Consider the reaction of ferric nitrate with ammonium carbonate, i.e., Fe(NO3)3 + (NH4)2CO3

Consider the reaction of ferric nitrate with ammonium carbonate, i.e.,

α Fe(NO3)3 + β (NH4)2CO3 −→ γ Fe2(CO3)3 + δ NH4NO3.

a. Write an equation that relates α and γ such that there are the same number of iron atoms on both sides of this chemical equation.

b. Do the same for each remaining atom type and hence write out a system of equations in terms of the coefficients of this chemical equation.

c. Solve this system using Wolfram Alpha (or any other package you like). Give the balanced chemical equation.

d. How many different sets of coefficients can this reaction be balanced with? Is it possible to have a chemical equation which can be balanced in exactly two ways?

e. Write the system you obtained in part

(b) as a matrix equation of the form Ax = b.

f. Suppose that the size of the coefficient matrix A is given by m×n. In this case what are the values of m and n? What features of the chemical equation do m and n correspond to?

g. Do you expect the inverse matrix method to work for this sort of question? Why/why not?