The divide is actually not between covalent and ionic, but rather a spectrum between localised and delocalised electrons. The history of all this is actually quite fascinating, and Phil Anderson in his book "More and Different" has a nice chapter on this. Essentially, around the time that people started doing quantum mechanics on molecules seriously, there were two schools of thinking which dominated.

On one side was Mott and more popularly, Hund and Pauli who thought of electrons as primarily attached to atoms and through electromagnetic interactions their motions/orbitals would be deformed and one gets molecules. This is the version usually taught in chemistry classes as with a few rules of thumb it is possible to qualitatively account for a vast range of behaviours.

On the other side was Slater with a dream of a machine which could simply compute the electronic structure by giving it the atoms and electrons. In this picture, the electrons are primarily thought of as delocalised over all the atoms, and through a rigorous procedure of perturbation theory one adds the effect of interactions between electrons and may achieve arbitrarily good precision.

The latter has the problem that the results are not intuitive --- there are no rules of thumb available and one is reduced to simply computing. The problem with the former is that to achieve high accuracy, the "rules of thumb" become exceedingly complex and are not really very easy to use or to compute with --- it lacks the simple regularity of the Slater dream machine. It is telling that essentially the latter has won, and nowadays it is routine to compute the electronic structure of quite large molecules (~1000 atoms) through brute-force (the technique is known as density functional theory, and there are commercial software available to do it).

In finite molecules one can actually show that in principle both approaches will work --- technically we speak of there being an adiabatic connection between the localised and delocalised states. The only practical difference is just how hard it is to carry out the calculations. However, in infinite molecules (e.g. solid crystals) this is not true, and there can be a proper phase transition between the two starting points. In that case, the localised approach corresponds to what is fancily called these days "strongly correlated systems" such as Mott insulators and magnetically ordered materials, and the delocalised approach are essentially metals (technical language: renormalises to be a Fermi liquid).

Nowadays there is a desire (from theoretical condensed matter physicists) to develop the localised approach again, as it may be possible to find some useful rules of thumb regarding magnetic materials, a prominent example of which are the high temperature superconductors.

There isn't a single formula because the process is an iterative one. The guiding principle is energy conservation, but you need to incorporate additional forms of energy transfer if a phase change occurs.

Example: Substance 1 (with mass $m_1$ and temperature $T_\mathrm{1,\,initial}$) starts off as a liquid, and substance 2 (with mass $m_2$ and temperature $T_\mathrm{2,\,initial}$) starts off as a gas. The total amount of energy gained by all substances must be zero according to energy conservation. Initially assume that no phase change occurs; thus, the final temperature $T_\mathrm{final}$ must satisfy

$$m_1C_1(T_\mathrm{1,\,initial}-T_\mathrm{final})+m_2C_2(T_\mathrm{2,\,initial}-T_\mathrm{final})=0$$

for temperature-independent (but material- and phase-dependent) heat capacities $C$. (If the heat capacities vary non-negligibly with temperature within a single phase, then you need to numerically or analytically integrate them.)

If the final temperature is above the liquid's boiling temperature or below the gas's boiling temperature, then the initial assumption is violated; some amount of phase change has occurred. Assume that it is partial. You need to revise the equation by adding $mxL$, where $x$ is the extent of the phase change (i.e., from 0 to 1, representing a lack of to a complete phase change, respectively) and $L$ is the latent heat of vaporization. The final temperature is the phase change temperature that was violated earlier. Now re-solve the equation.

If the extent $x$ is greater than 1, then your most recent assumption is violated. Set $x$ equal to 1 (because the phase change was completed) and add yet another term that represents a temperature change in the new phase. If the liquid was found to completely boil away, for example, then you have

$$m_1\left[C_\mathrm{1,\,liquid}(T_\mathrm{1,\,initial}-T_\mathrm{vaporization})+L_1+C_\mathrm{1,\,gas}(T_\mathrm{1,\,vaporization}-T_\mathrm{final})\right]+m_2C_2(T_\mathrm{2,\,initial}-T_\mathrm{final})=0$$

Solve again.

In general, you would conduct this iterative process with additional phase change temperatures and phase-dependent heat capacities until your most recent assumption is validated. Then you have obtained the equilibrium temperature.

## Best Answer

Let's look at the definition of Avogadro's number:

So let's say this number changes. This can occur in one of two ways. The first is the exciting but impossible one you are looking at: the mass of carbon-12 atoms changes. Our current physics assumes the conservation of mass. If "the class of things we call carbon-12" decreases in mass-per-atom, that mass has to go somewhere. Where does it go? The answer to that is 100% dependent on

howthese carbon 12 atoms change mass. If the mass is "converted" to gamma rays, the result will be very different from if a deity turns a knob on the universe (in which case, I would ask the deity this question).The more interesting and reasonable answer to this is that our definition of a kilogram changes. This is interesting because... well... our definition of a kilogram is a bit embarrassing. As it turns out, we currently define the kilogram with respect to an internationally recognized mass, known as the International Kilogram Prototype (IKP). This is literally a block of platinum-iridium alloy that everyone in the world has agreed is "the definition of what 1kg of mass is." That's it. That's all a kilogram is. End of story.

So that suggests that, the mystical and non-existent effect which changed Avogadro's number would change the mass of the IKP at the same time. If this happened, we would find the two effects cancel each other out, and we'd find that Avogadro's number didn't change at all! Hilarious!

Interestingly enough, there is an effort to change Avogadro's number. There's an effort to

setit to be equal to $6.02214X×10^{23}mol^{-1}$ (where X is one digit that has not yet been agreed upon). This would be done by setting the definition of the kilogram to be with respect to a certain number of atoms. This is being done to try to free ourselves from the joy of having our entire unit system built around a single physical block of metal locked in a vault. If the new definition took place, we could create a kilogram reference out of a polished sphere of silicon like this:These spheres are carefully polished to have a very exacting diameter, and thus a very exacting number of atoms within the sphere. If this change takes place, anyone with sufficient skill could construct a kilogram directly, rather than having to attempt to copy an existing physical kilogram mass! These spheres are currently undergoing long term stability study to make sure they don't gain or lose mass over time at an unacceptable rate. Metals pick up an oxide layer over time, and those extra oxygen atoms can add up when you care about parts per million! If it works, we can replace the IKP, which technically is losing mass slowly because they have to clean it every time it is used, and that cleaning pulls metal off!