Pauling's rules

These are two empirical rules which predict the strength of mononuclear oxoacids. I'm not sure why they are so commonly taught to undergrads - since I presume modern wavefunction software could make more advanced predictions.

1. For the oxoacid O_pE(OH)_q, pK_a ≈ 8 – 5p
2. The successive pK_a values of polyprotic acids (those with q > 1), increase by 5 units for
each successive proton transfer.

It should be obvious why oxo groups increase acidity, they can delocalize charge on the anion by resonance:

This allows us to rationalize why the acidities of chloro oxoacids decrease in the order HOCl₄ > HClO₃ > HClO₂ > HClO. Likewise for H₂SO₄ > H₂SO₃ and HNO₃ > HNO₂.

One good use of these rules is to notice structural anomalies. For example, if you dissolve carbon dioxide in water to make carbonic acid, you will find an empirical pK_a of 6.4 - but the rules predict a pK_a of 3.

The mistake is in assuming that all of the CO₂ dissolved in a sample of water exists as carbonic acid. In reality, only 1-2% of dissolved carbon dioxide exists in carbonic acid form. The pure pK_a is 3.6 when this difference is taken into account.

Many non-metal oxides, and some metal oxides, do not fully become their acidic form when dissolved in water. Deviation from Pauling's rules can help us detect that.

Bronsted acid classes

1. Aqua acid

This is an acidic proton located on a water molecule which is co-ordinated to a metal ion. Example:

2. Hydroxoacid

This is an acidic proton on a hydroxyl (OH) group, which does not have a neighboring oxo group (=O). An example is telluric acid:

Which is a white solid that dissolves in water.

3. Oxoacid

This is an acidic proton on a hydroxyl group, which has a neighboring oxo group. The most common ones are mononuclear, examples:

Often one or more of the OH groups can be replaced with an electron-withdrawing group such as F or CF₃, or an electron-donating group such as NH₂ - which can donate electrons by pi-resonance. Charge is more stable when spread out, so we can increase acidity by making an anion more stable by delocalizing charge (ie. pulling it off the oxygen atom).

Not all oxoacids follow the simple pattern of one atom surrounded by =O and -OH. For example, phosphonic acid (H₃PO₃) is only diprotic. Its easy to lose a mark in an exam by forgetting that one of the hydrogens isn't attached to an OH:

Solvent-system definition of acids and bases

This recognizes autoionisation of some aprotic solvents, such as boron trifluoride:

Notice the similarity with autoionisation (ie. autoprotolysis) of water.

In the solvent-system definition, a solute which increases the concentration of the cation generated by autoionisation of the solvent is called an acid, and a solute which increases the concentration of the anion generated by autoionisation of the solvent is called a base.

BrF₂AsF₆, called Difluorobromine(III) hexafluoroantimonate(V), is a salt without any obvious uses. But it is soluble in BrF₃. It disassociates into BrF₂⁺ and AsF₆^-, hence we would call it an acid.

Another example is dissolving sodium amide in ammonia. The autoionisation equation of ammonia is:

Since sodium amide splits into Na⁺ and NH₂^-, we would call it a base.

Solvent levelling

It is very hard to discriminate between strong acids in water since they are fully deprotonated, so a mol of HI and a mol of HBr each act like one mol of H₃O⁺. A solvent which is a weaker proton acceptor is needed to tell the difference.

The same logic applies to strong bases, one mole of any strong base can be treated as one mole of hydroxyl ions.

This is called the leveling effect - the limitation by the solvent of how strong acids or bases can be.

If two weak acids are put into a solvent which is a strong proton acceptor, such as ammonia, it is likewise hard to tell the difference between the two acids, since they will both act like a mol of ammonium ions. So the leveling effect changes with the solvent.

So a solvent HSol has a range for the allowed pH of a dissolved compound. Any acid stronger than the range will act like H₂Sol⁺, and any base stronger than this range will act like Sol^-. This is called the acid–base discrimination window:

The width of each bar is actually proportional to the pK_w of the solvents, we can see why below.

For a solute acting as an acid:

Notice that pK_{a depends on the solvent.}

An acid is considered strong at pK_a < 0, which corresponds to K_a > 1

So an acid with pK_a < 0 in a particular solvent has an acidity at the limit allowed by the leveling effect of the solvent, which is the same acidity as [H2Sol⁺]

For a solute acting as a base:

A base is considered strong at pK_b < 0, which corresponds to K_b > 1

So a base with pK_b < 0 has a basicity at the limit allowed by the leveling effect of the solvent, which is the same basicity as [Sol^-]

Now for the clever bit. The relationship between pK_a and pK_b is:

Therefore all bases with pK_a > pK_sol give a negative value of pK_b thus they behave like pure [Sol^-]

So the upper limit (strongest base) of pK_a is pK_sol

The lower limit (strongest acid) of pK_a is 0

Hence the windows of strengths that are not leveled in the solvent are is from pK_a = 0 to pK_a = pK_sol

Which explains why the window size is proportional to pK_w.

You may have difficulty grasping intuitively why a substance bad at protonating itself (high pK_w, so a small autopyrolysis constant) is also good at discriminating between acids. I have never been able to grasp it intuitively either. This explanation just shows you from the equations.

Rate of bond rotations

t_1/2 refers to the time taken for half the molecules in a sample to rotate.

I've always been told "double bonds don't rotate" so it is very interesting to see that some have half-lifes measured in days. I don't know why there is such a big difference in half-life for the bottom two molecules.

Arrhenius equation

This is a relationship between reaction rate, activation energy, and temperature. It is an empirical relationship, but it works remarkably well:

k = Rate constant of reaction
A = Constant, depending on the reaction
R = Molar gas constant
T = Temperature
E_a = activation energy for the reaction

Notice that this shows rate increasing with temperature, and decreasing with activation energy.

Examples will often give you some variables and have you calculate another, usually requiring you to rearrange the equation by making use of logarithm rules.

Isooctane

Isooctane is a major additive to petrol, it defines the octane rating - pure isooctane has an octane rating of 100. While pure n-octane has a rating of 0.

The strict meaning of isooctane would refer to 2-methylheptane, but 2,2,4-trimethylpentane ended up taking the name historically due to its far higher importance.

Combustion of isooctane has a ∆G° of -1000 kJ / mol, yet can exist comfortably at room temperature if there are no spark sources about. It is a good example of a kinetically stable but thermodynamically unstable molecule.