Input interpretation

Al2(CO3)3 → 2Al2O3 + 3CO2

Aluminum oxide carbon dioxide

Balanced equation

Balance the chemical equation algebraically:

Al2(CO3)3 → 2Al2O3 + 3CO2

Add stoichiometric coefficients, c1, to the reactants and products:

c1Al2(CO3)3 → c2 2Al2O3 + c3 3CO2 

Set the number of atoms in the reactants equal to the number of atoms in the products for Al, C and O:

Al: 2c1 = 2c2

C: 3c1 = c3

O: 9c1 = 3c2 + 2c3

Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c1 = 1 and solve the system of equations for the remaining coefficients :

c1 = 1

c2=1 

c3=3

Substitute the coefficients into the chemical reaction to obtain the balanced equation:

Answer:

Al2(CO3)3 → 2Al2O3 + 3CO2