We all know that Hydrogen molecules (H2) and Oxygen molecules (O2) combine into

Question

We all know that Hydrogen molecules (H2) and Oxygen molecules (O2) combine into water. We can express this as follows:

H2 + O2 ? H2O
This is called an unbalanced chemical equation because the number of Oxygen atoms on the

left side of the equations (2 atoms) is not the same as that on right side (just 1 atom).

To balance this equation means to add positive (!!) integer coefficients x,y and z to the unbalanced equation

xH2 + yO2 ? zH2O
such that the numbers of atoms of each type are the same on both sides of the equation. In

this case we can see at a glance that x = 2, y = 1, z = 2 will do the trick: 2H2 + O2 ? 2H2O

What this equation tells you is that you need two H2 molecules and one O2 molecule to make two H2O molecules. This information is very important in practice.

Note that you could have balanced this equation in infinitely many ways. For example, you could have chosen x = 4,y = 2,z = 4, or more generally x = n·2,y = n·1,z = n·2 for any natural number n. What we have done is to choose the solution with no common factors.

a) Balance the following equation:
Fe2(SO4)3 + KOH ? Fe(OH)3 + K2SO4

So, set up the corresponding system of linear equations, find the reduced row echelon form of the corresponding augmented matrix, and in this way find a solution to the linear system. Based on this solution find the smallest positive integer coefficients that balance the system.

5

Double-check that you get the same solution as the online balancer. You should use Math- ematica for calculating the reduced row echelon form of the augmented matrix and simply record the result.1 (15 marks)

b) Let’s make things a little harder. Your friends in chemistry are observing a chemical reaction that involves the following types of molecules H2O, VO2Cl, NH4Cl, NH4OH, NH4V O3. Your mission is to help them find all possible balanced equations involving these molecules (using linear algebra, of course). By doing so you are telling your friends what the possible reactions between these molecules are.

Explanation / Answer

(a)

Fe2(SO4)3 + KOH -------> Fe(OH)3 + K2SO4

The final balanced equation is,

Fe2(SO4)3 + 6 KOH -------> 2 Fe(OH)3 + 3 K2SO4

(b)

The possible balanced chemical equation among the given is,

VO2Cl + 2 NH4OH --------> NH4Cl + NH4V + O3 + H2O

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