how to mathematically predict reaction results
There are two parts to quantification of reactions: 

(1) How far it goes? (Thermodynamics, equilibrium). This all is dictated by ground state energy.

(2) How fast it goes? (Kinetics, reaction rates). This is dictated by  transition state energy vs ground state energy. 

Equilibrium is much easier to understand. Let [Y] be concentration of reagent Y. You say that for 2A + B = C+3D +4E you have:

K = [C]$^1$[D]$^3$[E]$^4$/([A]$^2$* [B]$^1$)

Note how powers are equal to coefficients in the equation.

$\Delta$G= -RT*ln(K)

$\Delta$G is Gibbs energy (measured and tabulated for all of inorganic chemicals from school textbook).
R is a constant (Universal gas constant)
T is temperature.

How to use it? Well, imagine that you have 

2*H2+ CO &lt;-> MeOH

Lets say that K=10 under that conditions. I am sure I am off. Correcr way to find it is to use $\Delta$G= -RT*ln(K). You know T, R is constant. $\Delta$G is known for MeOH, H2 and CO. Calculate the difference to find $\Delta$G. You will need to find $\Delta$G for methanol vapor or take it for liquid MeOH and add $\Delta$G of evaporation.

You start with 1M of CO ( atm at 273C) and 1.5M of H2 (67.2 atm at 273C). Total pressure 112 atm. (Mol to pressure conversion using ideal gas law). What will be the equilibrium amount of MeOH if ?  You say that

Let x be the amount of product at equilibrium. H2 = 1.5 M - 2*x and CO = 1-x.

x/(1.5-2*x)$^2$*(1-x)=10=K

Now you have a cubic equation to solve (1.5-2x)$^2$*(1-x)*10 - x = 0;

With more reagents you have algebraic equation of higher power, but there are methods to solve those numerically and the idea is simple enough to explain.

This gets a bit more complicated when you have multiple reactions going. But This is the basis. When system gets complex you start ignoring some small members to simplify it. (1.0001)$^5$ ~ 1.0005 (reasonably accurate). YOu do the same in chemistry.



Kinetics is trickier. For A+ 2B -> C the first approximation is that 

rate = k*[A]*[B]$^2$.

Also "k often increases by a factor of 2-4 per 10C of increase in temperature". 

Now to treat it accurately you need to solve a system of equations. each equation is either

r$_i$ = $\delta$[A$_i$]/$\delta$t

or 

r$_i$ = ($\delta$[A$_i$]*$\delta$[B$_i$])/$\delta$t

Rate if i$^{th}$ reaction = change of concentration of i$^{th}$ reagent per time period as the period goes to zero).

You end up with a system of ordinary differential equations. But don't get tricked by the word "ordinary". Most of them don't even have solutions in "elementary functions" (functions that you study in school or university as a chemist.

To understand what is a differential equation you would need to know what is an integral. We study differential equations in second year of university and that probably the most difficult subject in university.