### 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*