Melting points of compounds? Compare the melting points of:
  
  1) $\ce{BeSO_4}$
  
  2) $\ce{CaCO_3}$
  
  3) $\ce{BaCO_3}$
  
  4) $\ce{SrCO_3}$


Okay, so there are a few statements given by my teacher:

1) Thermal stability of ionic compounds is proportional to the counterbalance effect of electropositive field of cations(magnitude of +ve charge) and electronegative field of an anion (mag. of -ve charge). (I interpret this as the lesser the difference between the magnitude of charge, the more thermally stable the compound.)

2) The real magnitude of charge is directly proportional to the number of electrons lost(basically the number we write next to an element, like $\ce{Ca^{2+}}$, right?) and inversely proportional to the size of the ion.

3) Except the second group elements and halides, all anions can be considered as "large anions" and hence their effective magnitude of charge will be same (roughly).

So since all of them are "large anions", we have to compare the magnitude of charge on the cations. Now, being large, their charge is small. So for least difference, we want the cation with the smallest charge. This means the largest size, which simply means $\ce{Ba}$. So the answer should be 3. To confirm this, I Googled the melting points of these substances.

1) $\pu{110^oC}$
2) $\pu{811^oC}$
3) $\pu{825^oC}$
4) $\pu{1494^oC}$  

So according to me, the melting points in decreasing order should be:

3 > 4 > 2 > 1

When it turns out to be:-

4 > 3 > 2 > 1

Where did I go wrong?

I personally think:

1) Since the charge on anions is only roughly same, I think that when we consider the difference between the charges, that would be messed up and so we would end up with wrong answers(possibly).

2) That since this question is supposed to be for high school students, we make a lot of assumptions, which obviously don't hold true in the real world, and hence the answer is wrong? That being said,is my answer correct keeping these assumptions in mind?

3) Since chemistry has a lot of exceptionss , is this another one of those? Am I going to have to memorize this too?
First, in order to compare mp's you need to know the mp's. You have two choices: 1. run melting point measurements or 2. find literature written by someone who has run the experiments. Perhaps this is a translation problem from your native language? Perhaps you meant predict the ranking of mp's for those 4 compounds. 

You state that CaCO3 melts at 811 °C. As far as I know, that is incorrect. First, the thermodynamically stable polymorph is calcite, which according to wikipedia has a mp of 1339 °C but which decomposes at temperatures above ~840 °C (also according to Wikipedia!). I hope you see this is clearly contradictory. My first hand experience is that it does indeed decompose at around 820–840 °C, so I am unable to explain how they were able to measure its melting point 500 °C above that. 500 °C is an enormous gap, but perhaps they measured it under some enormous pressure (far from STP) - I really don't know. 

The other major problem I'm having is understanding what you (or your teacher) means by "counterbalance the effect of electropositive field of cations ... and electronegative field of an anion." It seems to me to be meaningless, at least I don't recognize this terminology in reference to the electrostatic forces usually invoked to account for ionic solids. BeSO4 is an obvious problem since Be is known to for its tendency to form covalent compounds. Indeed, according to Wikipedia, anhydrous Be sulfate has Be-S (covalent) bonding. While you could predict that the covalent bonding would reduce the mp, what you'd do with the polymeric nature of the solid is beyond me - I've no idea how you or your teacher can explain that, except by hand waving. 

This leaves the Ba and Sr salts. Simple logic of ion size would predict the order Ba &lt; Sr and ignoring the ridiculous assertion on Wikipedia that the Ba salt's melting point is 811 °C while at the same time (you did READ the article, right?) stating that that is the temperature at which it a "polymorphic transformation" occurs. A little further digging provides a safety data sheet which claims a mp of 1400 °C "close to its decomposition temperature", but such data should be suspect. 

Your teacher's choice of picking carbonate as the anion was a poor one, in my honest opinion. Because of the tendency of these salts to decompose, rather than melt, you need to be very careful where you obtain your data from. But perhaps that is the lesson your teacher hopes some of you will learn - to not just accept a number because it is readily available (without subjecting it to critical analysis (who, what, where, why, when, how - which in this case means how reliable is the reference? does it reference a primary (academic) source? if not, an authoritative secondary source? if not, then you should seek independent confirmation. Such confirmation is hard to find on the internet, since one lazy site steals from another until the noise drowns out the signal. 

I really don't know if density functional theory (DFT) quantum mechanical modeling by supercomputers is able to accurately predict the mp's of these material. My guess is that because of the change in crystal structure(s) that it remains beyond our current capabilities (for some things, calculating the value has become reasonably accurate – as far as I know (and I'm no expert) mp isn't one of the successes. If it was accurate it would be a third way to "compare" the mp's.