and 153 as exact values, i.e., mass numbers for the purposes of this calculation? I wouldn't say yes, but it's not exactly clear from the intent of the question. When dealing with things that could well be exact integers, it is the responsibility of the question asker to be explicit about that...

First, for reasons I'll point out later this is a poorly made-up problem which was only designed to test significant figures, not to teach anything real about chemistry.
Second there are no special rules for "word problems" using significant figures.
The gist is that significant figures are a simple method to do error propagation in calculations. It is essentially based on the notion that the error is +/- 1/2 of the last significant digit, as if the value had been rounded to that digit. So 151 means that the value should be between 150.5 and 151.5.
The whole point of significant figures is to prevent you from dividing 151 by 3.00 and getting some ridiculous precision like 50.333333333333333333333333333333.
Now on to the problem. 151 and 153 are mass numbers for the europium  isotopes. Mass numbers are poor values to use for the isotope  masses. If fact the known masses are 150.9198502(26)  and 152.9212303(26). The numbers in parenthesis give the standard deviation of the measurement. So for 150.9198502 the standard deviation is 0.0000026.
Likewise according to the Wikipedia page, $\ce{^{151}Eu}$ has an abundance of 0.4781(6) and $\ce{^{153}Eu}$ has an abundance of 0.5219(6). The point is that the isotopic variation in samples taken from all over the earth limits the precision of the atomic mass for any element, not the mass of the isotopes which are know with much greater precision.
The same Wikipedia page linked earlier gives the atomic mass of europium as 151.964(1) which is inconsistent with the given percentages. I do not know the how/why there are so many more significant figures in the atomic mass (and I am too lazy to turn this answer into a research project to figure that part out...).

....limits the precision of the atomic mass for any element....    While elements with odd atomic number have maximally 2 stable isotopes, some of them have just 1, like 19F or  23Na. In these cases, atomic mass is known with precision of isotopic mass.


text:
How can I get analytical form of GTO primitives for a atom?
As I know, for Hydrogen atom a $1s$ Slater Type Orbital (STO) equation is (I can get it from here):
\begin{equation}\label{STO}
    \mathrm{STO} = \sqrt{\frac{\zeta^3}{\pi}} e^{-\zeta r}.
\end{equation}
With remark from Szabo A., Ostlund N.S. Modern Quantum Chemistry: Intro to Advanced Electronic Structure Theory, Dover, 1996:

For example, the standard exponent  for the $1s$ basis function of hydrogen is , $\zeta = 1.24$. This is larger than the $\zeta = 1.00$ exponent of the hydrogen atom, since the hydrogen $1s$ orbital in average molecules is known to be "smaller" or "denser" than in the atom.

Gaussian Type Orbital (GTO) equation for $1s$-orbital (where did this coefficient $\left(\frac{2\alpha}{\pi}\right)^{3/4}$ come from?):
\begin{equation}
    \mathrm{GTO} = \left(\frac{2\alpha}{\pi}\right)^{3/4} e^{-\alpha r^2}
\end{equation}
So, I have good analitical form of Hydrogen STO and GTO, and using formula
\begin{equation}\label{}
    \sqrt{\frac{\zeta^3}{\pi}}e^{-\zeta r} \approx C_1 \left(\frac{2\alpha_1}{\pi}\right)^{3/4}e^{-\alpha_1 r^2} +  C_2 \left(\frac{2\alpha_2}{\pi}\right)^{3/4}e^{-\alpha_2 r^2} +  C_3 \left(\frac{2\alpha_3}{\pi}\right)^{3/4}e^{-\alpha_2 r^2}.
\end{equation}
and copyng $\alpha_i$'s and $C_i$ from basissetexchange.org
#-----------------------------------------------------
# Basis Set Exchange
# Version v0.8.13
# https://www.basissetexchange.org
#-----------------------------------------------------
#   Basis set: STO-3G
# Description: STO-3G Minimal Basis (3 functions/AO)
#        Role: orbital
#     Version: 1  (Data from Gaussian09)
#-----------------------------------------------------

BASIS "ao basis" PRINT
#BASIS SET: (3s) -> [1s]
H    S
      0.3425250914E+01       0.1543289673E+00
      0.6239137298E+00       0.5353281423E+00
      0.1688554040E+00       0.4446345422E+00
END

I can plot Hydrogen orbital

Now I want to do the same for a Lithium atom using data
BASIS "ao basis" PRINT
#BASIS SET: (6s,3p) -> [2s,1p]
Li    S
      0.1611957475E+02       0.1543289673E+00
      0.2936200663E+01       0.5353281423E+00
      0.7946504870E+00       0.4446345422E+00
Li    SP
      0.6362897469E+00      -0.9996722919E-01       0.1559162750E+00
      0.1478600533E+00       0.3995128261E+00       0.6076837186E+00
      0.4808867840E-01       0.7001154689E+00       0.3919573931E+00
END

But, I do not understand where I can get a analitical formula for GTO's primitives. All of references,  I saw:
\begin{equation}\label{GTO}
\mathrm{GTO}(x,y,z;\alpha,\ell_1,\ell_2,\ell_3) = N  x^{\ell_1} y^{\ell_2} z^{\ell_3} e^{-\alpha r^2}
\end{equation}
with  unknown normalizing factor $N$. Sometimes I saw for $1p$-orbital
\begin{equation}
\mathrm{GTO}(p_x) = \left(\frac{128\alpha^5}{\pi^3}\right)^{1/4} x \exp(-\alpha r^2)
\end{equation}
but I don't understand where the factor $\left(\frac{128\alpha^5}{\pi^3}\right) $ comes from.
So, my general question: where can I see the analytical view of the GTO primitive (like for STO's), and how can you find $\zeta$ for atom obital? (how to read such data?)

I believe this website (http://www.ccl.net/cca/documents/basis-sets/basis.html ) might be helpful, even if it does not answer all the questions. For the 1s STO-3G orbital, the $\mathrm{(\frac{2\alpha}{\pi})^{3/4}}$ is in fact, the normalization constant. So I believe that for the p orbitals (or other orbitals) you only need the C and $\alpha$, then you can normalize that. The 'factor' that you see is in fact the algebraic form of the normalization constant.

Main differenece betweet STO's and GTO's is a $r$-expotetnt. Normalizing factor of GTO one can get from common procedure:
\begin{equation}
N^2 \int_0^\infty \left(r^{n-1}e^{-\zeta r^2}\right)^2 r^2 dr =1
\end{equation}
Of course, computation is not so simple for $n > 1$, but we can use online WolframAlpha (clickable calculation) and we get the formulas from the question post.
For a Lithium atom we have contraction (6s,3p) -> [2s,1p], which means
the first 3s of 6s GTO's cotract to one s "1s"-STO
$$\mathrm{STO}(1s) = \sqrt{\frac{\zeta^3}{\pi}} e^{-\zeta_1 r},$$
second 3s of 6s GTO's contract to another s "2s"-STO
$$\mathrm{STO}(2s) = \sqrt{\frac{\zeta^5}{3\pi}} r e^{-\zeta_2 r},$$
3p GTO's contract to one p - "2p"-STO
$$\mathrm{STO}(2p) = \sqrt{\frac{\zeta_2^5}{\pi}} x e^{-\zeta_2 r}$$
(notation in orbitals in quotation marks "1s", "2s" means the same as for the hydrogen atom). So, as we can see, every atomic STO contract by only 3 GTO's (which justifies their name).

For a Litium atom we have for "1s" atomic orbital
\begin{equation}
\sqrt{\frac{\zeta_1^3}{\pi}} e^{-\zeta_1 r} \approx
C_1 \left(\frac{2\alpha_1}{\pi}\right)^{3/4}e^{-\alpha_1 r^2} +
C_2 \left(\frac{2\alpha_2}{\pi}\right)^{3/4}e^{-\alpha_2 r^2} +
C_3 \left(\frac{2\alpha_3}{\pi}\right)^{3/4}e^{-\alpha_3 r^2}
\end{equation}
where
\begin{align}
\alpha_1 = 0.1611957475E+02; C_1 = 0.1543289673E+00;\\
\alpha_2 = 0.2936200663E+01; C_2 = 0.5353281423E+00;\\
\alpha_3 = 0.7946504870E+00; C_3 = 0.4446345422E+00;
\end{align}

For "2s" atomic orbital
\begin{equation}
\sqrt{\frac{\zeta_2^5}{3\pi}} r e^{-\zeta_2 r} \approx
C_4 \left(\frac{2\alpha_1}{\pi}\right)^{3/4}e^{-\alpha_4 r^2} +
C_5 \left(\frac{2\alpha_2}{\pi}\right)^{3/4}e^{-\alpha_5 r^2} +
C_6 \left(\frac{2\alpha_3}{\pi}\right)^{3/4}e^{-\alpha_6 r^2}
\end{equation}
where
\begin{align}
\alpha_4 = 0.6362897469E+00; C_4 = -0.9996722919E-01;\\
\alpha_5 = 0.1478600533E+00; C_5 = 0.3995128261E+00; \\
\alpha_6 = 0.4808867840E-01; C_6 = 0.7001154689E+00;
\end{align}

For "2p_x" atomic orbital
\begin{equation}
\sqrt{\frac{\zeta_2^5}{\pi}} x e^{-\zeta_2 r} \approx
D_1 \left(\frac{128\alpha_4^5}{\pi^3}\right)^{1/4} xe^{-\alpha_4 r^2} +
D_2 \left(\frac{128\alpha_5^5}{\pi^3}\right)^{1/4} xe^{-\alpha_5 r^2} +
D_3 \left(\frac{128\alpha_6^5}{\pi^3}\right)^{1/4} xe^{-\alpha_6 r^2}
\end{equation}
where
\begin{align}
\alpha_4 = 0.6362897469E+00; D_1 = 0.1559162750E+00;;\\
\alpha_5 = 0.1478600533E+00; D_2 = 0.6076837186E+00; \\
\alpha_6 = 0.4808867840E-01; D_3 = 0 0.3919573931E+00;
\end{align}

(For $p_y$ and $p_z$ --- do the same)
Also, for STO's best fit $\zeta_1 = 2.69$ and $\zeta_2 = 0.81$ are consistent with those given in the article Hehre, W. J., Ditchfield, R., Stewart, R. F., & Pople, J. A. (1970). Self‐Consistent Molecular Orbital Methods. IV. Use of Gaussian Expansions of Slater‐Type Orbitals. Extension to Second‐Row Molecules. The Journal of Chemical Physics, 52(5), 2769–2773. doi:10.1063/1.1673374


text:
What reaction is used for calculating pH of the solution obtained after ethanol oxidation with potassium permanganate?

If $\pu{30.0 ml}$ of $\pu{0.20 M}$ ethanol solution reacts with $\pu{1.80 g}$ potassium permanganate, what will be the final $\mathrm{pH}$ of the solution? Assume a complete reaction and that only the products of the reaction contribute to the final $\mathrm{pH}.$

I am not sure what is the correct reaction, so I cannot solve for $\mathrm{pH}.$
Is it
$$\ce{2 KMnO4 + 3 C2H5OH -> 2 MnO2 + 3 CH3CHO + 2KOH + 2H2O}?\tag{R1}$$
But $\ce{KMnO4}$ can also oxidize $\ce{EtOH}$ to a carboxylic acid:
$$\ce{CH3CH2OH + KMnO4 -> CH3COOH + H2O}.\tag{R2}$$
Should I compute $\mathrm{pH}$ based on the $\ce{CH3COOH}?$
$$\ce{CH3COOH(aq) -> CH3COO- + H+}?\tag{R3}$$

Rather potassium acetate and hydroxide, as  stoichiometry says.

I would assume complete oxidation of ethanol to acetic acid. There appears to be enough permanganate to do that and even more. Technically, the medium should be acidified, but the author probably suggested complete oxidation as is.

If I assume complete oxidation, then I can compute pH from the ionization of acetic acid using Ka and ICE table right? But the answer I am getting is not in the choices. ( 13.6, 13.4, 0.574, 0.421)

Before doing any ICE calculation, balance the reaction equation first.


text:
Miller Indices of Goldnanoparticles from Turkevich and Frens method
I need the miller indices of gold nanoparticles that were synthesized after the route of Turkevich and Frens. I during my research I found a lot of publications, but it looks like no one measured it before.
Has someone an idea of what the miller indices can be? Or better a source or paper where I can found them?

How big are your particles. The method you mentioned produces average particle sizes of around 15 to 50 nm according to the paper I found. A study for Gold particles with average diameter of around 15 nm was conducted in the linked paper, they also assign the indices here. Maybe this helps
https://doi.org/10.1016/j.promfg.2019.02.025

Assuming you refer to a record like this:

which I found in Kimling et al. in «Turkevich Method for Gold Nanoparticle Synthesis Revisited» (2006JPhysChemB15700) when reporting X-ray diffraction.


text:
Why does a 57.15% ABV spirit (ethanol+water) have a density of 923 kg per cubic meter?

According to the UK proof standard, a 100 proof spirit was defined as a spirit with gravity of $\frac{12}{13}$ that of water or $\pu{923 kg m-3}$, which is equivalent to $\mathrm{57.15\% \ ABV}$.

One liter of $\mathrm{57.15\% \ ABV}$ spirit contains $\pu{571.5 cm3}$ ethanol and $\pu{428.5 cm3}$ water. If the densities of ethanol and water at $\pu{20 ^\circ C}$ are $\pu{0.789 g cm-3}$ and $\pu{0.998 g cm-3}$, respectively, then the density  of spirit should be $\pu{0.8785 g cm-3}$ or $\pu{878.5 kg m-3}$.
Where did I go wrong with that? How can a $\mathrm{57.15\% \ ABV}$ spirit have a density of $\pu{923 kg m-3}$?

See also wikipedia: Volumefraction : In chemistry, the volume fraction φi is defined as the volume of a constituent Vi divided by the volume of all constituents of the mixture V prior to mixing.

The flip side of Poutnik's comment is that mixing 100.00 ml of water and 100.00 ml of ethanol doesn't yield 200.00 ml of solution, but rather something less.

You also may understand this contraction by thinking that H2O are tiny molecules that are able to fill the vacuums between the bulky and cumbersome ethanol molecule

@MaxW  About 196 mL.

There is nothing wrong with your calculations: but some liquids don't play nice
Your calculations are, likely, correct.
But liquids, unlike ideal gases, don't necessarily obey simple rules when mixed. In particular the two components, ethanol and water, strongly interact with each other when mixed and those interactions mean that the volumes of the pure liquids are not additive when they are mixed.
The effect is well known and a chart of it looks like this:

This is a fairly common behaviour for liquid mixtures where the components of the mixture interact. But the effect for ethanol/water is particularly strong and of practical significance both to chemists, industry and the tax authorities.

I'll note that water and ethanol are the typical choice when providing a "lost volume" classroom experiment.  Often, such a demonstration is preceded by a similar experiment using ping pong balls, ball bearings, and sand.

This is very kind of you all! I know so much more than before I posted my question. The last afternoon I spent with understanding molar fractions and volume changes of water-ethanol mixtures yet I could not come up with an equation that would result 923 kg/m3. I can't tell if it's due to my poor arithmetic skills or getting the volume change incorrectly. If it was possible, could someone please show me the calculation done right? Thank you very much in advance!

@effmate - Because volumes don't add, you also can't interpolate to get the densities of mixtures. I'm sure that there is some curve fit formula for such an often used mixture like water and ethanol, but it is fit to experimental data. There is as of yet no good theoretical way to calculate the volume or densities of mixtures.

@effmate this might help you if you're interested https://www.mathscinotes.com/2016/07/volume-reduction-in-ethanol-water-mixtures/

What is the order of the maximum relative deviation? 10%? 1%? 0.1% Sub ppm?

The maximum deviation is 4% of the total volume.

OP’s question 1: Where did I go wrong with that?

OP’s only mistake on the calculation here is the assumption of alcohol and water are additive. However, as matt_black pointed out in his answer that alcohol and water are not additive since the smaller water molecules can take up some of the space between the larger alcohol molecules, causing volume reduction (see the amount of volume reduction of various aqueous alcoholic mixtures displayed in the plot in matt_black’s answer).

OP’s question 2:  How can a $57.15\% \ \mathrm{ABV}$ spirit have a density of $\pu{923 kg m−3}$?

According to this Wikipedia article, the United Kingdom has used the Alcohol by Volume (abbreviated as ABV) standard to measure alcohol content, as prescribed by the European Union (EU) since January 01, 1980:

ABV is a standard measure of how much alcohol (ethanol) is contained in a given volume of an alcoholic beverage (expressed as a volume percent). It is defined as the number of milliliters ($\pu{mL}$) of pure ethanol present in $\pu{100 mL}$ of solution at $\pu{20 ^\circ C}$ ($\pu{68 ^\circ F}$).
This can be done in two ways. For example:

One of the two ways to make $50\% \ \mathrm{ABV}$ from pure alcohol: One would take 50 parts of alcohol and dilute it to 100 parts of solution with water while mixing the solution (thus, the amount of water added would be a little above 50 parts).
The second way to make $50\% \ \mathrm{ABV}$ is by volume fraction: Here, one would take 50 parts alcohol and 50 parts water measured separately, and then mix these two 50 parts together thoroughly. The resulting final volume would not be 100 parts, but a little less (between 96 and 97 parts).
These two mixtures would have different densities since the water content in each is different. I assume, the way EU suggest is by the second method. The following calculations confirm it.
You can calculate the densities of series of solutions of $\mathrm{ABV}$ by using experimental density values published for $\mathrm{ABW}$ here at $\pu{20 ^\circ C}$ ($\mathrm{ABW}$: Alcohol by Weight).
$$
\begin{array}{|c|c|c|c|}
\hline\
\mathrm{ABW} & \text{density} & V_\ce{EtOH} & V_\ce{H2O} & V_\text{Total} & \mathrm{ABV}  \\
\hline
0 & 0.998 & 0 & 100.200 & 100.200 & 0 \\
10 & 0.982 & 12.675 & 90.180 & 102.855 & 12.32\\
20 & 0.969 & 25.349 & 80.160 & 105.509 & 24.03\\
30 & 0.954 & 38.023 & 70.140 & 108.163 & 35.15\\
40 & 0.935 & 50.697 & 60.120 & 110.817 & 45.75\\
50 & 0.914 & 63.372 & 50.100 & 113.472 & 55.85\\
60 & 0.891 & 76.046 & 40.080 & 116.126 & 65.49\\
70 & 0.868 & 88.720 & 30.060 & 118.780 & 74.69\\
80 & 0.843 & 101.394 & 20.040 & 121.434 & 83.50\\
90 & 0.818 & 114.068 & 10.020 & 124.088 & 91.91\\
100 & 0.789 & 126.743 & 0 & 126.743 & 100\\
\hline
\end{array}
$$
Here, $V_\ce{EtOH}$ is volume of alcohol in the $\mathrm{ABV}$ solution and $V_\ce{H2O}$ is volume of water in the same solution (e.g., in $10\% \ \mathrm{ABW}$ at $\pu{20 ^\circ C}$, volume of $\ce{EtOH}$ is $\frac{\pu{10 g}}{\pu{0.789 g mL-1}} = \pu{12.675 mL}$). Consequently, $V_\text{Total}$ is $V_\ce{EtOH} + V_\ce{H2O}$, the total volume of alcohol and water in the $\pu{100 g}$ of particular $\mathrm{ABW}$ solution without considering the volume lost.
When you plot the $\mathrm{ABV}$ versus density you get a polynomial curve with equation $y = -1.0 \times 10^{-5}x^2 - 0.0007 x + 0.9956$ with $R^2 = 0.9996$ (an excellent agreement):

Using the plot and the equation, now you can calculate the density of any $\mathrm{ABV}$ solution at  $\pu{20 ^\circ C}$. For example, let's calculate density for $\mathrm{57.15\% \ ABV}$:
$$y = -1.0 \times 10^{-5}x^2 - 0.0007 x + 0.9956 \\
= -1.0 \times 10^{-5} \times (57.15)^2 - 0.0007 \times 57.15 + 0.9956 =  0.923$$
This is an excellent agreement with the definition.
Also, the beauty of the data analysis in above table is you can find the $\% \ \mathrm{ABW}$ of any given $\% \ \mathrm{ABW}$. For example, if you plot the $\% \ \mathrm{ABV}$ versus $\% \ \mathrm{ABW}$, you get a polynomial curve with equation $y = 0.0023 x^2 + 0.7617 x + 0.1878$ with $R^2 = 1$ (an excellent agreement):

Using this plot and the corresponding equation, now you can calculate the $\% \ \mathrm{ABW}$ of any given solution if you know its $\% \ \mathrm{ABV}$ at  $\pu{20 ^\circ C}$. For fun, let's calculate $\% \ \mathrm{ABW}$ for $\mathrm{57.15\% \ ABV}$ in OP's question:
$$y = 0.0023 x^2 + 0.7617 x + 0.1878 \\
= 0.0023 \times (57.15)^2 + 0.7617 \times 57.15 + 0.1878 =  51.23\%$$


text:
electronic transition for polyenic molecules
I am having troubles with polyenes states symmetry.
I found an exercise on the pentadien, where they ask us to analyze the symmetry of the singlet excited states corresponding to:
State S1: π+ →π+
State S2: π+ →π-
State S3: π- →π+
State S4: π- →π-
1- I would like to understand what the signs + AND - refer to in this problem. Is there any forbidden transition?
I searched in plenty of books and I have not encountered  these signs, I thought that it corresponds to the wave function sign but I do not see the relation between the transition rules and the signs of the π MO, I thought +/- signs  matter only for transitions between Σ diatomic states .
2-In the case of a polyene molecule, in order to find the symmetry of the ground and excited states, do we need to find the symmetry of the π orbitals in relation to m and C2 operations only? or do we have to find the group symmetry of the molecule and apply all the operations of the groupe?
3-For an excited singlet state having two unpaired electrons, do we multiply the symmetry of the π molecular orbitals in order to get the symmetry of the state? Like m(S)*m(A)=m(A)? Can we do this?
4-Could you please help me and suggest books that are related to my questions?
Thank you all.

Could you please provide a source for this exercise? I'm not sure why they use capital Pi letter as an orbital symbol, and why an underscore is used for what is logically supposed to be minus.

Thank you for replaying It is a test given by my University. I also don't understand why they used the capitol letter. For the underscore it is supposed to represent a minus.

Capital $\Pi$ can be used as a label for molecular orbitals, but only in linear species ($D_{\infty\mathrm{h}}$ or $C_{\infty\mathrm{v}}$). For polyenes it appears that small $\pi$ is the appropriate description. However, this doesn't mean that they are doubly degenerate orbitals; it indicates that they are part of the $\pi$ system of the molecule (i.e. conjugated p orbitals). At least to me, the $+$ and $-$ labels don't seem to have an easy explanation: usually these denote symmetry with respect to some mirror plane, but it's not obvious how that applies here.

Thank you very much for your explanations, I corrected the post.

It is hard to know but if +/- are replaced with u/g  the $S_0 \to S_1$ transition is forbidden as the symmetry of both states is the same, and $S_0\to S_2$ allowed. However, $\pi-$ in $S_3 , S_4$ are then difficult to understand.

Thank you very much porphyrin for your suggestion, so you are proposing to consider the same logic as for homonuclear diatomics, and concider a center of symmetry. If this was the case we would have for pentadien MO the following symmetries regard to the application of a centre of symmetry: π1 Assymetric(u or -). π2 symmetric(g or +). π3 assymetric. π4 symmetric, and we would consider the translations between states of diffrent symmetries (  S0→S2 and   S0→S3) only and the other transitions would be forbidden (  S0→S1 and   S0→S4). I do not know if this is correct, but this was very helpful.


text:
Why is the sum of two inexact differentials exact?
From the first law of thermodynamics, $\mathrm{d}U = đQ + đW$, where $\mathrm{d}$ represents an exact differential and $đ$ an inexact differential. Exact differentials correspond to state functions and are path-independent.
How is it possible, and what does it imply, when we say that the sum of two inexact differentials is an exact differential? Is the sum of two path-dependent functions always a path-independent function? Also, what is the difference between a partial derivative and an inexact derivative / differential, apart from mathematical implications?

I saw essentially the question (somehow the answer is still unclear to me) posted in Physics SE. Perhaps you'll be able find it. It might be a case of notation abuse as per Wikipedia. I also think that an elegant answer might be given here too. When I say the answer is not clear to me, I mean it is my problem... I always remain with the same taste even if at first I think to understand...

It obviously is not valid generally, but particularly for the Q and W case. BTW, it is exact/inexact differential, not derivative.

@Alchimista Sir,could you provide me that quesion link?

@Poutnik Sir, how do you differentiate between a derivative and a differential?

@Chemistrystudent sorry not.. But owing to the comment by Poutnik I am not sure if it was right the same. It was more on the use of small differential in physics (and chemistry) as they would be exact or taken as derivatives. Tough my analysis skill comes from calculus so I somehow even wonder what the difference is. But it should be the second part of your question.

@Chemistrystudent  If y=f(x), then in dy=(df/dx) .dx, dy and dx are differentials, (df/dx) is derivative. For function of more variables, a partial derivative, respectively. By other words, derivative is a function, differential is an infinitely small but nonzero variable change. In geometrical analogy, the derivative is a line ( or curve tangent ) slope, differentials are 'by all means negligible changes" of variables y and x, shifting along this line.

There is a reason why it is a law (similar to an axiom): it is not trivial neither general. If it would be always true or if there were a simple derivation, it wouldn’t be a law in thermodynamics.

@Alchimista Here is a physics answer: https://physics.stackexchange.com/questions/385555/why-dq-and-dl-are-not-exact-differentials-while-instead-du-is-exact

I have a pie. Amy and Bill eat pieces of pie. From the fact that the pie is gone there is no way to show who ate how much pie...

@KarstenTheis Thank you. But I have no problem with this specific case Q + W. It is more on the treatment of differentials replacing derivatives that I am confused. But it does not really pose me operative troubles. It is more on reading discomfort here and there that alone I can't even perceive :)

There's not much to do, as you nearly spotted the difference by yourself: $U$ is a state function, thus is path-independent. In other terms, one can estimate it at any moment only with an initial and a final value (and express it in terms of its variables only). But with $Q$ and $W$, it's different: these are path functions (or process functions) consequently depending on the path. Hence, their differential is not something one might express depending only of its variables. (these are not "real" functions for mathematicians...)

Is the sum of two path-dependent functions a path-independent function?

The sum of inexact differentials is an exact differential in that particular case. In other cases, it depends on the units involved: for instance, with entropy, we have $\mathrm{d}S = \delta Q_\mathrm{rev} / T$. So, no typical case here!

what is the difference between a partial derivative and an inexact derivative?

These are absolutely not the same! A partial derivative is a differentiation of a multi-variable function regarding one of its variables only, while what we have here is an inexact differential, thus not a derivative as 1) no variable is specified here, and 2) an inexact differential can be of a function depending on only 1 variable.

How is it possible, and what does it imply, when we say that the sum of two inexact differentials is an exact differential?

In the example at hand it means that we divide the ways we can change the energy of the system into exactly two bins. The first we call heat, and all the other ones we call work.
Heat is an energy transfer that occurs when two entities of different temperature are in contact. The difference in average kinetic energy of the particles
causes an energy transfer during collisions which overall increases the temperature of the cooler one and decreases the temperature of the hotter one.
Work is everything else, from compression of a gas to stirring to powering a heating coil inside the system with an electrical power source outside of the system.
We can have different amount of heat and work depending how we run a process. If the starting and final state match for two processes, the change of the system's energy will be the same, no matter what path we choose (i.e. what the individual contributions are).

Is the sum of two path-dependent functions always a path-independent function?

We could have divided up the work into pV-work and non-pV-work. Both would be inexact differentials. If we add them up, we would still have an inexact differential.
So the answer to your question is no.

Also, what is the difference between a partial derivative and an inexact derivative / differential, apart from mathematical implications?

A partial derivative is when you form the derivative of a multi-variable function with respect to a single variable. So if my function T(r) describes the temperature distribution in 3D space, and I form the derivative with respect to the height $z$, that is a partial derivative. This is different from the total derivative, which would tell me the gradient of the temperature at a given point (i.e. in which direction it changes most). So a partial derivative and an inexact differential are quite distinct.

For more math, see also https://chemistry.stackexchange.com/questions/22171/why-is-du-an-exact-differential-and-dq-an-inexact-differential?rq=1

Imagine that you propose to climb Mount Everest. From your desk you can compute exactly how much energy you will need to reach the top of the mountain starting from base camp. That would simply be the gravitational energy difference between the two locations. With that information at hand you load up on supplies - dividing the gravitational potential energy difference by the energy density (calories/weight) of your favorite granola brand - and get underway. Not surprisingly however you find yourself out of granola before getting very far and decide to turn back. You then have some free time to puzzle over what went wrong.
After some thought you realize that not all of that granola was turned into work, and that different members of your climbing team exhibited different efficiencies converting granola into work. One of them seemed to convert it mostly into heat and did not get very far at all.
So every step required an exact amount of energy at minimum to raise your body up the gravitational potential (performing the desired work), but the amount of energy actually spent was inexact and varied between people, some requiring more energy just to stay warm in the Himalayan summer. As you dwell deeper into the subject you realize that climbing Everest was more complicated than envisioned. In fact much energy from the granola was spent changing your latitude and longitude, rather than your elevation, as well as in keeping your body warm and functioning.
After some days a couple of your climbing companions surprise you by announcing that they managed to reach summit and get back alive. More importantly they also monitored their metabolism, position and granola consumption on the way up. From this data you manage to estimate how much granola was used up to change their latitude and longitude and how much they used to keep warm and their bodies functioning. The energy accounted for by the change in height did not change. But now you have a better estimate of how much granola to pack next time you attempt the climb.


text:
What is the general phenomenon taking place here?
For many cases while calculating the activity of a particular species I find them calculating like this:
$$a=\frac{p_{Mn}}{p^{\circ}_{Mn}}$$
What I really do not understand is what is evaporating into what. A detailed explanation of the topic and quantification of the parameter as activity is most welcome.
This link very well explains how thermodynamic activities are defined. However what I really do not understand is how the "estimating activity" technique is to be applied. A detailed answer to that is most welcome.

Have you tried just looking up definitions of thermodynamic activity? That would be a good way to start.

What is the meaning of "Mn" ? Is it manganese ? Is so, what is manganese doing here ? And what is $p_{Mn}$ ? Is it a pressure ? Which pressure ? Please explain !

@Maurice Yes Mn is Manganese. What is it doing here..I do not know.Yes that is partial pressure of Manganese.Please explain this.

Title is vague and moreover there is not a phenomenon taking place.

At low pressures the activity of a gas can usually be related in a straightforward way to its partial pressure as
$$a=p/p^{\circ}$$
Since the activity of a substance present in multiple phases is the same in all of the phases, for a volatile compound it suffices to determine the partial pressure in the gas phase to know its activity in condensed phases. This is how the activity of water in different materials including foodstuffs is usually determined.
For the case of a non-volatile solute in a condensed phase things are not so simple. For electrolytes, theories such as Debye-Hückel do a reasonable job of predicting activities at low concentrations, and other theories do better at higher ionic strengths. Electrochemical measurements can provide experimental values of activities. Because ions usually exhibit strong deviations from ideality this field has been studied extensively and even introductory physical chemistry or analytical chemistry textbooks will address it at some length.
One path to determine the activity of a non-volatile non-electrolyte - for which a vapor-pressure measurement is impractical - is to determine the activity of the solvent and to invoke the Gibbs-Duhem equation relating the activities of the solute and solvent. This is what is meant in the Libretext:

The activity coefficient for a nonvolatile, neutral solute is often estimated by non-linear curve fitting, taking into account the molality of the solute and the activity of the solvent (usually its vapor pressure).

Ok.But tell me somethin can you explain clearly the section on "Estimating Activities."

@RajorshiKoyal It's difficult to summarize, after all that's the point of the libretext you link to. You use different methods depending on the type of solute. You mention Mn. This is typically an ion in solution. Then you determine the ionic strength of your solution and look up or compute the "activity coefficient" for Mn at that ionic strength and temperature. You multiply the activity coefficient and concentration of Mn to obtain its activity.

I still cannot get can you get into the chat once?


text:
Balancing reaction between lead(II) sulfide and ozone
I came across a question, asking to check whether the reaction is correctly balanced or not and one of the options were
$$\ce{PbS + 2O3 -> PbSO4 + O2}.\tag{R1}$$
The reaction seems to be a balanced one (atoms-balanced and charge-balanced).
But my teacher told that it is not the correct balanced reaction.
The reason given to me was that ozone breaks into $\ce{O2}$ and $\ce{[O]}$ as:
$$
\begin{align}
\ce{O3 &-> O2 + [O]}\tag{R1.1}\\
\ce{PbS + [O] &-> PbSO4}\tag{R1.2}
\end{align}
$$
Hence, the correct one is
$$\ce{PbS + 4 O3 -> PbSO4 + 4 O2}.\tag{R2}$$
But both reactions seem to be balanced and should depend on the conditions.
Am I thinking right? Or the reaction always proceed in this way only? If so, then why?

Formal balancing is one thing and reaction mechanism another thing. If you think that any O atom can oxidize PbS, than correct balancing would have no O2 Left. And you would not need O3 at all in the first place.

It's perfectly balanced, but that doesn't mean it's the right reaction that actually takes place. How you're supposed to know that for this problem is, I have no idea...


text:
How many structural isomers does 1,2-dimethyl-cyclohexane have?
Can someone tell me how many structural isomers exist for 1,2-dimethyl cyclohexane? My teacher said there is one structural isomer but I believe there aren't any because there is no other way to define the structure of the above compound such that they have the same molecular formula but a different structural formula. Also, we need two or more compounds to define isomerism, so how can a single molecule be ever defined as an isomer if there isn't any other compound to compare it with?
Also can structural isomers be defined if the position of substituents is already defined as in the case of above compound where the positions of the two methyl groups are defined beforehand (i.e. 1, 2)?

How many ways can you attach two methyl groups to a cyclohexane ring such that none of the structures has the same atom connectivity? Let's see some effort.

Did you search it on a search engine? Did you try anything yourself? What and how much progress did you make? Without these inclusions, we cannot answer your question because this is not a question-solving website. I hope you understand our point. Nothing personal and, welcome to Chem.SE

I guess there are 3 ways to connect two different methyl groups.And yes i did search for it everywhere. Peace.They say that there can be structural isomers for dichlorohexane which makes sense as i have 3 arrangements to place the two methyl groups.But what in the case of the above compound?

We have already specifed the positions of the substituents so structural isomers are out of question right? Had it only been C6H10Cl2 i could have made different structural isomers but i am confused as the above compound is already a structural isomer.

The molecular formula for 1,2 dimethyl cyclohexane is $\ce{C8H16}$ which is the same as numerous compounds. It would seem that the teachers question was some (stupid?) play on words. Could you give the exact wording of the question?

If you are specifying it as 1,2 dimethyl cyclohexane you cant make any structures but with a general formula of dimethyl cyclohexane, you can make a few structures.
once you have named the compound completely, you can't really make any structural isomers of it since the name ensures that you can make only one compound out of what name you have been given, which is the entire point of IUPAC nomenclature. If this were however dimethyl cyclohexane, you could make 1,1 dimethyl cyclohexane, 1,2 dimethyl cyclohexane, and 1,3 cyclohexane.

This was exactly what I was thinking. Thanks a lot. Also does methane have any isomers coz there is just one possible structure. Although wiki shows that it does have one. Tysm again :)

again, methane is IUPAC named so no, it can't have any isomers, of any type whatsoever

My teacher said there is one structural isomer

I think (hope) you are talking about stereo isomers (i.e. same Lewis structure, different substance).
There are two ways of counting. Either you can ask "How many substances are stereo isomers of cis-1,2-dimethylcyclohexane?" Or you can ask "How many stereo isomers exist of 1,2-dimethylcyclohexane?". The correct answers are off by one.
This is like asking "how many siblings do you have" vs. "how many siblings are there in your family (including you)".

How many structural isomers does 1,2-dimethyl-cyclohexane have?

The molecular formula for this substance is $\ce{C8H16}$. There are lots of substances with that formula but different Lewis structure.

Yeah that makes sense.sorry about the wrong molecular formula lol.Could you also tell me why methane has 1 structural isomer.It shouldnt have any right? Becoz structural isomerism involves two or more molecules.But here we have just one.So how can we compare when there isnt a second molecule to compare with.

How many siblings in a single-child family?

Zero? Coz there is just one child.Had there been two or more we could have concluded that they were siblings of one another right?


text:
kinetic description of an autocatalytic system
I have previously asked this question at physics SE here and it was suggested to post it here.
I am looking at the system:
$2X + Y \Leftrightarrow 3X $
$A \rightarrow Y$
$X \rightarrow B$
The description in terms of differential equations is this:
$\frac{dx}{dt} = x^{2}y - x$
$\frac{dy}{dt} = a - x^{2}y$
What is puzzling me is that the fact that 3X are produced is not captured in these equations.
Why is the description not something like
$\frac{dx}{dt} = 3x^{2}y - x - x^{3}$ ?
What fundamental thing am I missing? Help is greatly appreciated.
The source for this is "mathematical models in biology (1987), p 357" by Leah Edelstein-Keshet.
(also, I have a hard time finding relevant tags for this, so please feel free to change)

In the first reaction only one X is produced net, since two are consumed and three produced. The missing $x^3$ term seems to be due to an assumption that the reverse of the first reaction is negligible. Note that there should be rate constants associated with all reactions that also factor into the rate equations

ok, that makes sense. My guess is that they set all rate constants to 1 to make the analysis of the system more convenient. thanks! What would the equation look like if the $x^3$ term was not ignored?

Let's first assign rate constants to each reaction for completeness:

$\ce{2X + Y <=>[k_1][k_{-1}] 3X}$

$\ce{A ->[k_2] Y}$

$\ce{X->[k_3] B}$

Then let's consider what's happening overall. A is converting to Y, Y is converting to X, and X is converting to B:
$\ce{A ->[k_2] Y <=>[k_1X^2][k_{-1}X^2] X ->[k_3] B}$
Y and X may be in equilibrium, and X catalyzes the X-Y interconversion.
Since X and Y are intermediates, I'm guessing that you are writing the rate equations for them in order to do a steady-state approximation?
Regardless of the purpose, we can see that X is created only in the reaction $\ce{Y -> X}$, which has $\frac{d[\ce{X}]}{dt}=k_1[\ce{X}]^2[\ce{Y}]$. However, it is consumed in two possible reactions, the back reaction $\ce{X -> Y}$ and the forward reaction $\ce{X-> B}$. So the consumption rate is $-\frac{d[\ce{X}]}{dt}=k_{-1}[\ce{X}]^3+k_3[\ce{X}]$. Combining the two equations, we find that
$$\frac{d[\ce{X}]}{dt}=k_1[\ce{X}]^2[\ce{Y}]-k_{-1}[\ce{X}]^3-k_3[\ce{X}].$$
This equation is similar to yours, but complete with rate constants and including the extra term for the reverse reaction. If that reaction is negligible, that term would drop out and give an equation like yours.
For Y, you can use the same process to again get a slightly longer equation than what you have written, because it includes an extra term for formation of Y from X in the back reaction. Clearly the derivation of the equations you provided assumes that only the forward reactions are significant.

A and B are source and sink, respectively. The book chapter is about the dynamics of the X-Y system and discusses criteria for oscillatory solutions. I believe your assessment of neglectiing the $X^{3}$ term is correct. What puzzled me is that the factor 3 for 3 X produced never appears explicitly, but I assume it is stuffed into the $k_1$ term?

The 3 doesn’t appear because only one X is produced in that reaction. You could describe it as 3 produced and put in that 3 factor, but then you would have an additional term for the 2 “consumed” in the same reaction and they would add up to what I have written


text:
Are all exergonic reactions spontaneous?
Exergonic reactions have a negative $\Delta G$: the system loses free energy. Spontaneous reactions are also defined in the same way, as far as I know. Does this mean the two are synonymous?
There are some questions (e.g. here) asking the same question for exothermic reactions, but not all exergonic reactions are exothermic.

That depends on conditions under which your process is taking place. If process happening under constant temperature and pressure, then negative $\Delta$G  < 0 $\equiv$  spontaneous. Elif happening under constant entropy and pressure, $\Delta$H  < 0 $\equiv$  spontaneous


text:
Why isn't calcium carbide more corrosive?
Acetylene has a pKa of 26, I think.  While that's pretty acidic ... for a hydrocarbon ... I still expect calcium acetylide (carbide) to be a very strong base indeed.  Yet the NFPA fire diamond health code is just a 1, compared to a 3 for both sodium and calcium hydroxides, even though each mole of the carbide ought to create a mole of calcium hydroxide the moment it touches water.  Little kids play with toy cannons powered by somewhat impure calcium carbide, taking no special lab precautions.  Why is that possible?
Update: I have since noticed that those NFPA diamonds don't all agree. The Santa Rosa Fire Department and Wikipedia say Health rating is 1.  Fisher Scientific says it is 2.  NOAA says it is 3.  I may never look at one of those little diamonds the same way again...

It is indeed corrosive to eyes, skin and respiratory tract.

In these Safety Data Sheets for $\ce{Ca(OH)2)}$ and for $\ce{CaC2}$, both compounds are rated at "Causes serious eye damage – Category 1" and "Causes skin irritation – Category 2".
That said, $\ce{CaC2}$ is often sold as pellets or "stones". Because of large particle size, only a small amount of $\ce{Ca(OH)2)}$ is produced at a time from the action of water on $\ce{CaC2}$ since the release of acetylene bubbles slows penetration of water into the pellets.
$\ce{Ca(OH)2)}$, on the other hand, is more often sold as a finely divided powder. That dust is, in my experience more of a respiratory hazard. The "lime", as it's slaked in water, also evolves considerable heat, which exacerbates the caustic effect on skin.
Of course, $\ce{CaC2}$ has it's own hazards... it can cause considerable damage from an acetylene explosion.


text:
Is CH₃CH(CH₂CH₃)₂ the same as CH₃CH(CH₃CH₂)₂
The carbon in front of the parenthesis is bonded to 2 CH2 which then bonded to CH3, it cannot bond directly to CH3. I assume the correct way of writing the formula of this molecule will be CH₃CH(CH₂CH₃)₂.
However, the university lecturer says its ok to write CH₃CH(CH₃CH₂)₂ because it is a common knowledge that CH3 cannot bond to both CH2 and C at the same time which indicate that the carbon in front of the parenthesis is bonded to CH2.
Trying to understand the lecturer's explanation, does it mean that in a parenthesis, it doesn't matter whether one person writes the order of bonding forward or backward and it is up to the reader to figure out whether the carbon in front of the parenthesis is bonded to the first or the last carbon in the parenthesis?
I am a non-native English speaker and I hope my question is explained clearly. Tried my best to phase this. Please let me know if any part of the question does not make sense.

The first way in the title is the normal way, the second is an abnormal rendition. Yes the second way can be puzzled out, but why make it hard on the reader?

Calcium acetate is sometimes written as (CH3COO)2Ca, sometimes Ca(CH3COO)2. Regardless of which way is correct, it is the same compound.

@MaxW So the order does not matter, it is just courtesy to write in the correct way according to the order of bonding. Do I understand this correctly? Me being too accurate, answered a test question and said these two are not the same molecule, got mark down for my answer.

@DanL - It is much more than a courtesy, but your teacher is right they are the same molecule. Frankly I think asking if the two are the same molecule on a test is a stupid question, but just let it go. If your teacher says the earth is flat, then in that classroom the earth is flat.

@MaxW the earth is flat until one can report him while not getting caught ;)


text:
Why are rare earth metals and platinum group metals are often found clustered together in ores
Rare earth and platinum group metals are often found clustered together in the earth's crust. Mining for platinum, for instance, also yields Rhodium and Ruthenium belonging to the same group. Likewise, rare earth elements such as Neodymium, Europium and Samarium also cooccur in the same ore, so much so, that they are difficult to chemically separate.
It could be reasoned that it's the result of nucleogenesis where elements are formed consecutively based on their atomic number. While it might explain the first row and the second row of each group, where each metal is only one atomic number apart, it doesn't explain why metals from both rows are found together which are much further apart.
Alternatively, the similar chemistry of each group could explain the clustering. The two groups are the only group with this property. It fails to explain, however, how these metals found each other in a molten soup of heterogeneous elements. There may be some geological factors in the clustering, but it's unclear.
Why are the two groups of elements found clustered together?

Why shouldn't similar elements be found together?

Edited my question to answer yours.

It is very unlikely that nucleogenesis is the cause at least for non-radioactive ores as the earth's crust is largely the product of geological processes and not "primordial" in the sense that it is a collection of raw material from the early solar system unmodified by time.

Perhaps check out this: https://en.wikipedia.org/wiki/Goldschmidt_classification as a start. Good question, by the way.

Most ores are not coming from “molten soup of heterogeneous elements” (whatever it means), though even it is so, chemically similar elements crystallize together. Also, this can be an observation bias, too: elements, which are harder to separate are perceived as “found together”.  Both of your examples are elements which often found in very low concentration even in their ores. That means that per definition they are found together with many other elements, even in large quantities, yet you notice only the ones that cre for.

The title may create confusion it is meant rare earth and platinum group metals together, instead of  each group separately.

@Poutnik I tried really hard but ran out of text space.

@user148298 Perhaps using OR instead of AND ? And there is an extra "are". Just suggestion.

A single element is frequently "clustered with itself", not being scattered homogenously across the whole Earth volume. Why should not elements with very close – sometime almost identical – properties be clustered together as well ? They are usually older than Earth, often being ash of past supernova explosions, getting together to Earth foundations.

@Poutnik Can you provide a less ambiguous wording?

@user148298  Sure, but provide a less ambiguous question for me to know what to focus on.

The factors that generate mineral concentrations are complex and often only partly known
Introduction: geology is complicated
The one thing we can be very certain about is is that the distribution of minerals in the earth's crust has very little to do with the primordial origins of the component elements (that is where they came from in the early solar system and how they were originally generated). Most "heavy" elements are originally formed in the cores of supernovae and not in either the big bang or in normal stars.
The distribution of elements in the earth is mostly unrelated to the cosmic origins of elements because the earth's crust is not static but is frequently churned up by a variety of processes on a geological timescale. If we go back far enough in the history of the planet, everything was molten and this allowed some of the denser components to separate out before the surface cooled enough to be solid. The led to the core being mostly metallic (and consisting of mostly iron and nickel). Higher layers contain less dense minerals containing a lot of silicate minerals. At the top there is a thin layer, the crust, which is where we find useful minerals and it is even more concentrated in silicate minerals and even less dense.
But those early processes are mostly irrelevant to what we see in the crust. The crust is subject to a variety of processes that churn up the content, many of which concentrate specific components.
On a very large scale we have plate tectonics where large arts of the crust are both made and recycled on a geological timescale. To simplify greatly, new continental rock at emerges at one place (eg the mid atlantic ridge) and is consumed by subduction at other plate boundaries (eg the Andean belt in South America).
On a smaller scale (though often related to plate tectonic boundaries) volcanism takes molten rock from relatively deep in the crust and spews it out to the surface, bringing minerals of new compositions to the surface and altering the surrounding minerals by heat and pressure.
Also the surface is subject to weather which causes erosion (leading to both chemical and physical separation of the mineral content of rocks) and the uncovering of rock layers originally formed much deeper in the crust by the cooling of liquid mantle. Another product of erosion is sedimentary rocks where the things being eroded reform into new types of rock.
Plus life itself leads to the creation of some rocks. Some creatures collect carbonate minerals to make their protective bodies, for example, and if these concentrate when they dies, they may deposit layers which over time become new rock types (eg limestone).
To make things even more complicated these processes may interact. Volcanic heat or pressure caused by burial or major stresses may cause major changes to other types of rock, altering their mineral content in the process. Limestone may be recrystallised into marble; plant deposits may be transformed into coal or oil. And other separations are caused by related processes. Metamorphism is often associated with fluid flow which, depending on the composition of the fluid, may move specific minerals around, extracting specific components from some minerals and recrystallising them in voids left by the stresses associated with the metamorphic processes.
In short, things are pretty complicated in the crust and the dynamics will churn things up a lot over geological time. The one thing we can be sure of is that what we see now is not  primarily dominated by the primordial origin of the elements.
There are three major processes that concentrate specific ores
I'm going to greatly simplify some of the things that matter here but there are basically three important processes that concentrate things. Not that geologists can typically reach a consensus on what specifically happened with many deposits.
The three processes are:

separation due to erosion
separation due to differential crystallisation of liquid rocks
separation caused by metamorphic processes

Some major mineral deposits of economic importance (such as the Klondyke deposits in Canada) are caused by the first type of process. Some major platinum and related mineral deposits are from similar processes. What is basically happening is that the metals or minerals containing the metals are concentrated by flowing water because they are denser than the bulk of other minerals from the source rock. This is the same process that prospectors practice when panning for gold in rivers (fast flowing water tends to wash away the less dense clay minerals and leave the denser specs of gold). Over a geological time scale this process sometimes leads to very significant concentration of "heavy" minerals. The association depends on the density of the specific minerals and their specific presence in the rock being eroded. But, if the eroding rock contains many dense minerals, then the process can concentrate them all in the alluvial deposit.
But why would some rocks originally contain more than their fair share of specific minerals? One reason is the second geological process that leads to selective concentration of some minerals. This is that, as liquid rocks in the mantle cool, different minerals will crystallise from the mix at different times. a visible manifestation of this process can be seen in many of the polished granites used to decorate kitchen tops or the floors and walls of buildings. Granites consist of three key minerals: feldspars, quartz and mica each with very different mineral contents. The rock is usually formed deep in the crust when a large body of liquid rock cools. But the feldspars crystallise first, giving the large colourful crystals that make the polished surfaces so attractive. Sometimes the large crystals even show patterns of flow in the liquid source rock. The important general point is that the composition of the liquid changes as crystals form and this may concentrate some components. But this process of selective crystallisation is very general and explains why some particular concentrations exist.
The largest concentration of platinum group minerals is in a formation in southern africa called the Merensky "reef". The key concentrations of minerals appear to have been caused by separation as the rock crystallised (according to this book):

“Present opinion is that the Complex was intruded from a magma that was undergoing some differentiation, but was intruded in discontinuous phases. There is an overall trend in the mineralogy and chemistry of the basic rocks that is normal, and the layering of individual rock units is thought to be due to settling out of crystals according to density modified by connection currents flowing in the magma.”

The third process is also important for many valuable minerals. Metamorphic processes, for example, often involve heat and pressure but also hydrostatic processes. The pressure may crack existing rock leaving voids which are filled with high pressure liquid water containing various minerals that can selectively solubilise the contents of the rock and, later, deposit it in the voids. Once chemical property that can selectively separate gold and platinum group metals occurs when the water contains a lot of sulfur, selenium or tellurium and is a reducing environment (eg sufides rather than sulfates). Many precious metals will go into solution in such environments only to be deposited later from the solution as the state changes. Many gold deposits are like this as are some platinum group deposits.
Rare earth (lanthanide-containing) minerals are thought to be concentrated by the same sorts of processes but are, despite rare earths being pretty common in the crust (far more common that precious metals), much less common as economically viable deposits. This may be because the specific chemical process that concentrate them in the first place are less common. This is partially because they have large atomic radii and high charge and that means they don't fit well into the commonest silicate types of mineral. The key minerals they do occur in are carbonate and phosphate based. And these are often thought to occur near locations where continental crust is being consumed at a plate boundary where metamorphic processes may increase the presence of phosphate and carbonate in the resulting rock. See this presentation for some ideas. But they can also be concentrated by sedimentary processes where solutions eroded from source rocks are selectively absorbed into clay minerals elsewhere.
In general the reason why rare earths are found together is that they are chemically similar so there are few natural processes that will separate them (heck, the industrial processes are very hard and expensive).
Summary
There are many processes, both physical and chemical, that can cause concentrations of particular minerals in the earth's crust. Some of these depend on chemistry but others are simple physical processes. But geological chemistry is pretty messy and complicated and, even now, geologists can't always agree what particular process created a deposit. But there are broad types of process that probably contribute some of which depend on the similar chemistry of particular groups of elements. Rare earths are very chemically similar, for example, and precious metals have some chemical similarities (especially solubilisation in reducing environments with sulfur and other group 16 elements) that enable geological processes to concentrate them in some locations.
Some material here is from The Atlas of Economic Mineral Deposits which, though fairly old (1979) is worth a read to get a feel for how complex this subject is.


text:
what does "overlapping" of orbitals mean and why does it effect bond strength(VBT)?
according to valence bond theory, bonds are formed due to the pairing of unpaired valence electrons due to the overlap of half-filled orbitals, and the strength of the bond depends on the extent of overlap.
the concept of "overlapping" sounds visually intuitive and a good qualitative explanation, but the dependence of the strength of the bond on the extent of overlap implies there is a quantitative framework behind this.
Orbitals, as far as I understand, are just physical representations of the 3d probability distribution of finding an electron in a given region given by modulus-squared of its wavefunction. So what does it actually mean when atomic orbitals "overlap"? Secondly, what exactly is the extent of overlap and why does it affect bond strength?

You might search for S the Overlap Integral.

Overlap -> constructive interference. VBT is not a good place to start for this.


text:
Numbering for the IUPAC name of this benzene derivative

My first guess was 2-chloro-4-nitrotoluene, but this was not among the choices for this question. My teacher says we will begin numbering from Cl, as halogens have higher priority than a nitro-group. However, this compound is named 2-chloro-1-methyl-4-nitrobenzene on PubChem.
I am confused. Please explain where should I begin numbering from.

"as halogens have higher priority than a nitro-group" there is your mistake (or the mistake of your teacher).

@Loong And what do I tell him so he understands? He says the same thing, that before considering the lowest sum, we give the main functional group the number 1.

Your teacher is also talking about "the lowest sum"? That's his second mistake.

@Loong I mean he is talking about the lowest locant rule

Neither "chloro" nor "nitro" nor "methyl" can be the principal characteristic group (which would be expressed as a suffix or implied by a traditional name); there are no priorities for these three groups. So there is no principal characteristic group in this compound that would automatically get the lowest locant.

The main goal of IUPAC names is to keep them simple and understandable by anyone. So, you basically want to keep numbers the lowest possible. Hence, you shall start numbering where it will give the lowest numbers for your substituents.
For instance, if you began numbering from the carbon bonded with the chlorine, your molecule would have been named 1-chloro-2-methyl-5-nitrobenzene or 1-chloro-6-methyl-3-nitrobenzene. Or, if you chose your numbering to begin from the other group, you'd have named it 3-chloro-4-methyl-1-nitrobenzene or, even worse, 5-chloro-4-methyl-1-nitrobenzene. With these examples, you can notice that the simplest name, i.e. the one that has the lowest numbers, is the one PubChem gave you : and that's the reason one should start numbering by the methyl.

Please see How to ask and answer nomenclature questions?

My teacher says the same thing, that before considering the lowest sum, we give the main functional group the number 1

I meant the lowest locant rule

@AkshatVats There is no "main functional group" in this compound. All three substituent groups are considered together.

@Loong Can you write a short answer so I can accept it?

@AkshatVats I already did. You can find it if you follow the duplicate link at your question. My answer is here: https://chemistry.stackexchange.com/a/53566/101286


text:
Which ceramic-like material is used in halogen MR16, GU5.3 and so on bulbs?
I hope this question belongs in here; I cannot think of any other better place to ask it.
Which kind of material is used in dichroic halogen bulbs to attach the bulb itself to the reflector and keep it in there? Looks to me like a ceramic or some kind of terracotta, but I wish to know the exact kind and if it is available for home use or, in case it isn't, a good recommendation as a domestic substitute. Of course, I understand it's main property is, appart from its hardness, the ability to be fireproof and/or refractory, due to the high temperatures being reached in there. For this same reason, something like epoxy resin or anything plastic based probably wouldn't work as it would melt or even burn.

Most halogen reflector bulbs of this type (now nearly obsolete due to more efficient LED bulbs) contained a quartz inner tube but did not connect that tube directly to the outer reflector. Usually only the metal terminals of the inner tube were connected to the outer shield which, in turn, were anchored into the base with the certamic.

Yes @matt_black; is that ceramic the one I'm referring to

Actually, aside from heat resistance, a primary qualification is that the adhesive cement thermal expansion coefficient match that of the quartz (or glass or alumina) envelope over the temperature range of storage and operation, to avoid cracking the envelope (the metal fixture is more flexible and "forgiving").
There are a number of cements in use, such as, "aluminum phosphate refractory cement... a mixture of aluminum phosphate... phosphoric acid [and] alumina". Glassbond sells a variety of adhesives, such as a phenolic/melamine adhesive for glass lamps with operating temperature below 300°C. Sauereisen has a long history making high-temperature adhesives, including those of silicate and of magnesium oxysulfate composition. One could try making these cements at home or in the lab, though they're readily available commercially. You could experiment with refractory furnace cement, though it likely would have a different coefficient of expansion, cracking the envelope.
BTW, I remember, in school, attaching thermocouples to incandescent lamps with a variety of cements... and watching the glass envelope form small star-shaped cracks at each joint, for many of those adhesives, as the lamp warmed. Sorry, but I don't remember which formulations actually succeeded past a few on/off cycles.


text:
ORCA: meaning of numbers in ORCA.out of MOLECULAR ORBITALS for STO-3G Lithium
For Lithium STO-3G basis set
BASIS "ao basis" PRINT
#BASIS SET: (6s,3p) -> [2s,1p]
Li    S
      0.1611957475E+02       0.1543289673E+00
      0.2936200663E+01       0.5353281423E+00
      0.7946504870E+00       0.4446345422E+00
Li    SP
      0.6362897469E+00      -0.9996722919E-01       0.1559162750E+00
      0.1478600533E+00       0.3995128261E+00       0.6076837186E+00
      0.4808867840E-01       0.7001154689E+00       0.3919573931E+00
END

I see the for representing Lithium wave function (Single Slater's Determitatn) I need 3 basis STO-functions (STO(1s), STO(2s) and one STO(2p)) for compilation spin-orbitals. For Lithium we have $1s^22s$-eclectronic structure, so I need compile:
\begin{align}
\chi_{1s} = \sum\limits_{j = 1}^{K} C_{(1s)_j} STO_j,\\
\phi_{1s} = \sum\limits_{j = 1}^{L} D_{(1s)_j} STO_j,\\
\chi_{2s} = \sum\limits_{j = 1}^{M} C_{(2s)_j} STO_j.\\
\ldots.
\end{align}
(As I understand)
So, I started to calculate with ORCA Lithium atom
! UHF STO-3G

%coords
    CTyp xyz       # the type of coordinates = xyz or internal
    Charge 0       # the total charge of the molecule
    Mult 2         # the multiplicity = 2S+1
    Units Angs     # the unit of length = angs or bohrs
    coords
        Li        0.000000       0.00000        0.00000
    end
end
%output
    Print[ P_Basis ] 2
    Print[ P_MOs ] 1
end

and get information
------------------
MOLECULAR ORBITALS
------------------
                      0         1         2         3         4
                  -2.36917  -0.18012   0.13013   0.13013   0.13013
                   1.00000   1.00000   0.00000   0.00000   0.00000
                  --------  --------  --------  --------  --------
  0Li  1s         0.992528 -0.276813  0.000000  0.000000 -0.000000
  0Li  2s         0.029310  1.029989 -0.000000 -0.000000  0.000000
  0Li  1pz       -0.000000  0.000000 -0.607531  0.786960 -0.107701
  0Li  1px       -0.000000  0.000000 -0.176173 -0.265720 -0.947816
  0Li  1py       -0.000000  0.000000  0.774512  0.556854 -0.300075

                      0         1         2         3         4
                  -2.33786   0.10225   0.19092   0.19092   0.19092
                   1.00000   0.00000   0.00000   0.00000   0.00000
                  --------  --------  --------  --------  --------
  0Li  1s         0.991218 -0.281468  0.000000  0.000000  0.000000
  0Li  2s         0.034144  1.029840 -0.000000 -0.000000 -0.000000
  0Li  1pz       -0.000000 -0.000000  0.170191 -0.976799  0.129992
  0Li  1px       -0.000000 -0.000000 -0.983678 -0.160587  0.081175
  0Li  1py       -0.000000 -0.000000 -0.058416 -0.141685 -0.98818

So, how can I determine $K$, $L$ and $M$ numbers and $C_{(1s)_j}$, $D_{(1s)_j}$, $C_{(2s)_j}$ coefitients?

I think that question hasn't gotten the attention it should have. At the time of posting [mattermodeling.se] did not exist. It does now, but the question is now too old to migrate. I would suggest to just ask it there (again) and delete it here. I am quite confident you'll find an answer there. (Finally. (I guess.))


text:
Is cyclohexane‐1,3‐dicarboxylic acid a correct IUPAC name?
I did the numbering by taking all the functional groups in principal chain (scheme A), but my teacher did it differently and proposed the name cyclohexane‐1,3‐dicarboxylic acid (scheme B):

The principal chain in my teacher's answer is shorter. Also, he did not put any $\ce{-COOH}$ in the principal chain which he could have done.
Where am I wrong?

The principal "chain" is the ring of six atoms.

The truth is naming organic compounds is screwy. There is a massive set of rules for naming which is still growing as inventive organic chemists synthesize weirder and weirder compounds. So it takes practice to learn to name properly.

There are two problems with your attempt at naming. First the carboxylate is a functional group. So it might or might not be part of the primary carbon chain. Second if the carboxylate group had been a methyl group then the molecule would be 1,3-dimethylcyclohexane (which doesn't completely specify the particular isomer). So there is no one word name for that particular carbon structure, eg toluene.

The answer to this question is actually pretty interesting, I think.  @user55119 's comment that the principal chain is the cyclohexane ring is correct -- but it seems like you understand that that's what the teacher is saying, and you're asking, "why?"  The best short answer, too, is imho in your comments: @MaxW 's "naming organic compounds is just screwy" is the bottom-line answer, because there are so many crazy special cases to deal with that it sometimes seems like sorcery to come up with them.  But if one is willing to dig into it a little, 99% of them do actually have consistent reasoning behind them -- even if coming up with that reasoning can feel pretty byzantine right up to the point where you get it.  This can be particularly true for cyclic compounds, which can in some cases even have more than one valid IUPAC name.
In this particular case, the reason your answer is incorrect is because what you defined with your numbering isn't a chain.
Per IUPAC, a chain is a sequence of linked units that is bounded by precisely two "boundary units" -- either a branch point or an "end unit", which is itself defined by IUPAC as a unit* of the macromolecule that is bound to only one other unit.
Now, this clearly causes problems with cyclic compounds, so the IUPAC has some caveats included within the definition of a chain -- one being that a cyclic macromolecule with no end groups is also a chain.  So, a chain is either linear and has two boundary groups terminating it, or it's strictly cyclical and includes no end units.  That means a cycloalkane -- including the cyclohexane in your example -- is a valid chain.
Your numbering, however, contains one boundary group.  The unit at position 1 is a valid boundary group, as it is connected to only one other group.  The unit at position 7, however, is not a boundary group; it is connected to a total of two other units (#6 and #2), and worse, it's a non-boundary that you can't continue counting from either since you've already counted the other molecule it attaches to!
"Maybe it solves the problem if I start from the unit I called #3, and leave the hanging methyl group to be the last part of the chain instead of starting from it -- so the chain would start at current #3 and end at current #1, 3-4-5-6-7-2-1."  (You may want to be looking at your illustration while you read this; it'll probably make the counting I am referring to clearer than just imagining it.)  No, that also doesn't work; it obviously that just puts the problem at the other end -- it still has only one boundary unit, because while the unit at the end of that new "chain" attempt, #1, is only connected to one other, the first unit in the "chain" (#3) is connected to two units, not one, so is not a boundary unit.  Still stuck!
And of course, you can try counting from your #2 instead of your #1 or #3, but then you go all the way around and never have a way to include that methyl group hanging off of #2 -- you'd have to "step" onto #2 again, effectively counting it twice, to then "step" onto the tail CH.  (I wish I could make a video of this "pointing" at each unit in the count; it would come out much clearer, I think!)
So in effect, really the only way you have to count the components of the macromolecule and get a coherent chain out of it is to start on #2 and end on the connection between #7 and #2 -- meaning you end up with the most practical solution being exactly the caveat that IUPAC settled on in specifying that a cyclic alkene can itself also be counted as a chain.
From there, I imagine you can figure out the rest: the cyclohexane as a valid chain is also the longest chain,  you start numbering from the functional group, etc.  Hope that helped explain the teacher's answer!

Edit/addendum: Some in the comment have asked for authoritative sourcing of the above.  Good point, and thank you for bringing to my attention that I only stated what I used for sourcing but neither completely cited nor offered links to said sourcing.  First post here in the chemistry StackExchange; please forgive my error.
IUPAC's authoritative reference work for nomenclature is their so-called Gold Book -- the Compendium of Chemical Terminology.

IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific
Publications, Oxford (1997). Online version (2019-) created by S. J.
Chalk. ISBN 0-9678550-9-8. https://doi.org/10.1351/goldbook.

I cite various definitions from within the Gold Book, the following two being of particular importance:
IUPAC - chain (Note 2). https://goldbook.iupac.org/terms/view/C00946
IUPAC - end-group. https://goldbook.iupac.org/terms/view/E02092
To address one of the comments in particular: it should be noted that nowhere in the Gold Book is there an authoritative definition of the term "ring."  That would make claim that "according to IUPAC a ring cannot be a chain," already dubious based on the definition I cited above, even less likely to be the case -- they certainly aren't going to "prohibit" something they don't even define.
The complaint about the definition of "chain" referring to "polymers" as if it were a notation of exclusivity and implying that the Gold Book's definition somehow contradicts or does not apply to the Blue Book should be pretty handily refuted with a bit more reading in both the Blue and Gold books. The Blue Book states it doesn't deal with preferred naming of polymers, but does still define the systematic naming of organic structures whether polymeric or not.  (Blue Book P-11, p.3)  The Gold Book defines "polymer," very simply and with no caveats, as "a substance composed of macromolecules."  Since "chain" and "polymer" thus both use the term "macromolecules," one would naturally be led to read that definition as well, where along with the (hopefully) uncontroversial definition of being a high-molecular mass chain of repeated low-molecular mass components, one might stumble onto Note 2:

"If a part or the whole of the molecule has a high relative molecular mass and essentially comprises the multiple repetition of units derived, actually or conceptually, from molecules of low relative molecular mass, it may be described as either macromolecular or polymeric, or by polymer used adjectivally."

No clearer acknowledgement of the lack of some "hard line" apparently perceived by some between polymers and "regular" organic macromolecules should be necessary.
When it comes to systematic naming, especially, polymers aren't a "special class" of substance which are somehow privy to different definitions and procedures -- indeed, the Blue Book tells us that's precisely the opposite of the case.  So, for those strictly systematic purposes (which is the entire point of the question, and should be in most introductory academic settings because the point isn't to have students memorize some esoteric rules but instead to teach them something about the structure of molecules and their function within a larger compound) - the definition of "chain" given applies just fine. In fact, the definition of "polymer" is expressly defined in the Gold Book, again IUPAC's authoritative text, such that it could apply to any simple alkane with a side branch for the purposes of that text.  Rather than second-guess clearly written prose, I'd rather assume the working group knew what it was doing there by leaving it vague and allowing common usage to define terms that are inherently ambiguous.  (Also see: What is the difference between Alkanes and Polymers?)  They seem more aware that strict legalism doesn't serve their purposes than most of the practitioners of their work do.
And for those of you who skipped this addendum entirely: good for you.  As interesting as some of the contentions below are, it seems generally agreed by all that none actually change the correct answer to the original question asked anyway; whatever your take on the semantic issues around the Blue and Gold (and Purple!) books that took up half the comments, they're just that -- semantics.  One can think that an answer is based on a definition that is "irrelevant" due to its source, which I find an odd and not particularly useful criticism (but hey, that's just me); but thinking then that said definition is "incorrect" is false logic.  If someone who has never seen a math book in their life believes 2+2=4 because some hot dog vendor on a street corner told them so, it doesn't make 2+2 equal anything other than 4.  Fortunately for them, just because their source has "no relevance" doesn't mean that they can't have a grasp of basic math.

(to explain the asterisk in the "end unit" definition)

IUPAC states that a "feature group" that provides a macromolecule its name, like a carboxyl group in a carboxylic acid, can count as an end unit as well.  Figured somebody might mention that, if I didn't. :) Doesn't directly impact the core problem, though.

I am missing authoritative sources for most of these claims; and a couple of ones I find misleading. For what it's worth, I think in the latest edition the terminology of 'principal chain' is superseded by 'parent compound'. It's not crazy sorcery to name the compounds, there are just many rules to follow and it might not be easy to know them all. But that is just studying and has little to nothing to do with the chemistry that is behind it. I don't agree with "[…] which can in some cases even have more than one valid IUPAC name." There is always exactly one preferred name.

Related: https://chemistry.stackexchange.com/q/93534/4945

"IUPAC has some caveats included within the definition of a chain -- one being that a cyclic macromolecule with no end groups is also a chain" No. According to IUPAC nomenclature, the parent structure can be a ring or a chain, but a ring cannot be a chain.

@Martin-マーチン,   thank you for noting my lack of specific sourcing. As I said in the original post, the sourcing was IUPAC; I have edited the post by adding an endcap to specifically cite the Gold Book and the entries within that were applicable.
To answer your two specific issues w/the answer: I did not say it was "crazy sorcery" to name compounds; in fact, we largely agree:
"...it sometimes seems like sorcery to come up with them. But if one is willing to dig into it a little, 99% of them do actually have consistent reasoning behind them..." (emphasis added)
1/2

And IUPAC agrees wrt possible naming ambiguity (ref. earlier citation, "chain", Gold Book): "Note 1: Except in linear single-strand macromolecules, the definition of a chain may be somewhat arbitrary." * Your second issue: "I don't agree with "[…] which can in some cases even have more than one valid IUPAC name." There is always exactly one preferred name." Those two statements do not contradict. There is one preferred name, agreed. There can still be multiple valid names. I am reminded (due to the comment below yours) of benzene, or cyclohexa-1,3,5-triene. One preferred, both valid. 2/2

@Martin-マーチンone final note: you cite https://chemistry.stackexchange.com/q/93534/4945 in defense of your comment re: preferred and valid names. The accepted answer in that very same post begins by stating precisely my point: "The problem with systematic IUPAC names is that many compounds can have more than one systematic IUPAC name. A compound may be named correctly in two or more ways in accordance with the several methods recommended by IUPAC." (emphasis added)
I hope that puts that issue to bed.  Thank you again for your attention to improve this answer.

@Loong "IUPAC has some caveats included within the definition of a chain -- one being that a cyclic macromolecule with no end groups is also a chain" No. According to IUPAC nomenclature, the parent structure can be a ring or a chain, but a ring cannot be a chain.  I'm sorry, but the IUPAC definition, which I referenced and now explicitly cite in the answer, says quite the opposite.  IUPAC Gold Book, "chain" https://goldbook.iupac.org/terms/view/C00946, Note 2: "A cyclic macromolecule has no end groups but may nevertheless be regarded as a chain."

Perhaps you were meaning that a ring (or cyclic structure in general) can't be a component of a chain?  That still would unfortunately require some caveats, but on the whole it would certainly at least apply to the OP's issue, since their error could be described as misnumbering the "chain" as starting behind the methyl branch, which effectively results in  calling the branch and the ring two "components" of the same "chain" which is clearly incorrect.

@George "A cyclic macromolecule has no end groups but may nevertheless be regarded as a chain." – You quote the Glossary of basic terms in polymer science (IUPAC Recommendations 1996), which is not applicable here since it applies to the polymer chain of a macromolecule. You should have looked into Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names 2013 instead.

There is a misunderstanding here. The Gold Book entry explicitly says "chain (in polymers)". The given compound is not a polymer, and even if it were, the cited definition does not help in choosing a preferred IUPAC name. In this context the "chain" that user55119 mentioned refers to something entirely different, namely the "parent structure" as described in P-12 of the IUPAC Blue Book. I don't mean to be unkind, but I do mean to be blunt, since this "discussion" has gone on so long already: you have based your answer on a definition that is irrelevant, which unfortunately makes it incorrect.

@Loong Sorry, you are incorrect.  I did not quote the "Glossary of basic terms in polymer science."  As I said, I quoted the Gold Book: https://goldbook.iupac.org/terms/view/C00946  In that link, the proper way to cite the definition I gave is clearly specified by the Gold Book itself:
Cite as: IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. https://doi.org/10.1351/goldbook. 1/2

Perhaps you did a generic academic search for the text I provided?  Because yes, you would've certainly seen a hit for the 1996 publication that you mention, published by IUPAC's Commission on Macromolecular Nomenclature.  The Gold Book made that the canonical definition by incorporating it, probably with some minor edits as the Gold Book editors specify in its preface text that they tend to do.  (As I'm sure you know, the Blue Book "Nomenclature of Organic Chemistry" is rather light on glossary-style definitions.) 2/2

@orthocresol the definition applies -- your assertion that the Blue Book's "parent structure" is what is being referred to is itself actually incorrect.  As most of the Blue Book is primarily concerned with preferred nomenclature, they describe a "parent structure" simply as a structure for which they will select a preferred name.  (P-12.1 Preferred IUPAC Names, p.3 Blue Book (2013): "It is necessary to select a preferred alternative in many instances in the construction of the names of organic compounds. Preferred IUPAC names are given to parent structures") 1/2

They later go on to more strictly define "parent structure" (in bold), and they give examples in that definition -- one of which is quinoline.  That is what demonstrates your error: quinoline, while having one "simple" preferred IUPAC name, is actually two linked structures, as its systematic name reveals: 1-benzopyridine.
So, you as with others prior are also conflating conversations on preferred vs systematic IUPAC naming, and missing the point of the question and the answer given -- teaching a student what the systematic naming explains about the structure of the compound itself. 2/2

(as for the Gold Book's use of the "in polymers" tag, I go into that a bit in the latest edit to the answer.)

So your claim is that, while the Blue Book assigns a preferred name, you can use polymer terminology from the Gold Book to assign a systematic name to a molecule that is decidedly neither a polymer nor macromolecule?

I'm sorry, but the question doesn't make any sense.  The Blue Book is clear that the assigning of a preferred name doesn't invalidate any of the (possibly multiple) valid systematic names of a compound.  And the Gold Book doesn't have any method of "assigning a systematic name" at all.  It is a glossary, a compendium of definitions.  Perhaps you could restate your question?

Why do you think the Gold Book definition of chain is at all relevant to a molecule that is neither a polymer nor a macromolecule?

Looking at your edit: you claim that there isn't a clear line, but there is at least some kind of line: which part of cyclohexane-1,3-dicarboxylic acid satisfies this definition "If a part or the whole of the molecule has a high relative molecular mass and essentially comprises the multiple repetition of units derived, actually or conceptually, from molecules of low relative molecular mass"? Answer: it doesn't. It's not a macromolecule or a polymer.

The system tells me this discussion should be moved to chat.  But since you asked a question -- methyl groups are low relative molecular mass, and repetitions of the said group make up any and every alkane, including cyclohexane.  For the purposes of systematic nomenclature that's all you need.  The original poster doesn't need to understand the difference between polyethylene and any other alkene chain to correctly systematically name either.

Also to that point, and particularly to the arbitrary distinction btw polymers and "just another chain" (especially when it comes to systematic naming): https://chemistry.stackexchange.com/questions/48159/what-is-the-difference-between-alkanes-and-polymers
I'd be happy to continue discussing this with you over chat.  This has gone widely off relevance from the original question.

That is OK, as I have no intention of continuing this discussion. I understand now where the disagreement lies. It is not about systematic or preferred naming (I never brought that up, so you saying that I conflated it with something else is slightly ironic), nor is it about the provenance of your Gold Book citation (note that there's no need to perform a generic search for the text, as the Gold Book tells you where the definition is taken from). The issue is just that you think this thing can be called, or considered, a polymer.

Of course there's not -- which is why I found it odd to be told I quoted something other than the Gold Book.  And the issue isn't my thinking it's a polymer; it's a combination of two heterogenous "chains," certainly not a polymer.  What I said was that the definition of "chain" in the Gold Book is perfectly applicable to the student's issue here, and is not incorrect in said context -- and that neither the Gold nor Blue books give any reason to think it would be incorrect in said context.  So, really, the disagreement lies in whether or not we should be answering the question that was asked.