text:
Why is octaoxygen diamagnetic?
I tried considering that according to LCAO-MO theory $\ce{O2}$ is paramagnetic, which is confirmed by experimental evidence. Since octaoxygen has the crystal structure in figure, I thought there is a kind of overlapping of the molecular orbitals $\pi^{\ast}$  of each $\ce{O2}$ with the others so that the unpaired electrons of one molecule pair with the unpaired electrons of the adjacent molecule, one by one.
I realise this is only an intuitive answer, but I am not much acquainted with quantum mechanics and applied group theory.

This picture of O8 isn't a crystal structure, more of a lame picture of a thing that defies such depiction. The thing is that it is an actual O8 molecule, not some loose tetramer. But no, I don't know how it is possible.

I think what I really mean is sufficiently clear. Anyway, thanks for the invaluable help, I would never have imagined.

I think one would need to use something like cluster MO theorey here.

Each oxygen seems to have the standard O$_2$ double bond ($3-1$, actually), plus two other single bonds, so oxygens are in a 10-electron exception to the octet rule, like PCl$_5$. As such, $d$-orbitals must be considered, perhaps in a $\pi^*$ mix (see here for a similar $sp^3d$ mix).

But you would need to perform the actual orbital calculations (say using a DFT program) to know how these hybrid orbitals order in energy, so you can aufbau these eight electrons on them. Perhaps a paper worth publishing.

@Arc Regarding your first comment, oxygen cannot expand the valence shell since it belongs to the second period.

Oh, yes, I guess you are correct... $d$ orbitals are too far away in energy. Perhaps then there are 2 electrons in each of the two $\pi^$ molecular orbitals of O$_2$, and only those get mixed. These $\pi^$ mixed orbitals are strongly bent into the monoclinic structure due to high pressure, but these intra-cluster bond lengths are pretty long as well (almost the double of the O$_2$ bond length).

I've asked a related question here.


text:
Lead vs Carbon Properties
Lead and carbon are part of the same group on the periodic table, so they have the same number of valence electrons. However, their chemical and physical properties are dramatically different. But why and how?

Compare with Si, Ge, and Sn…

Consider what happens as the outer electron shell gets farther from the nucleus, screened by the inner shells. Also consider the definition of a metal, in relation to outer electrons.

I understand that the differences in ionization energy, electron affinity and electronegativity heavily impact the behaviour of these elements but how does it impact their physical properties?

Why would graphite have been confused with lead?

@user121618, physical properties are also determined by the electronic structure by large. When the bonds are strong, the material is tough; when they are not, the material is brittle or soft. Similarly, the conductivity is determined ultimately by the atomic radii, ionization energy and electron affinity (the last two also define the electronegativity and polarizability).

source: Stack Exchange

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

sort: votes


text:
Does 'k' in the rate law change with a change in volume
I'm a high school AP Chem student and we recently learned about the rate law and the Arrhenius equation. In school, we learned that rate constant 'k' is only changed with temperature or catalyst. However, I saw in my school's textbook that if we look at the Arrhenius equation through a collision model, the frequency factor 'A' can be re-expressed as 'pz', where 'p' is the orientation factor and 'z' is the collision frequency. If this holds true, wouldn't rate constant 'k' be affected by stressors that influence the rate of collision like volume?
The image below is my school's textbook(Chemistry-a molecular approach 4th edition page 647).

Useful links for text and formula formatting (not to be applied to titles):
Notation basics ,  Formatting of math/chem expressions  and
upright vs italic
For more, see Math SE MathJax tutorial.

Note that using photos/screenshots of text instead of typing text itself is highly discouraged.  The image text content cannot be indexed nor searched for, nor can be reused in answers.  Specifically handwritten scripts can be difficult to decipher.  Consider  copy/pasting or rewriting of at least essential parts.

(Disclaimer: It's been a long time since I did this.)
The collision frequency (or collision density, to use the term in Atkins' Physical Chemistry 9ed) is indeed proportional to concentration. We assume here a bimolecular reaction of the form $\ce{A + B -> P}$. Eq. 22.3a in Atkins writes:
$$Z_\ce{AB} = \sigma \sqrt{\frac{8k_\mathrm{B}T}{\pi\mu}} N_A^2 [\ce{A}][\ce{B}] = \sigma \bar{c}_\text{rel}N_A^2[\ce{A}][\ce{B}].$$
Here, $Z_\ce{AB}$ refers to the collision density between two molecules $\ce{A}$ and $\ce{B}$. $\sigma$ is the collision cross-section (essentially a function of the molecule's shape and size), $\mu$ is the reduced mass $m_\ce{A}m_\ce{B}/(m_\ce{A} + m_\ce{B})$, and $\bar{c}_\text{rel} = \sqrt{8k_\mathrm{B}T/\pi\mu}$ is the mean relative speed of the reactants (i.e. how fast they are moving with respect to one another).
It's, however, strictly incorrect to write that the pre-exponential factor $A$ is proportional to the collision density, otherwise that double-counts the concentration factor in the rate. Indeed, Atkins never writes that $k$ or $A$ are proportional to the collision density. Rather, the entire rate of reaction (denoted $v$) is proportional to the collision density $Z_\ce{AB}$, times the probability of effective collisions $\exp(-E_\mathrm{a}/RT)$, times a factor of $1/N_\mathrm{A}$ which isn't physically important (it's just to make sure that our rate is expressed in terms of concentrations):
$$\begin{align}
v &= Z_\ce{AB} \cdot \exp\left(-\frac{E_\mathrm{a}}{RT}\right) \cdot \frac{1}{N_\mathrm{A}} \\
&= \sigma \bar{c}_\text{rel}N_A[\ce{A}][\ce{B}] \cdot \exp\left(-\frac{E_\mathrm{a}}{RT}\right)
\end{align}$$
But we also know that the rate of a bimolecular reaction is given by $v = k[\ce{A}][\ce{B}]$, which allows us to identify an expression for the rate constant $k$:
$$k = \sigma \bar{c}_\text{rel}N_A \cdot \exp\left(-\frac{E_\mathrm{a}}{RT}\right)$$
and hence the pre-exponential factor:
$$A = \sigma \bar{c}_\text{rel}N_A.$$
At some point in this chain of events (it doesn't matter exactly where), the fudge factor $P$ (where $0 < P \leq 1$) is introduced to 'explain' the observation that not all collisions are successful. So, taking this into account, we have that
$$A = P \cdot \sigma \bar{c}_\text{rel}N_A.$$
which is decidedly not of the form $A = PZ$. (In fact, it is pretty much $PZ$ but divided through by $N_\mathrm{A}$ and the concentrations of the reacting species.) We might like to think of this as being $A = PZ'$, where $Z'$ is some kind of scaled collision density where the concentration factors (and $N_\mathrm{A}$) are removed from the equation, and that would be fine; but it's not right to say $A = PZ$.

The original formulation gives the temperature-dependence of the rates:

Source: https://zenodo.org/record/1749766#.YhWZ85ZOklw
The given formula is showing the relationship between two rates (same concentration of reactants, different temperature). The pre-exponential factor cancels out here:
$$\sigma_{t_1} = \sigma_{t_1} e^{A \frac{T_1 - T_0}{T_0 T_1}}$$
The $A$ in the formula is $-\frac{E_A}{R}$ in modern formulation. The text roughly translates to:

Those [reactions] which are investigated at common temperature are obeying the relation of the following form: [formula], where $\sigma_{t_0}$ and $\sigma_{t_1}$ are the reaction rates at two temperatures $t_0$ and $t_1$, $A$ is a constant and $T_0$ and $T_1$ are the respective absolute temperatures.

The collision frequency is introduced in collision theory, also explaining the rate and not the rate constant:
$$r(T) = k n_A n_B = Z \rho \exp\left(-\frac{E_\mathrm{a}}{RT}\right)$$
Source: https://en.wikipedia.org/wiki/Collision_theory
If you mix and match these without being careful, you get the confusing (and incorrect) statement that the rate constant is concentration dependent. Your textbook is not the only one that is fuzzy about this.
Patrick Fleming uses the following formulation in Libretext:

$$\text{rate} = Z_{ab} F$$
$$Z_{AB} = \left( \dfrac{8k_BT}{\pi \mu} \right)^{1/2} \sigma_{AB} [A][B]$$

Here, the equations are only dimensionally correct if the concentration is given as number of molecules per volume, and the rate is given as number of molecules per time. The square-root term has dimensions of length per time (speed), and the cross section is an area. The author mentions that this is for bimolecular reactions only. If you write down the rate law and compare the $k$ from collision theory with that of the Arrhenius equation, you get the following expression for $A$:

$$A= \left( \dfrac{8k_BT}{\pi \mu} \right)^{1/2} \sigma_{AB}$$

In a historic paper, $Z$ is defined differently (not concentration-dependent):

Source: https://pubs.acs.org/doi/10.1021/ja01347a011
So you have to be careful about the order of reaction (because the dimensions of $k$ and $A$ depend on it), and how $Z$ is defined.
In any case, however, the rate constant is not dependent on concentration (or volume).

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


text:
Would the addition of Citric and Phosphoric Acid or Potassium Carbonate to agricultural water supply result in health/safety concerns?
I am doing a small greenhouse project for fun. As a side benefit of this project, I was hoping to consume the food that I will be producing. I have been checking all of the products that I will be using for safety in this application.
However, there are two products I am not entirely certain of. They are:

Root Farm pH Down
Root Farm pH Up

I'm not entirely certain of the ingredients. However, on the back of each, there is a warning label which indicates that it contains the following:
Root Farm pH Up

Potassium Carbonate

Root Farm pH Down

Phosphoric Acid

Citric Acid

My recollection of high school chemistry is limited, and so I was looking for advice on the following:

Would it be safe for me to add these products to the water my vegetables will be using?

Are there any potential "side effects" of adding this solution that
could cause health concerns when eating the plants?

Should I be staying away from this solution and using a different
product for any reason?

There are many levels and contexts of safety. Responsible chemists would comment just small part of it. Explicitly, users of CH SE site avoid to comment medical aspects of safety and health.
There are no safe nor harmful nor dangerous chemicals. Their doses or concentrations or exposure patterns make them safe, harmful or dangerous. Water (a propagator of drinking extreme daily volumes died because of that) or table salt will kill you if swallowed in large quantity, while sub-milligram amount of potassium cyanide is harmless.
Make the decision if it is safe yourself. Generally, any solution, especially concentrated, is dangerous to eyes, concentrated carbonates also attack skin, making it soapy, like washing soda as sodium carbonate does.

Potassium carbonate $\ce{K2CO3}$:

Carbonate creates in the irrigation water with proper dosing a bicarbonate  pH buffer ($\ce{HCO3-(aq) + CO2(aq)}$), similar as humans have in their blood.
Potassium is a part of fertilizers, is essential for plants.
It is important nutrition (bananas are famous in that), .
Bicarbonates are used in baking powders, forming carbonates.
Potassium carbonate is directly used in industrial processing of most of world cocoa to alkalize cocoa beans/mass/powder. If you see dark cocoa powder, it is the processed one due darkened oxidized polyphenols. The similar for chocolates, as very most uses this processed cocoa.

Citric acid:

You consume it in citruses.
Salts of citric acid are essential part of the citrate cycle, the central part of aerobic metabolism.

Phosphoric acid $\ce{H3PO4}$

Diluted one is present in Coca-cola.
It's salts are essential nutrition for plants, a part of fertilizers
Phosphates, respectively their bound forms in DNA, RNA, ATP, phospholipides, milk casein are essential nutrition and common part of food.
Dihydrogen phosphates are often a part of ionic drink formulas.

I applaud your bravery! ;)


text:
Does the process of extraction of chondroitin sulfate change the molecular structure of the bovine source it is extracted from?
I have been prescribed Chondoritin Sulfate for my joints.  For religious reasons, I don't have bovine.   Hence my question.  Does the process of extraction of chondroitin sulfate change the molecular structure of the bovine source it is extracted from?  If it changes, then it's not bovine anymore and hence okay for me to consume.
There is a paper here that explains the extraction process in detail.
It's too technical for me, but would be grateful if a chemist could read it and verify if the molecular structure of the source is changed.
Thanks so much!

Short answer: bovine chondroitin comes from cows. There are other sources (marine) that might work. Have you considered a vegan/vegetarian supplement containing chondroitin?

Thank you for your response @ToddMinehardt!  Vegan supplements are indeed an option.  However, though it comes from bovine source, if the extraction process changes the molecular structure, then it's no longer "bovine".
Therefore posting this paper here.  Does this process change the molecular structure?


text:
Energy change of isentropic expansion of ideal gas
I'm trying to get a better grasp on dealing with different processes thermodynamic, and this one is giving me trouble.
The differential of energy is given by
$$dU= \delta Q + \delta W~.$$ I'm interested in the ideal gas for a closed system, so $\delta W = -pdV$. For an isentropic process, there is no heat exchange, so $\delta Q =0$. This gives us the result that
$$dU = -pdV ~.$$
Further, for the reversible process, the external pressure against which the system expands is the same as the pressure of the gas, which for an ideal gas is $$p=\frac{NkT}{V}$$
Substituting this into the differential of the energy, we can integrate both sides to find
$$\Delta U = -Nk\int_{V_0}^{V_f}\frac{T(V)dV}{V}$$
In this case, if I'm not mistaken the temperature is not constant (this is an isentropic, not isothermal process), so how does one calculate the energy change of this compression? Is there a relation between $V$ and $T$ I am forgetting?

It sounds like you're talking about an isentropic reversible expansion, i.e., one for which dq_rev = 0.  That is an adiabatic reversible expansion.  For that, you want to use the relationship between T1 and T2 for an ideal gas for an adiabatic reversible expansion to determine $\Delta U$: $ {\displaystyle T_{2}=T_{1}\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}.}$ where $\gamma = \frac{C_p}{C_v}$, $C_p = C_v+nR$, and $C_v = 3/2 nR$ for a monatomic ideal gas and $5/2 nR$ for a diatomic ideal gas.

You need to also make use of the equation for an ideal gas $dU=NC_VdT$ so that $dU=NC_VdT=-pdV$


text:
Why are the 1s bonding and antibonding molecular orbitals excluded while making Molecular Orbital diagram for diatomic homo/heteroatomic molecules?
Do these molecular orbitals not form or are they left out as something general that doesn't require repeated mentioning?
I'm in my first semester of college so please keep the explanation simple:)

Unless it is hydrogen, these orbitals do not take part in atomic bonds, so they are not considered.

When there are orbitals other than 1s, 1s do not participate in bonding because they are too compact. Other orbitals take up much more space (partially also because of radial nodal surfaces), so when the atoms come closer to one another, the bond is formed using the outermost shells.
To form a bond means that the atomic orbitals on more than one atom are to combine in such a way so that the energy of one of the combined orbitals is significantly lower than those of the initial two orbitals. For that, You need the atomic orbitals to be:

close in energy (1s orbitals fulfill this);
close spatially.

But You also must reckon in all the other orbitals which are occupied with electrons at the same time. What happens with them when You move the atoms closer together?
If atoms tried to get close enough so that the inner shells get overlapped enough to form bonds, the electrons in outer shells would be repulsing so hard, the energy of their combination would overshoot whatever bond is formed by the 1s orbitals so hard that the full energy of the new molecule would be much more than that of individual atoms, and even more than that of atoms bonded with their outer shells.
This is why the inner shells (not just 1s) are typically not shown in the MO diagrams.


text:
Integrating structural information to carry out Rietveld refinement
I have just started using Xpert highscore for analyzing my XRD raw data. I have access to PDF2 database(Powder diffraction file) using my university license. I have also just started using reitveld analysis for quantification analysis of my matched phases. The problem is the reference cards for my phases don't have the necessary structural information to carry out reitveld refinement. Then I found out that ICSD database, to which my institute has access to, has the necessary structural information for the reference cards that I require. Now I am facing trouble on how to proceed further.
Do I

Integrate the structural information found from ICSD database in the corresponding PDF2 reference cards ?
Create a new custom database in XPert using all the required cards?

Is the first option even possible? if yes, how to do that? or is the second option more easier?
I am pretty new to this, so sorry if this sounds like a basic doubt. Any help will be appreciated

I finally managed to create my own database.
https://www.researchgate.net/post/Integrating_structural_information_to_carry_out_reitveld_refinement#view=62305644adecda35c8001480

I never really managed to set up my own database in Highscore Plus. I think it works but I never really got it to work. It does work in other programs though. What you can do is, download the .cif from ICSD or COD and then in Highscore Plus go to "File" and then "Insert" to add the phase to your current project.
Also make sure you really have Highscore Plus and not just Highscore. To my understanding only the Plus version allows for Rietveld refinement. An alternative would be to use one of the Highscore Plus COD database options that directly adds those phases.
You can find a link here. Just make sure to select a year close to the version of Highscore as older versions aren't really supporting the new COD versions. If you click on a year go to "PANalytical". You can get a file there that can be added to the user databases under "Customise" "Manage Databases". It will be a file ending with .hsrdb. Those will also contain structure information that are required for the refinement.
Finally my advice, if you are getting into Rietveld refinement also try things like GSAS or FullProf. It tends to crash more but that's sometimes a good thing. Those "blackbox"-type programs like Highscore and others sometimes refine things automatically where you have to be careful. So perhaps try to get a first good fit and then use the parameters for a more advanced refinement in a program where you have more control over each single step.

Thank you for taking out the time to answer my question. I tried using the COD database intially but a lot of my expected phases are not present in the COD database.
How do I create a custom database using the ICSD cif files to carry reitveld refinement ? My main aim is to get the crystal lattice parameters to figure out if dopants are entering the crystal structure and do quantitative analysis of my matched phases.

Well, since I also use other programs I don't have to rely on Highscore all the time. I always just import structures manually. The database creation never really worked for me. If you have a rather new version or it came with the machine you might contact your sales guy or customer service. They usually have all the information and they are quite fast.

If I may ask, what all programs do you use to perform reitveld analysis, I am very new at this, any help will be appreciated

Mostly FullProf and PDXL2, but it's expensive and comes with the Rigaku Diffractometers. It's quite fast and useful. The problem is all of them are more like black boxes. They refine quickly and you have no control. FullProf takes work but you can really select what to refine. So I just use them all for getting nice starting values and then I refine them manually in FullProf.


text:
Python and RDKit to extract sub-structures in a SMILES
I am not a chemist, I come from a computer science background. I am involved in a cheminformatics project. I have a list of molecules in SMILES format, which I want to extract sub-structures from.
I found some interesting sub-structures that I want to look for in a given molecule in the paper https://www.mdpi.com/1420-3049/21/1/75 published in 2015.
In the abstract it is mentioned that: We first uncovered three important criteria closely related to drug-likeness, namely:

(1) the best numbers of aromatic and non-aromatic rings are 2 and 1, respectively;

(2) the best functional groups of candidate drugs are usually -OH, -COOR and -COOH in turn, but not -CONHOH, -SH, -CHO and -SO3H. In addition, the -F functional group is beneficial to CNS drugs, and -NH2 functional group is beneficial to anti-infective drugs and anti-cancer drugs;

(3) the best R-value intervals of candidate drugs are in the range of 0.05–0.50
(preferably 0.10–0.35), and R-value of the candidate CNS drugs should be as small as possible in this interval

also, Acyclic groups as mentioned in this paper (figure 4), https://bmcchem.biomedcentral.com/articles/10.1186/s13065-021-00737-2

My question is, is there a method in RDKit (or other Python libraries) that extracts these criteria from smiles?

Are you asking about only substructure search, or all of the 4 criteria? Because I believe that you would need some kind of numerical analysis to get those criteria.

No, each substructure/criteria alone. Not all of them at once.

I chose the example in Figure 1 in the article for your first three points.
from rdkit import Chem
from rdkit.Chem import Draw, Descriptors, rdqueries

m = Chem.MolFromSmiles('NC(=O)C1(CCN(CCCN2C3=C(CCC4=C2C=C(Cl)C=C4)C=CC=C3)CC1)N1CCCCC1')
Draw.MolToImage(m, size=(400,200))

print('Aromatic ring count =', Descriptors.NumAromaticRings(m))
Aromatic ring count = 2

print('Non-aromatic ring count =', Descriptors.NumAliphaticRings(m))
Non-aromatic ring count = 3

You have to define SMARTS for all functional groups.
fg = Chem.MolFromSmarts('C(=O)[NX3;H2]') # SMARTS for -CONH2
print('Functional group:', len(m.GetSubstructMatches(fg)), '-CONH2')
Functional group: 1 -CONH2

If I see it correctly, the R value is (heavyatoms - carbons) / heavyatoms.
heavyatoms = Descriptors.HeavyAtomCount(m)
q = rdqueries.AtomNumEqualsQueryAtom(6) # 6 for carbon
carbons = len(m.GetAtomsMatchingQuery(q))
r = (heavyatoms-carbons)/heavyatoms
print('R value =', round(r, 2))
R value = 0.18

What you call Acyclic groups just means, that there are no rings in molecule.
from rdkit.Chem.Scaffolds import MurckoScaffold

m1 = Chem.MolFromSmiles('CCC')
core = MurckoScaffold.GetScaffoldForMol(m1)
s = Chem.MolToSmiles(core)
if len(s) == 0:
    print('No ring in the molecule')
No ring in the molecule


text:
How to use Python RDKit to remove stereochemistry, salts and molecules with undesirable atoms or groups?
I am not a chemist, I come from a computer science background.
Bung et al. [1] say in the Data preprocessing part that they used Python RDKit to remove stereochemistry, salts, and molecules with undesirable atoms or groups.
I was looking for a way to do so in the RDKit documentation but couldn't find any. Can anyone give a code example to achieve this?
Reference

Bung, N.; Krishnan, S. R.; Bulusu, G.; Roy, A. De Novo design of new chemical entities for SARS-CoV-2 using artificial intelligence. Future Med. Chem. 2021, 13 (6), 575–585. DOI: 10.4155/fmc-2020-0262. (Free Access)

+1 For stereochemistry, try https://www.rdkit.org/docs/RDKit_Book.html#stereochemistry, for salts: https://www.rdkit.org/docs/source/rdkit.Chem.SaltRemover.html. For removing undesirable atoms or groups, the best thing to do is to try a substructure search: https://www.rdkit.org/docs/GettingStartedInPython.html#substructure-searching

Beyond what @SRMaiti said, I'd suggest asking the RDKit mailing list.

Here's the code in Python
from rdkit import Chem
from rdkit.Chem.SaltRemover import SaltRemover

smiles = "Cl.C[C@@]1(O)CCCN1"
mol = Chem.MolFromSmiles( smiles )

print( Chem.MolToSmiles( mol  ) ) # mol
#>>> C[C@@]1(O)CCCN1.Cl

# remove salt
# remover = SaltRemover( defnData="[Cl,Br]" ) # define custom list, No spaces allowed
remover = SaltRemover() # use default saltremover
stripped = remover.StripMol( mol ) # strip salts
print( Chem.MolToSmiles( stripped ) ) #  mol w/o salt
#>>> C[C@@]1(O)CCCN1

# remove stereo
Chem.RemoveStereochemistry( stripped )
print( Chem.MolToSmiles( stripped ) ) # mol w/o salt & stereo
#>>> CC1(O)CCCN1

# check for specific atom
atomlist =  [ atom.GetAtomicNum() for atom in stripped.GetAtoms() ]
print( 8 in atomlist ) # check for atom for removal
#>>> True


text:
Chemical formulas with non-integer coefficients
Let's consider the composition $\ce{Hg_{0.7}Cd_{0.3}Te}$ which appears in my data.
As I remember from my chemical knowledge it's not possible having non-integers numbers as coefficients of elements. Moreover, this is clearly not the percentage representation, since we have $1$ atom of tellurium. So is this some sort of reduced chemical formula that should be multiplied by a smallest suitable integer to get an appropriate result? If not, what does this exactly represent?

Useful links for text and formula formatting (not to be applied to titles):
Notation basics ,  Formatting of math/chem expressions  and
upright vs italic

The rule that coefficients have to be integers applies to compounds containing discrete molecules, but some classes of compounds don't
There is an important rule in chemistry that the formulae of molecules must contain integer ratios of elements. But not every substance in the (very broad) field of chemistry is made of discrete molecules.
There are at least two major exceptions where the units don't contain discrete molecules: many minerals and metal alloys.
Metals don't consist of molecules. They are more like a sea of ions in a soup of free electrons. And many metals can freely mix in any ratio (though in many cases it is even more complicated and some alloys consist of a fine-grained mix of multiple alloys of different composition). But for the simpler cases virtually any ratio of several metals is possible (think of this as being like a solution of both salt and sugar dissolved in water: a wide variety of ratios of sugar and salt are possible).
This appears to be the case that prompted the question. Many metal alloys are, in effect, solid solutions of one or more metals in another metal and any ratio of the components is possible.
Another class where non-integer ratios are common is minerals. Many consist of a variety of continuous chains of silicate (Silicon-oxygen) structures making up sheets, chains or other complex structures. These have a net negative charge which is balanced in the mineral by a variety of different metal ions. But, because any metal with the right charge and size can do that job, they often consist of non-integer ratios of metals.
So, for some classes of substance where the building blocks are not discrete molecules, non-integer ratios of components are perfectly possible.

I support the Matt's answer, well written. The third major exception ( aside of allloys and minerals) are synthetic ceramic or semiconductor materials.

Formulas with non-stoichiometric rational number coefficients do not represent molecular structures, but just empirical molar ratio of involved elements. For solid matter, unless it is composed from molecules, even formulas with small integer coefficients do not represent molecular structure, but are expressions of element molar ratios.
E.g. $\ce{CaF2}$ does not mean the respective mineral is composed from $\ce{CaF2}$ molecules, but it means the ratio of $\ce{Ca^2+}$ and $\ce{F-}$ ions is in the ratio 1 : 2.
Some natural or man-made compounds or materials do not have element ratios in small integer numbers, so their formulas use rational numbers. Formally, any multiple of given ratio can be used, but practically at least one coefficient is normalized to integer number. For cases 2 elements are interchangeable in composition, their coefficients often represent their mutual molar fraction, or its integer multiple. In other cases, there is taken an ideal formula as a template and non-integer coefficients express deviation from it.
For your case of $\ce{Hg_{0.7}Cd_{0.3}Te}$, the mixed cadmium/mercury telluride has both metals mutually interchangable with molar fraction coefficients. Note that they may not be quite nice and round 0.7 or 0.3, but generally any rational number between 0 and 1.
Take it as a particular formula for the general empirical formula $\ce{Hg_{x}Cd_{1-x}Te}$, $x \le 1$, $x \ge 0$.
For $x=0$, it is $\ce{CdTe}$, for $x=1$, it is $\ce{HgTe}$.
It is quite common form for formula notation of mixed chalkogenides where the coefficients are not stoichiometric.
Typical  cases are metal oxides with more than 1 oxidation states, where coefficients are empirical. $\ce{FeO}$ is rather $\ce{Fe_{0.9x}O}$ as there is, aside of $\ce{Fe^{II}}$, also  $\ce{Fe^{III}}$. The general formula could be $$\ce{Fe^{II}_{1-x}Fe^{III}_{x}O_{1+0.5x}}$$ or $$\ce{Fe^{II}_{\frac{1-x}{1+0.5x}}Fe^{III}_{\frac{x}{1+0.5x}}O}$$.
It could be formally written as $\ce{a FeO . b Fe2O3}$, but such a notation does not bring any advantage, as it does not represent any real molecular structure.
$\ce{Fe2O3}$ does not represent any real molecular structure either. It just happens that the molar ratio of elements is in this (idealized) case expressed in small integer numbers.

many thanks for your answer. Anyway, could you elaborate a bit more on that? I mean, I still don't understand what is the meaning of considering 0.7 atoms of Hg..

So here we have exactly $1$ atom of $O$ (constant) and I guess (in light of what you said before) that this chemical formula might be seen as $Fe_xO$ but I don't see specific constrains for the $x$ here. I'm sorry but I haven't any experience in Chemistry/Materials Science

You may be too focused on an idea of a molecule, where there must be integer atom numbers.  Consider it as the molar fractions of metals in the $\ce{MTe}$. What alternative formula would you suggest for $\ce{Fe_{0.9678 \pm 0.0002}O}$?

Exactly 1 O atom means nothing here. The formula expresses empirical ratio between atom counts, with deliberate conventional choice of a small integer for one element. For mixed substances, the formula is conventionally kept in the form of pure forms, with fractional coefficients.

I don't know... what alternative formula might be suitable?

None, really. this is the best one.

Let us continue this discussion in chat.

Maurice's answer is correct, but let me try to explain my own way.
The fractional coefficients aren't just picked out of a hat:  they add up to 1.  That's not an accident!  The point is that this is a solid solution with Te2- ions and X2+ ions, where X is Hg2+ or Cd2+, potentially occupying the same position in the crystal lattice.  You could have a 69% and 31%, or 71% and 29%, and it would work just as well.  Converting the percentages to integers would be misleading, because it would give the impression that they are, or should be, exact proportions, which have to be maintained to avoid some fundamental change in structure.  Also, using the fractional coefficients typically makes it quite clear who has to match up with who to fill up a specific position in the lattice together.

It may be "correct", but it is irrelevant to the question which is not about this specific compound but about fractions in formulae in general.

They don't always add up to 1 though; suboxides might be writte as integer metal, fractional oxygen.

The formula $\ce{Hg_{0.7}Cd_{0.3}Te}$ means that $\ce{Hg}$ and $\ce{Cd}$ have the same dimension, nearly same radius, and same valence. They can be interchanged, in any proportion between $0$ to $100$%. Here there are $70$% mercury and $30$% cadmium. But it could also have been possible to get any other coefficient $x$ for mercury ($x<1$}, provided the coefficient of cadmium is $(1 - x)$.

The formula doesn't mean that: it simply describes the relative atomic composition. And you have miscalculated the proportions for the whole compounds as you ignored the proportion of Te.

Les coefficients $0.7$ and $0.3$ are not depending on the proportion of $\ce{Te}$. For each Te atom, there is $x$ atom $\ce{Hg}$ and ${1-x}$ atom Cd

But what people want to know for an alloy is the atomic proportions of the whole alloy, not just the proportion of the ingredients other than the commonest one. Eg the whole alloy has 35% Hg not 70%. Nothing in the formula says that a version of this alloy couldn't have more Hg than Te, just that this version of the alloy doesn't.

@matt_black. Who tells you it's an alloy ? It may be a compound like $\ce{ZnS}$ where $\ce{Zn}$ has been replaced partly by $\ce{Cd}$ (30%) and partly by $\ce{Hg}$ (70%), which are all in the same 12th column. And where the sulfur $\ce{S}$ atom is replaced by $\ce{Te}$, which is also in the same 16th column.

132pm vs 144pm not the same, but perhaps substitutable without too much change in arrangement?

@matt_black I believe Maurice is right about the composition of this specific compound—and, correspondingly, the meaning of its formula—because it's not a simple combination of Hg, Cd, and Te. Rather, it's a combination of HgTe and CdTe. Hence its composition is always (HgTe)_(1-x) + (CdTe)x, and thus its composition is always constrained as Hg(1−x)Cd_xTe. See: https://en.wikipedia.org/wiki/Mercury_cadmium_telluride

@Maurice The disagreement between us may arise because you are providing an answer based on this specific compound not one based on the question which is about how fractions arise in chemical formulae in general. Nothing in the formula says alloy but alloys are a common example of where such formulae arise. Any specific knowledge of this compound is not relevant to the general answer and adding it is confusing.

@theorist This may be the source of the confusion here. I answered the question (which was about how fractional formulae make sense). The Maurice answer brings in a whole bunch of evidence about a specific compound (making assumptions based on the compound that are not justified in general about formulae like this). Hence confusion: the question was about a general principle, not this specific compound.


text:
Atomic formula obtained by mixing given percentages of oxides

Calculate the atomic formula of a compound which is made by
$93\,\%$ of $\ce{SnO2}$ and $7\,\%$ of $\ce{Sb2O5}$.

The molar mass of $\ce{SnO2}$ is $\pu{150.71 g mol^-1}$ and the molar mass of $\ce{Sb2O5}$ is $\pu{323.517 g mol^-1}$. I can find the corresponding amounts of each substance as follows:
$$
\begin{align}
n(\ce{SnO2}) &= \frac{93\,\%}{\pu{150.71 g mol^-1}} = \pu{0.61 mol} \\
n(\ce{Sb2O5}) &= \frac{7\,\%}{\pu{323.517 g mol^-1}} = \pu{0.022 mol}
\end{align}
$$
and multiply these by the number of atoms that I have obtaining $0.61~\ce{Sn}$, $1.24~\ce{O}$ for $\ce{SnO2}$, and $0.043~\ce{Sb}$, $0.108~\ce{O}$ for $\ce{Sb2O5}$.
Finally, summing similar atoms coefficients for oxygen, what I get is
$$\ce{Sn_{0.62}Sb_{0.043}O_{1.35}},$$
and choosing $x=0.5$ and $y=2,$ the formula becomes $\ce{Sn_{0.5}Sb2O6}.$ Is this correct?

Better is to compute molar amount ratios for elements. $\ce{Sn_xSb_yO_{2x+(5/2)y}}$

thanks, could you elaborate on the example please?

Useful links for text and formula formatting (not to be applied to titles):
Notation basics ,  Formatting of math/chem expressions  and
upright vs italic

I know arithmetics, I just didn't understand what you meant, to calculate it more generally or what. So I just asked to be more explicit on your comment

Imagine 93 g of $\ce{SnO2}$ and 7g of $\ce{Sb2O5}$. How many moles of Sn, Sb and O is it ? then, normalize it for at least one of elements has integer index. Not mandatory, but it is nicer. // Requests for elaboration should be elaborated, otherwise it may not be clear what needs elaboration.

got it! many thanks :) you simply meant to re-normalize in order to make at least a coefficient integer^^ I'll edit the question with the updated formula

We say (molar) amount of X, not moles (of) X, like we say mass of X, not kilograms of X. Note that the mole is the unit like kilogram, mol is unit symbol like kg. It is often confused. // Yes, it is similar like normalizing of chemical equation coefficients to have the smallest possible integers ( what is not possible here.)

About the Edit: Only if Sn and Sb are in molar ratio 1 : 4. // By other words, you have just 1 degree of freedom, you can choose either x either y but not both. Like for trivial equation y = 2x. You can freely choose either x either y as the other is determined by the single choice.

Technically, your approach is in general correct.
There is, however, no indication that the compound should be stoichiometric, and there are additional less obvious details you can use to prove this.
First, you are not presented with the data elemental analysis, rather composition expressed in terms of oxides of the elements in their highest oxidation states, which usually means either of the two scenarios:

it's data obtained with DTA or another thermoanalytical method;
it's the precursors used for high-temperature synthesis (homogeneous, high-purity oxides usually contain fully oxidized elements).

What should be taken from this is that the amount of oxygen cannot be determined from its content in given oxides, and that the elements in the target compound could be reduced.
Second, pay attention to the numbers: $7\,\%$ of the relatively heavy element's oxide $\ce{Sb2O5}$ is likely a dopant for $\ce{SnO2}.$
Third, I checked ICSD database for $\ce{Sn-Sb-O}$ system and all entries (24) deposited prior to 2017 (I don't have newer version) are for the defect rutile structure of tin-antimony oxide $\ce{Sn_xSb_{1-x}O2},$ a phase of variable composition which sustains cassiterite antimony-doped structure [1, 2].
Having found the formula unit $\ce{Sn_xSb_{1-x}O2}$ by inference and literature research, it is now possible to compose an equation with one unknown:
$$
\begin{align}
\frac{x}{1 - x} &= \frac{w(\ce{SnO2})}{M(\ce{SnO2)}}\cdot\frac{M(\ce{Sb2O5})}{2\cdot w(\ce{Sb2O5})} \\
  &= \frac{93\,\%}{\pu{150.71 g mol^-1}}\times\frac{\pu{323.52 g mol^-1}}{2\times 7\,\%} \\
  &= 14.26 \\
\implies x &\approx 0.93
\end{align}
$$
and propose the formula $\ce{Sn_{0.93}Sb_{0.07}O2}.$
The coincidence of the composition with the coefficients of the formula unit is accidental and is due to the numerical values of the molar masses.
References

Berry, F. J.; Greaves, C. A Neutron Diffraction Investigation of the Defect Rutile Structure of Tin–Antimony Oxide. J. Chem. Soc., Dalton Trans. 1981, 12, 2447–2451. DOI: 10.1039/DT9810002447.
Tena, M. A.; Sorlí, S.; Llusar, M.; Badenes, J. A.; Forés, A.; Monrós, G. Study of Sb-doped SnO2 Gray Ceramic Pigment with Cassiterite Structure. Z. anorg. allg. Chem. 2005, 631 (11), 2188–2191. DOI: 10.1002/zaac.200570038.

The only reliable formula is probably made with $\ce{28 SnO2 + 1 Sb2O5}$, if it exists.
$28$ mol $\ce{SnO2}$ weighs $28·150.7 = 4220$ g. One mole $\ce{Sb2O5}$ weighs $323.5$ g. So the total weighs $4543.5$ g. The proportion of $\ce{SnO2}$ is $\frac{4220}{4543.5} = 0.929 = 93$%.


text:
The use of "splitting" in 17th century ironmaking?
I'm reading a book about spycraft in the 1650s. At that time Sweden was taking over the iron industry so England sent a spy to learn the new technique.
The technique is called "splitting" and it required the construction of a new machine. That is the entire detail the book provides.
Anyone have any idea what this might be?
UPDATE: The book is A History of the British Secret Service. It is not very good, it basically talks about random events and provides few details or background. Its so poor, my copy even left the word "the" out of the title on the cover. Yet widely talked about.

Might it refer to a skimmer, used to separate iron from slag?

The correct term is “slitting”. See https://en.m.wikipedia.org/wiki/Slitting_mill for info on the process and the espionage

In modern usage, "slitting" is similar. Steel coils ( such as 1500 mm wide with thickness of 10 mm) are slit to narrower widths. The strips are then formed to a round and welded ( ERW) to make pipe and tube: Unless it is seamless , pipe is very likely to be made  with this technique.  Some  narrow slit widths are also use to make flat products.

I’m voting to close this question because it's not related to chemistry. It's about the history of a mechanical process.

Is metallurgy not chemistry?

@Andrew - ah, yes, the original text got it wrong! The portion below the lede clearly speaks of the same person, although that is also spelled differently in the book.

Well, in some wider sense, chemistry is everything from astronomy to psychology. But it does not mean chemistry as science bother with all of that. I would rather day metalurgy, engineering, material science, technology of metal processing and last but not least, history of technology.

I would include metallurgy with chemistry but slitting isn't metallurgy in my opinion. The ore has already been processed into bar iron, and this is just mechanical processing of the bars to make smaller bits that can be turned into parts like nails. On a side note, I think the confusion about the spying is that Swedish iron was higher quality, but not because of the process. Rather it was the source of the ore (Dannemora) used in Sweden.  So the same "Walloon" process with other ores didn't yield the same quality of iron.

The question deals with what is generally called "mechanical metallurgy".

I disagree with the close votes.

@Poutnik - you fail to conclude your thought - which SE sub is the "proper" one then? I suspect people that know things about the history of ironmaking would be much more likely here than, say, the non-existent "technology of metal processing" sub. The fact that one of the comments comes from "blacksmith37" gives credence to that opinion, as do the many outright answers that are for some reason not put into answers.

I have not failed to conclude it as I have not intended to. I have been mentioning domains, not SE sites. @blacksmith37 is a retired engineer very close to metallurgy and similar domains.

How about [hsm.se]?


text:
COSMO Segment charge density via NWChem
I'm struggling to get COSMO segment surface charge densities that I need to create the sigma profiles in COSMO-SAC.
I am not a chemist by training, so please explain like I am five. I've read papers that used DFT to accomplish that, I have a general understanding of DFT but not enough to parametrize it with ease. Any help will be highly appreciated!

+1 This question might be more suitable for https://mattermodeling.stackexchange.com/ imho. Duplicate posting is usually discouraged here, so if you wish to ask the question on that site, then please raise a flag and ask for migration.

I’m voting to close this question because this is better suited for the Matter Modeling Stack Exchange (very specific to a program and not directly chemistry-related).


text:
Definition of Oxidation
Most textbooks define "Gain of Oxygen" as oxidation. Why the gain of Fluorine is not included as part of the definitions since Fluorine is more electronegative than Oxygen?

Your statement is completely incorrect. Oxidation is all about change of oxidation state, not specific elements.

There is more than one meaning of "oxidation", just as a mole can be a small furry creature, and "organic" food is not defined fro m organic chemistry (and "organic meat" referred to viscera).

Most chemistry textbooks don't define oxidation like that.

Please wait for next week's lecture, or check the next two pages of your textbook. It is surely going to introduce a more refined definition of oxidation. If not, get a new textbook, or a new teacher.

See also IUPAC Goldbook and Wikipedia

Gain of oxygen is the 19th century definition of the word "oxidation". Today it has been generalized to an increase in the oxidation number, which can be done by oxygen, or by some other reagent.


text:
What would happen to the cell potential if two half cells of a galvanic cell were at different temperatures?
I'm doing an experiment where I'm investigating the effect of temperature of the galvanic cell on the cell potential. But during the experiment, I noticed that the two half cells were at different temperatures. Could this be a limitation to the data that I collected? If so, how would it impact the cell potential that was measured?

It is important you include the compact summary of your current knowledge, involving also conclusions of search for existing related or duplicate info or answers. It would prevent others to tell you what you already know or what you can easily find yourself. It also serves as evidence of your mandatory effort. Effort not shown can be considered as effort not done.

The standard electrode potentials are temperature dependent, because the standard reaction Gibbs energy is temperature dependent too.

Good experimental design means ensuring that you have repeatable and well defined experimental conditions - by not adequately controlling the temperature of the two half-cells you've introduced the variable $\Delta T_\text{half-cell}$. Since you aren't varying $\Delta T_\text{half-cell}$ in a systematic way and don't know if it's constant, you now have an undefined aberration convoluted in with whatever effect you wanted to measure. Either ensure that $\Delta T_\text{half-cell}$ is small enough to ignore, change your experimental setup to eliminate the temperature difference and repeat your measurements, or preform a series of measurements where you alter $\Delta T_\text{half-cell}$ in a systematic way. (This latter option is a lot of work since you'd have to vary $\Delta T_\text{half-cell}$ at several different cell temperatures.)
With that out of the way, what effect would $\Delta T_\text{half-cell}$ have on the overall cell potential? Lets start with the Nernst equation for the half-cell reaction $\ce{pP +ne^- -> qQ}$, which is:
$$
E\ce{(P|Q)} = E°\ce{(P|Q)} - \frac{RT\ce{(P|Q)}}{nF}\ln{\frac{([\ce{Q}]/c°)^q}{([\ce{P}]/c°)^p}}
$$
(from Chemical Structure an Reactivity 1e by Keeler and Worthers, p 842f). $E°$ is the cell potential at standard conditions, $R$ is the molar gas constant, $T\ce{(P|Q)}$ is the temperature of the $\ce{(P|Q)}$, $n$ is the number of electrons transferred, $F$ is the Faraday constant, and $[\ce{Q}]/c°$ etc. is the concentration of $\ce{Q}$ relative to the standard concentration.
For the other half-cell reaction $\ce{aA +ne^- -> bB}$ we can write:
$$
E\ce{(A|B)} = E°\ce{(A|B)} - \frac{RT\ce{(A|B)}}{nF}\ln{\frac{([\ce{B}]/c°)^b}{([\ce{A}]/c°)^a}}
$$
Remembering that the overall cell potential is $E = E\ce{(P|Q)} - E\ce{(A|B)}$, we arrive at the following:
$$
E = E° - \frac{R}{nF}\left[ T\ce{(P|Q)}\ln{\frac{([\ce{Q}]/c°)^q}{([\ce{P}]/c°)^p}} - T\ce{(A|B)}\ln{\frac{([\ce{B}]/c°)^b}{([\ce{A}]/c°)^a}}\right]
$$
So, is $\Delta T_\text{half-cell}$ an important factor? It depends on the magnitude of $\Delta T_\text{half-cell}$ relative to the temperature range studied, the precision with which you measure $E$, and whether it's a constant difference or changes with time and/or cell temperature. You'll have to figure this out on your own, but the equation above should give you some numbers to work with.

Note that $E°(T)=E°(\pu{298.15 K})+f(T)$ as the standard reaction Gibbs energy  for $\ce{ox(aq) + H2(g) -> red(aq) + 2 H+(aq)}$ is function of temperature as well.  $\Delta G^{°}\mathrm{r}(T)=\Delta G^{°}\mathrm{r}(\pu{298.15 K})+g(T)$, and therefore $E^{°}(T)= \frac{\Delta G^{°}_\mathrm{r}(T)}{nF} $

Relating $E$ and $\Delta G(T)$ is important since it gives thermodynamic insight, but I think the Nernst equation alone is enough to quantify the aberration.

@The N.E. addresses E change with activity, with the rate T dependent, but it does not address E° change with T. By other words, using the unit activities of relevant components, considering just the N.E. the galvanic cell voltage would not depend on temperature. But that is not true, as $\Delta G = \Delta H - T\Delta S$. The different thing is, if we can or cannot afford to neglect it, what is case dependent.


text:
Excess of OH- ions in electrolysis of sodium chloride solution
In the electrolysis of dilute or concentrated sodium chloride solution, at the cathode as hydrogen ions discharge and cause an excess of hydroxide ions, why doesn't the negativity of the cathode repel the hydroxide ions as the electrode is the negative electrode?

The reaction taking place at the cathode is : $\ce{2 H2O + 2 e- -> 2 OH- + H2}$  The negative $\ce{OH-}$ ions are repelled by the cathode as soon as they are produced. They pass into solution where they neutralize the $\ce{Na+}$ ions which have been attracted by the negative cathode, and cannot be discharged.

The site expects that you include the compact summary of your related current knowledge, involving your conclusion of searching for existing related  info or answers. It would prevent others to tell you what you already know or what you could easily find yourself. It also serves as evidence of your mandatory effort. Effort not shown can be considered as effort not done, possibly leading to the question closure. How do I ask a good question?.


text:
What sugar substitute behaves the most like sugar when baked or cooked?
I'm not a chemist. I'm looking for a sugar substitute that I can use for a cheesecake that behaves as much like sugar when cooked or baked. I've tried stevia (a plant based sweetener)but the filling takes longer to set and the crust doesn't hold up when cut. I'm looking for something that binds to fats the same way real sugar does.

How about some seasoned advice? https://cooking.stackexchange.com/questions/1350/when-baking-what-works-well-as-a-sugar-substitute

Try saccharide derivatives like https://en.wikipedia.org/wiki/Xylitol

Sugar alcohols like xylitols have disadvantage the bowel microflora can digest them and cause digestion troubles. some of them can have also undesired metabolical side effects in bigger amount. In some food preparation context, sugar is hard to replace for this reason or another, e.g. the mass of sugar would be missing if replaced by highly sweetening artificial substances. Dozens grams of xylitol can make a feast for bowel bacteria and a bowel crisis for a person.


text:
Filling 3d and 4s orbitals
So the 3d orbital comes after the 4s orbital on the periodic table because it has a higher energy level, but then why are the electrons removed from the 4s orbital before the 3d orbital? For the 3d orbital to be filled after the 4s orbital, it must have greater energy, thereby it should be farther away from the nucleus, and if it is farther away from the nucleus than it should then be the outermost orbital, so electrons should be removed from it first right?

Energies of different orbitals depend on electron configuration. See e.g. http://www.graylark.com/eve/orbital-energies-table.html

According to the image and the Aufbau principle, the 3d orbital has greater energy than the 4s orbital but that supports the idea that it (the 3d orbital) is farther away from the nucleus, it is the outermost shell and thereby electrons should be removed from it first?

According to the image , the 4s orbital has greater energy than the 3d orbital?

My bad, but my textbook states that the 3d orbital would have greater energy than the 4s orbital, while this image proves otherwise?

For the 4th period, 3d orbitals have lower ( more negative ) energy since Sc. The important  thing is 4s orbital is filled. For K and Ca it is the opposite. You can see how 3d energy at Sc is falling down.

The electronic configuration tag should be added to the list of related tags of this question.

Filling of electrons follows the aufbau principle. So according to this rule $3d$ orbitals are filled after the filling of $4s$ orbitals. This is because $3d$ orbitals have slightly more energy than $4s$ orbitals.

Why are the electrons removed from the $4s$ orbital before the $3d$ orbital ?

The electrons are removed from the $4s$ orbital before the $3d$ orbital. This is because the effective nuclear charge $(Z_{eff})$ is more for $3d$ electrons than $4s$ electrons. As $Z_{eff}$ is more for $3d$ electrons they are tightly bound to nucleus than that of $4s$ electrons. So that's why we remove $4s$ electrons before $3d$ electrons.  This can be simply illustrated by Slater's rule.

For example consider iron ($Fe$)  By using Slater's rule it was found that $Z_{eff}$ for $3d$ electrons is $6.25$ whereas for $4s$ electrons it was just $3.75$ .

Similarly this can also be used to illustrate for other atoms.

NOTE : Slater's rule will give you an approximate value for $Z_{eff}$ but not exact values.

Do do you think the order of filling is according to energy level. And removal, is based on effective nuclear charge? Or would you say filling is also based on effective nuclear charge? By the way, Slaters rule on Iron indeed shows 4s as lower effective nuclear charge than 3d.   But for scandium the effective nuclear charge of 4s and 3d is the same.  https://www.omnicalculator.com/chemistry/effective-charge  (Though as you say slaters rule only gives approximate values).  Are you aware of a computational calculation of effective nuclear charge that works better?

There is a subtle effect when you compare transition metal cations with neutral atoms: the ions have greater effective nuclear charge. This overwhelms electron-electron repulsion and tends to force orbitals into the same shell order they would have with only a single electron (meaning $\color{blue}{3}d$ drops below $\color{blue}{4}s$ in the ion). See this answer for a discussion of this effect.


text:
On the idea of heavy atmospheric Xenon
I am wondering about the plausibility of an idea for a Si-fi planet, mostly seeing if it would be like I imagine, and what else would be needed for what I want.
I am thinking of a planet with large amounts of atmospheric Xenon. For an explanation I have the idea of uranium under the surface being put under intense pressure, forming into iodine-129, which flows out of geothermal vents, volcanos, and hot springs as stabilised Xenon-129. Is my chemistry there correct? It seems correct that Iodine-129 can form from spontaneous fission of Uranium, and that Xenon can form from Iodine-129, and is often found flowing out of springs.
I want this to be a case where it flows into the atmosphere from this, in very large amounts, and makes it highly toxic. But reading into Xenon more it seems like it might be too dense to actually be able to spread through the atmosphere and become a part of it in high numbers, instead of sinking to the ground. Is this true, or is my idea plausible?

Is Xenon more toxic than Nitrogen, which makes up 80% of the Earth's atmosphere?

Argon seems to stay relatively well mixed in the atmosphere.

Xeneon is commonly used in anesthesia, https://pubs.asahq.org/anesthesiology/article/92/3/865/39666/Xenon-Anesthesia , and we can tolerate 70% Xe, 20% O2.  It would be helpful if it weren't so expensive on Earth: ~US$10/l at STP. Great in flashtubes, too!

See this post: https://space.stackexchange.com/questions/34630/sources-of-xenon-or-other-noble-gases-in-space ... You can ask this question in Worldbuilding.SE. You will find great answer there.

Producing large amounts of xenon would require large scale uranium fission and possibly intensive volcanic activity.

The degree to which gasses mix and stratify in an atmosphere is dependent on a number of parameters for the planet (e.g. surface gravity, average temperature, length of day, tidal forces...). But all of these complications aside, there is a notion of scale height, which indicates roughly how high you might expect a gas to reach in an atmosphere. Importantly, this height is inversely proportional to the molecular weight of the gas. The molar weight of xenon is about four times heavier than a typical terrestrial planet atmospheric gas (e.g. nitrogen), so it would concentrate near the ground much more. However, for Earth-like conditions, the scale height of xenon is still measured in kilometers.
The only real "problem" I see is that xenon is a fairly rare element in the Universe, and uranium much more so still, especially considering fissile U-235 (the proposed source of your xenon) has a half-life of 700 million years, which is reasonably long but not outrageously so. It seems fairly unlikely there is any natural mechanism by which a planet could have a substantial atmosphere composed of even 1% xenon. But then, these details can be just brushed away.
You might be interested to know that under the right conditions on Earth, even CO2 (less than half the weight of xenon) can concentrate enough near the ground to be deadly, and for xenon this would be much easier. This means that even a relatively small abundance of xenon could still have deadly effects.

I do know that it is unlikely, I am simply seeing if it is scientifically possible given high amounts of uranium in crust and such. Around what conditions would be best for this, in terms of gravity and temperature? Current plans are a lower gravity, with rather high temperatures.

High temperatures, low gravity and maybe also intense UV irradiation favor lighter gasses escaping from the top of the atmosphere, which would slowly enrich the atmosphere with xenon over time.

I see, that does fit with what I have now. Heavy gases in the air, and volcanic activity, and being closer to the star, all works together for hot temperatures. So that is good in my favour. Thanks.


text:
Mass spectra interpretation for monitoring Buchwald–Hartwig coupling
I am conducting a synthesis involving Buchwald-Hartwig coupling. The starting materials are 2,3,5-tribromothiophene (MW=320.83) and 1-aza-18-crown-6 (MW=263.33). I used $\ce{Pd_2(dba)_3}$ (MW=915.7) as catalyst, tBuXPhos (MW=424.64), and NaOtBu (MW=96.1) as base. After running the reaction at 80 ℃ during 24 h, the solvent (toluene) turned brown, and first decanted toluene layer using water. Below is the spectrum of decanted toluene layer after filtration and drying. (named Sample3-Oil)

And I also separated rest of the toluene layer by separatory funnel. Below is the spectrum of separated toluene layer after filtration and drying. (named Sample3-Sep) Seems similar to the first spectrum.

It seems that m/z=115, 120, 142 peaks are from methanol, which is used as mobile phase in MS. I presume that m/z=264 peak is 1-aza-18-crown-6 and m/z=286 peak is [1-aza-18-crown-6+Na]$\ce{^+}$. As far as I know P ligands are slowly oxidized during reaction, forming P=O bond. So I presumed that m/z=442 peak is oxidized tBuXPhos (424+16=440≈442). Also this peak was increased after drying the sample, simultaneously m/z=425 peak disappeared. Because the molecular weight of wanted product is 503.25, I expected that m/z=505 would be the peak of the product.
Meanwhile, I also requested MS of the sample which mixed Pd catalyst and P ligand, stirred overnight at 80 ℃. (named Sample0)

This spectrum also has m/z=505 peak. Therefore I requested MS/MS to determine whether this peak is from the catalyst/ligand or product.

In the MS/MS spectrum of m/z=445, one can observe the loss of iPr(m/z=402) and tBu(m/z=388), so it might be oxidized tBuXPhos. The m/z=505 peak of Sample0 has several fragments while that of Sample3-Oil and Sample3-Sep have only one fragment. But they have m/z=425 peak in common. I think this might be the peak of tBuXPhos (MW=424.64). Does this interpretation seem correct? Then should I judge that the reaction was not successful? One alternative interpretation might be loss of Br, but I'm not sure that this is correct interpretation.
----------------- +) additional spectrum
Sample1-Oil (decanted toluene layer right after the reaction)

Sample2-Oil (filtered through Celite, and rotoevapored)

I would certainly expect a very strong peak from the oxidised phosphine ligand and I would not expect to see much unoxidised ligand. Your 425 could be loss of Br from the product, does the peak show the expected isotope split from the remaining Br present?

@Waylander I added additional spectrum. My desired product has 2 Br, so there would be 1:2:1 isotope peaks, but I can't clearly say the existence of Br isotope peaks. Actually I have once requested the MS experiment of standard 2,3,5-tribromothiophene expecting Br isotope peaks, but there were not. (https://chemistry.stackexchange.com/questions/155648/why-is-the-base-peak-of-my-ms-spectra-of-2-3-5-tribromothiophene-at-m-z-382)

@Waylander Although the reason that if m/z=425 is really tBuXPhos then why there are no m/z=425 peak in Sample0 is somewhat weird, but without that assumption I can't explain why m/z=425 peak exist in Sample1 and Sample2 but don't in Sample3. Sample3 is vacuum-dried Sample2 (130 ℃, nearly 24 h). I thought that in the process of vacuum drying the remaining tBuXPhos is totally oxidized.

I think it unlikely that the 425 is tBuXPhos. These phosphine ligands usually completely oxidise by the completion of the reaction.

@Waylander Hmm.. Then I think I should check the MS/MS fragments of m/z=425...

@Waylander Can I ask one more question? I requested MS/MS analysis of m/z=425 using ESI, and it resulted no fragmentations at all. Just m/z=425 itself alone. Then how can I interpret it? At least definitely it seems that it is not tBuXPhos.

Difficult to know what it is then. If it were loss of Br from the product I would expect further fragmentation (loss of the second Br perhaps). I am not a MS expert.


text:
What is the relationship between the concentration of potassium chloride in water and its specific heat capacity?
I am curious about the effect that adding potassium chloride to water in varying concentrations has on its specific heat capacity. I have been unable to find any online information about this? Theoretically, would one expect a linear relationship or something different? Furthermore, how would this change if we added another soluble material to water? Any insights on the same would be much appreciated.
Note: This question has been previously asked here but received no responses even with a bounty. Hence, I am posting it here.

How exactly I have been unable to find any online information about this looks like? Explicit effort evidence is required, even if no usable info was found.

Generally, solutions are not like a mixture of peas and beans, where the specific heat capacity would be a linear combination of the ones of pure peas/beans.
The relationship is generally nonlinear. Solutes and solvents form bonds and structures not present in pure substances, having different participation in heat capacity. OTOH, the lattice stractures of the solid disappear. All that is furthermore concentration dependent.
For $\ce{KCl}$ and water, there is various degree of $\ce{K+}$ and $\ce{Cl-}$ hydration, affecting the specific heat capacity value. As $\ce{H2O}$ molecules bound to each other by hydrogen bonds have different effective degrees of freedom than if they are partially bound to ions.
This can be approximated by linear relationship, but deviations of that have to be evaluated experimentally, unless there is already empirical handy data for that, in form of a table or empirical formula. As water has, AFAIK, the highest specific heat capacity of all condensed matter, the specific heat capacity would generally decrease with concentration.


text:
What is a better method when finding the iron content in spinach: Using titration or a spectrometer?
For my chemistry experiment, I want to boil spinach in water for different timings. Using the water that is left after boiling it, I was to determine the amount of iron content in the water solution. However, I am very confused on what method to use, etheir through titration (which I find easier to do) or through using a spectrometer. I am not sure if one will cause difficulty when I am doing the experiment. I need to decide this very soon, and I am very confused.

Spectrophotometric method is reliable. What method do you have in mind?

Mineralisation of the sample and than inorganic iron measurement by AAS or by colorimetry, i.e. with SCN- complex.

There are plenty of difficulties in your project. 1) Iron atom is probably included in one or several colored complexes whose formula are not obvious. 2) The amount of iron in spinach is not huge : $3.4$ mg in $100$ g fresh spinach, according to CIBA-Geigy Scientific Tables, Basel 1972. This small amount is difficult to measure whatever the method used. 3) Iron in plant is usually Fe(II). But in air, it is oxidized into Fe(III) and the spectrum of both ions are rather different. If you want to extract iron out of its complex, you would have to dry the spinach sheet and burn them, then extract iron out of the ashes. In the ashes, iron is probably under the form $\ce{Fe2O3}$, and, if heated to a high temperature $\ce{Fe2O3}$ is not soluble any more in concentrated acids like $\ce{HCl}$ or $\ce{H2SO4}$. It has to be dissolved in melted $\ce{NaHSO4}$ in a platinum crucible at $400°$C. Not easy !
The amount of iron present in vegetables does not vary much. Per $100$ g vegetables, one finds $0.7$ mg iron in carrots, $1.3$ mg in artichokes, $0.9$ mg in celery, $1.1$ mg in cabbages, $1.1$ mg in cauliflower, $3.1$ mg in dandelion, $3.1$ mg in spinach, $6.11$ mg in beans, $8.6$ mg in lentils, $6.2$ mg in parsley, $8.4$ mg in soya. Whatever your choice, these values are rather small.
Look ! $ 8.4$ mg iron is $0.15$ mmol, and needs $\ce{0.03 mmol KMnO4}$ to be titrated. If this $\ce{KMnO4}$ is contained in a $0.01 M$ solution, these $0.03$ mmol are contained in a volume $\ce{V = n/c = 3 10^{-5} mol/0.01 mol/L = 3.00 mL}$. And remember that this value is a maximum ! Most of the time, you will obtain volumes lower than $1$ mL.
Furthermore, as stated by M. Farooq, titrating a vegetable extract will above all determine the amount of organic substances. For example, sulphuric acid will hydrolyse cellulose into reducible sugars like glucose, which reacts with permanganate.

Hi So I changed my experiment a bit, instead of looking at the boiling time of the spinach, I will be using different vegetables to find the one with the most iron concentration. My process will be to boil the vegetables, extract the liquid and mix it with sulphuric acid (H2S04). After doing so, I will titrate with potassium permanganate. Is this better? Please let me know if I need to change anything else.

KMnO4 is not going to work as it will lead to misleading results. KMnO4 will react with all the organic matter first. For trace amounts of iron, spectrophotometric methods are reliable. This is why I was asking which spectrophotometric you had in mind?

The answer to your question given one hour ago has been edited in my answer sent yesterday.


text:
Computing full Electron-Nuclear Interaction Integrals using Obara-Saika Scheme?
Following my previous question Here, I had been trying to implement One and Two electron integrals in the code. I am currently stuck at the implementation of the OS Scheme, where I read the references [1] and [2] to look for the implementation. I understood the recursion parts where the electron is transferred from one center to another using the following recursion relations:
$$ \theta^N_{i+1,j,k,l,m,n}=\theta^N_{i,j+1,k,l,m,n}-X_{AB}\theta^N_{i,j,k,l,m,n}$$
$$ \theta^N_{i,j,k+1,l,m,n}=\theta^N_{i,j,k,l+1,m,n}-Y_{AB}\theta^N_{i,j,k,l,m,n}$$
$$ \theta^N_{i,j,k,l,m+1,n}=\theta^N_{i,j,k,l,m,n+1}-Z_{AB}\theta^N_{i,j,k,l,m,n}$$
$$ \theta^N_{0,0,0,0,0,0} = F_N(pR^2_{PC})$$
where A and B are centers of the the basis functions and ordered set (i,k,m) and (j,l,n) are the angular momentum terms in x,y and z direction, and N is the order of Boys function. My question concerns the calculation of total integral from this scheme.
References:

Helgaker, _Modern Electronic Structure Theory
Obara. S, and Saikia. A, Efficient recursive computation of molecular integrals over Cartesian J. Chem. Phys. 84, 3963 (1986)
Gaussian functions

Perhaps, you can specify in a bit more detail what your question is.

@ErikKjellgren, I am trying to understand the implementation of OS Scheme for computing one and two electron integrals. I have understood what the individual terms in the equation are, and how the integrals are computed. My question was regarding the total value of the integral, like do we stop when we reach the max of i, j, k, l, m and n?

yes we stop when we reach the angular moment we want.


text:
Type of process of a system of high specific heat interacting with a system of low specific heat
Consider two systems A and B. Let the Molar Specific Heat Capacity of A be very, very, very, very great. The walls of (A+B) be of adiabatic nature from three sides and diathermal from another side (as in picture). A and B share a diathermal wall. Initially the temperature of A, B and Surroundings are the same. If we increase the temperature of surrounding then heat transfer will occur between surroundings and system B. Since A and B are separated by a diathermal wall then heat will also transfer from B to A thus increasing temperature of A. Let the heat exchanged by B be low in magnitude such that there will be an infinitesimal change in the temperature of A (because of the high Specific Heat Capacity of A).
Now my question is :

Is this an quasi-static process ?
Is this process reversible ?

The answers to your two questions are no and no.  Are you familiar with the Transient Heat Conduction equation?

@ChetMiller No, actually. Can you elaborate please ?

Is the system in equilibrium when it reaches its final state where the temperature of A has changed differentially, while the right boundary of B is raised a finite amount in temperature?  If I understand correctly, you are raising the temperature at the right boundary of B, and heat is being conducted through B to flow into A, correct?

@ChetMiller Yes. Your intuition is correct.

How can the system be at equilibrium if the boundary of B is higher in temperature than the temperature of A?

@ChetMiller Sorry I didn't read your comment properly. The answer to the first part of your comment is no. The system A and B are "trying" to achieve equilibrium when a differential amount of heat is transferred. However, the temperature is raised at the right side of B (near the diathermal wall) and heat is made to flow into B then further into A.

If the final state is not an equilibrium state, how can you talk about the entropy change (since entropy is a thermodynamic equilibrium property)?

@ChetMiller My bad I didn't think of this. If I understood you correctly, then since A and B have varying temperature therefore they don't are in any equilibrium state and therefore the entropy change cannot be defined and thus the reversibility of the system cannot be predicted. That's the answer to the second part. What will be the answer for first part of the question ?

Whether or not it is quasi static depends on the thermal conductivity of B.  If the thermal conductivity of B is very low, the change experienced by A can be considered quasi static.

@ChetMiller Got it! Thanks for your responses. I guess these responses in a form an answer below will be useful for others as well ;)


text:
Does a node require Change in sign of wave function
In a quantum Chemistry course we were asked to find the number of nodes of the wave function $$\Psi=\frac{\sin^2 x}{x^2} :  -3\pi \le x \le 3\pi$$ Clearly this has a removable discontinuity in x=0 so for a node it must satisfy the  equation $\Psi =0$ with $x\neq 0$ we get six solutions or six nodes.But I have also noticed that the hydrogenic wave functions seem to change their sign (phase) after each node.In this case $\Psi$ doesnt seem to change its sign,so can i say there are zero nodes!?

There is no sign change here because it is the square of (sin x)/x, i.e., the square of one of the two common sinc function definitions.

Yes you can say that a node without sign change is a node anyway. You won't encounter them often in real problems, though, because that would take an improbable coincidence.

More generally discontinuities are allowed in the wavefunction, but I believe that requires a non-continuous (step-wise) change in the potential.


text:
What is the mechanism of aldol condensation between two diketo-compounds with sodium bicarbonate?

In particular, what is the mechanism of aldol condensation of dimethyl-1,3-acetonedicarboxylate and 2,3-butanedione with sodium bicarbonate?

I'm trying to work out the mechanism of this aldol condensation using aqueous sodium bicarbonate as a base. I came up with this following mechanism:

However, I showed this to a Ph.D. student and they said that because the solution is aqueous the bicarbonate would form carbonic acid, a very weak acid which would be unstable and decompose to $\ce{CO2}$ and $\ce{H2O}$. I know this reaction can occur with this base but now I don't know how the mechanism works if it isn't in the way outlined below. Can anyone help with this?

If the carbonate forms carbonic acid some other species has to remain as a sodium salt. That species is basic.

Ask another PhD student, or maybe just measure the pH.

Your final product is missing the double bond in your proposed mechanism.

@KarstenTheis You're right my mistake, other than that though does the mechanism make sense?

I agree with  Karsten Theis and Waylander in their comments. Also, nothing wong with asking your teacher for his/her opinion. Keep in mind that your reaction is not completed (also you forgot the double bond at the end). It is thermodynamically possible to eliminate another water molecule to give much stable product.

Was that a Chemistry PhD student you asked?

The mechanism makes sense to me, but I'm a biochemist. I'm pretty sure about acid base chemistry, but not so much about organic synthesis (my track record in the lab was mixed).

@MathewMahindaratne This is only the first step of this reaction, a michael addition reaction follows during which the water is lost anyway. It may be lost before that as you say but I don't know how I'd go about working that out since the reactions all happen in one solution.

I think you basically have the mechanism right, one or other of the -OH groups is eliminated to form the double bond, could be the first one, could be the second.

With the double bond in place in your final product, elimination of a second equivalent of water is less likely owing to the formation of an unstable cyclopentadienone. If formed they tend to dimerize in a Diels-Alder fashion.


text:
How much heat is exchanged by this system?
I am having trouble with the following question:
We allow $\pu{18 g}$ of oxygen to react with $\pu{23 g}$ of ethane. The reaction is shown below.  Since the heat of combustion of ethane is $\pu{-1560 kJ mol-1}$, how much heat is exchanged by the system if the reaction is the system?
$$\ce{C2H6 (g) + 7/2 O2 (g) -> 2 CO2 (g) + 3 H2O (g)}$$
express $q$ in $\pu{kJ}$.
The answer I keep getting is $\pu{1193 kJ}$ because $\frac{23}{30.07} \times (-1560)$ would be $-1193$ and we are meant to express heat as being positive so it would finally be 1193. This is wrong apparently. What am I doing wrong?

If $\Delta H$ is negative, the emitted heat is often taken as positive, according to some scientists studying combustions. Of course, it is contrary to the usual definition of thermodynamics.

At constant pressure, $\Delta H$ = q, so their signs are actually the same: If thermal energy flows out of the system the heat flow (q) is negative, and visa versa.  [Less precisely, you can think of it as: Heat lost by the system is negative, while heat gained by the system is positive—if you are defining heat flow relative to the system.]  If you think q always has to be positive, that would be (as you can see) incorrect.  If your teacher is telling you to always report q as positive, what they're asking for is not q, but |q| (the absolute value of q).  You should clarify this with them.

I have a slightly pedantic objection to the question: the "reaction" can't really be a "system", the set of all atoms that undergo the reaction might be a system.  We won't know how much heat is "exchanged" between the system and its surroundings without more information.  (Is this isothermal combustion or adiabatic?). Thus IMO the literal answer is UNKNOWABLE


text:
How does the MO-LCAO theory explain the direction of valence bonds?
As all the bells sound, the common explanation of geometry of a molecule (consider  the water molecule) is due to  overlaping electron density.
The valence bond theory of the water molecule describes the two O-H bonds as resulting from the overlap of the H 1s orbitals with the two half-filled 2p orbitals of the oxygen atom. Since the two 2p orbitals are at right angles to one another, valence bond theory predicts a bent geometry for the water molecule with a bond angle of 90°. To do this, draw the following picture:

The opening of the angle to a value greater than the predicted one of 90° can be accounted for in terms of a lessening of the repulsion between the hydrogen nuclei.
Ok.
But what do we have in MO-LCAO (aka HF) theory?
Methods of quantum chemical calculations give us the following picture of orbitals

For me personally, the picture of molecular orbitals in the second case does not at all agree with the picture of atomic orbitals in the first case. How can you identify the first in the second picture? Or in other words, how does the MO-LCAO (aka HF) theory explain the direction of valence bonds?

You calculate the MO diagram for all possible directions (or a sufficiently large number of directions), and then find out which direction minimises the energy: https://en.wikipedia.org/wiki/Energy_minimization

@orthocresol Yes, let's say I determined the minimum energy and the molecular orbital that corresponds to it. By the form of the orbital, I do not see any overlap, as in the VB- theory. What then is the point of VB-theory?

I completely disagree with the described way in the VB model. It's valence bond for a reason, it accounts for bonding domains naturally, so, if all you start with four domains about oxygen, idealised as sp³, and go from there. Modern calculations have shown that this approach does not represent the mathematically ideal solution. Are the lone pairs in water equivalent?

As I understand it, and correct me if I'm wrong, you seek to 'reconcile' the MOT and VBT pictures. I would contend that there's no reason that MOT should explain VBT (although people have tried; I'm not the right person to summarise this, though, as it's way outside my domain of knowledge). The theories of bonding exist not to rationalise one another; rather, their aim is to explain experimentally measurable things such as geometries, chemical reactivity, or various spectroscopies. In this case, both MOT and VBT correctly explain the H–O–H bond angle. Beyond that, though, all bets are off.

@orthocresol Yes, I seek to 'reconcile' the MOT and VBT pictures. Even if in VBT these pictures at least make it possible to visualize the direction of the connection, then in MOT it is generally not clear what the pictures of orbitals mean and why they are drawn.

The relevant MO analysis for understanding the effect of bond angle on energy is a "Walsh diagram," which for compounds of the type $\ce{AH2}$ looks like this:

Source is this post on ChemSE which copies the image from the well known textbook Orbital Interactions in Chemistry by Albright, Burdett and Whangbo.
What it shows is how the energies of each MO are affected as the bond angle decreases from 180 on the left to 90 on the right, in this case for the specific molecule $\ce{SH2}$. The diagram for $\ce{H2O}$ would look qualitatively similar but differ quantitatively such that the minimum total energy would fall at the observed bond angle for that molecule.
Things to notice:

s-p mixing between orbitals with "a" symmetry creates electron density on the oxygen that is similar to an sp hybrid orbital on the z axis
Decreasing the H-A-H bond angle from 180 reduces the overlap of the hydrogen atomic orbitals with the central atom $p_x$ orbital, which increases the energy of the $1b_2$ MO, but it creates overlap with the $p_z$ orbital (with which there is zero overlap at 180), stabilizing the $2a_1$ MO. It is largely the balancing of these two effects that determines the optimum bond angle.
The large effects seen on the anti-bonding orbitals are irrelevant as long as they are not occupied.

+1 - my immediate thought was "that's exactly what I'd say" and then I saw you linked to my previous answer. :-)


text:
stability of Cu(II), Cu(I) and Zn(II) ion
I would like to ask about the stability of $\ce{Cu^{2+}}$ and $\ce{Cu^{+}}$ and also $\ce{Cu^{2+}}$.
$\ce{Cu^{2+}}$ has a configuration of $(3\mathrm{d})^9$ but $\ce{Cu^{+}}$ has a configuration of $(3\mathrm{d})^{10}$. Why does $\ce{Cu^{2+}}$ are more stable and more common than $\ce{Cu^{+}}$. I am thinking of LFSE but I am not sure is it the correct way of thinking.
If $\ce{Cu^{2+}}$ $(3\mathrm{d})^9$ is more stable than $\ce{Cu^{+}}$ $(3\mathrm{d})^{10}$, then why we cannot see a $\ce{Zn^{3+}}$ where it is also $(3\mathrm{d})^9$?

Notice the difference between meaning of M(II) and M(2+). The former is the metal atom with oxidation number +II, the latter the true ion with the charge +2e. So better to say Cu(2+) than Cu(II) ion. M(II) may part of covalent molecules, can have charge ligands etc.

Useful links for text and formula formatting (not to be applied to titles):
Notation basics ,  Formatting of math/chem expressions  and
upright vs italic
For more, see Math SE MathJax tutorial.

Does this answer your question? Why Cu+ is unstable in aqueous medium?

@Poutnik u r right. I am a new user and I dont know how to type M(2+) neatly sorry for that I will change it after reading that passage

@NilayGhosh but why Zn(II) is stable in aqueous medium?

@someone Try to type $\ce{M^2+}$ to get $\ce{M^2+}$, or $\ce{C2O4^2-}$ to get $\ce{C2O4^2-}$. Or $\ce{M^{II}}$ to get  $\ce{M^{II}}$

Filling subshells is not everything with transition metals. You also have differences in electrostatic interactions, especially with hard-base anions or dipoles. With softer bases there is a different outcome.

The link given by Nilay Ghosh 5 hours ago does not yield an answer. It says simply that hydrated $\ce{Cu^{2+}}$ is more stable, because it is more charged than $\ce{Cu+}$, so that it attracts more strongly the water molecules. If this was the reason, it could be applied to the case of the hydrated zinc atom, which should be more stable at the oxidation number +III. And of course,$\ce{Zn^{+3}}$ does not exist

@Maurice finally someone understand what I mean

@someone It would be faster if the question was clear from the beginning, not giving space for misinterpretation.

@Poutnik I am not a native speaker of english. Sorry for the misunderstanding.

No problem, neither am I. I have meant the note rather about the content than the language itself. If the question, its context and/or background are unclear, not receiving what has been expected is what was paid for by the question. // You e.g. do not specify that(or if) you mean hydrated ions.

It boils down to the balance between ionization energy and increased electrostatic attraction of a more highly charged ion to solvent molecules.
If we look at ionization energies here and compare these with the maximum charge seen for forming a water-solvated metal ion, we see a pattern: the maximum charge corresponds to the point where the ionization energy surpasses 3000 kJ/mol, which is about 31 electron volts, at least for metals through the fourth period. In effect, the additional attraction to water molecules imparted by adding one more electronic positive charge to a metal ion is enough to balance 3000 kJ/mol of ionization energy. For instance, the second ionization energy of magnesium is 1451 kJ/mol whereas the third ionization energy is about 7733 kJ/mol, so magnesium will form solvated ions up to +2 charge.
Applying this to copper, we find that thecsecond ionization energy is about 1958 kJ/mol, so copper can form water-solvated copper(II) in aqueous solution. For zinc this second ionization energy is about 1734 kJ/mol, decreased from the copper value by using an electron from the 4p subshell versus 3d. But then the third ionization energy of zinc is about 3833 kJ/mol, so zinc is limited to forming aqueous +2 ions like copper. The solvating power of water molecules is enough to break into the 3d subshell of copper, but not the more tightly bound 3d shell of zinc.
Computations suggest that zinc actually can reach the +3 oxidation state in a very specific, nonaqueous environment using highly stabilized counterions with three negative charges. See the entry for zinc in Wikipedia's list of oxidation states.

But why the second ionization of $Cu$ is $1958 kJ/mol$ while 3rd ionization of $Zn$ is $3833 kJ/mol$? It seems that the value is unusually large. Both of the ionization involves removing an electron in $3d$ subshell turning it from $3d^{10}$ to $3d^9$. Since Zn has 1 more nuclear charge, it is expected to have a slightly larger value. But in real case, it is almost a double.

But the net charges attracting the electron are different. More charge on the zinc ion = bigger ionization energy.


text:
Why is reaction of Li less vigorous than that of Na although the former has a more negative SRP value?
My textbooks says:

It may be noted that although lithium has most negative E0 value (Table 10.1), its reaction with water is less vigorous than that of sodium which has the least negative E0 value among the alkali metals. This behaviour of lithium is attributed to its small size and very high hydration energy. Other metals of the group react explosively with water.

So, basically if Li has more negative SRP value it basically means it's a very good reducing agent, right? Water in the presence of a strong reducing agent starts acting as an oxidising agent. But when water combines with Li, the hydration energy released is very high due to very low charge density on Li. So how would any of that cause the reaction of Li with water to be any less vigorous than Na?

Li melts at 180°C, and Na at  95°C, i.e. below the Bp. of water.

Note that the amount of (total or free) energy a process releases  has generally no direct relation to the rate of this release. // In outdoorsy real-life analogy, the time how to get to 20 km far destination is not determined by the difference of destination and start altitude, but the altitude profile of the route plays bigger role in that.

Yes it has a correlation here, the foundation of that is described by Marcus theory. Rate of SET is usually faster the higher the free enthalpy of reaction is, and in good approximation the reaction of Li and water is an SET. But as Karl pointed it out, the physical state change is responsible here.

Li melts at 180 °C, and Na at 95 °C. That means the surrounding water keeps the Li piece cold enough so it cannot melt.
The lattice enthalpy of Li is higher.
Also Li is very light, $\pu{0.53 g/cm^3},$ while Na has nearly $\pu{1  g/cm^3}$. Li floats on the water.
Please note: the reaction speed is lower. That doesn't say much about the reaction enthalpy. Have you looked it up?

Apparently the hydration enthalpy of Li is much higher than the rest of the alkali metals. So that must mean that the reaction enthalpy of water reacting with Li must have a higher negative value than Na, right?

Not necessarily. You need to look up all the values of all the compounds and add them up according to the stochiometric of the reaction! Formation enthalpies of water and hydroxide,  hydration enthalpies, lattice enthalpies, etc.


text:
How does Hyperconjugation stabilize a Carbon Free Radical?
I tried drawing the resonance structures but just cannot see how donating two electrons to a carbon that only needs one electron make it more stable?
I stumbled upon this question asked years ago where they say that hyperconjugation stabilizes the carbocation, but does not stabilize free radical that much.
I cannot seem to find a solid reasoning for it other than a Free Radical requires electron from an electron donating group. Note that I am just just highschooler knowing learning about intermediates for the first time. Any help would be much appreciated!

Hyperconjugation means that the $\sigma$-bond orbital interacts with an adjacent empty anit-bonding orbital. This means that the interaction between a filled orbital and an empty orbital is the factor that stabilizes the carbocation in this case. However in the case of a carbon radical, there would be at least one electron in the anti-bonding (or non-bonding) orbital, which would be destabilizing the interaction. Just to clarify on the point why Hyperconjugation cannot stabilize a Carbon Free radical as much as a carbocation, the repulsion between the electrons would be larger in the case of a carbon free radical, than in the case of a carbocation.

I tried drawing the resonance structures but just cannot see how donating two electrons to a carbon that only needs one electron make it more stable?

As you said only 1 electron is needed,actually only 1 electron is donated as you can see in hyperconjugation structures above.


text:
How is propene more reactive as well as more stable than ethene?
I know that hyperconjugation stabilises a double bond. But in propene an electron-donating group $(\ce{-CH3})$ is increasing the electron density at the double bond, so its nucleophilicity should be higher. How can it be more stable as well as more reactive?

you said more reactive, but with what are you reacting both of them.

@TeslaBolt I meant that propene has higher nucleophilicity than ethene. I am reacting them both with the same electrophile.

What do you mean by "stable"?

@user55119 The more stable compound would start to disintegrate at a higher temperature.

By "stable"' do you mean the one that has the less positive (propene) heat of formation or possibly the one that reacts less rapidly with a particular electrophile? As to disintegration, I don't know what that process entails.

@user55119 The one that has less positive heat of formation. I think of the measure of what reacts less rapidly with a particular electrophile as their reactivity.

The heats of formation decreases by -5 kcal/mol for every -CH2- group that is added to each homologous. the n-alkanes . This doesn't mean that n-hexane is more stable tha n-pentane. Look here.

@user55119 Then what do we mean when we say, "more substituted alkenes are more stable"? I have seen this statement in a lot of places.

I don't say that. Is benzene more stable than cyclohexene in the presence of bromine? Yes, it ia kinetic difference.  Is 1,2,4-tri-t-butylbenzene more stable than cyclohexene in in a UV photochemical reaction ? No, the benzene compound absorbs light to form a Dewar benzene and cyclohexene doesn't. Stability is relative to conditions..

you need to go with the mechanism.
1st

in this case propene will form a 2nd degree carbocation which is more stable.
2nd

when the electrophile is having a lone pair then a 3 membered ring is formed as intermidiate.then the other Nucleophile attack to open the ring and thus product is formed.
you can refer to Markovnikov's Rule for further info(https://en.wikipedia.org/wiki/Markovnikov%27s_rule)