## Word equation

** aluminum nitrate + water → nitric acid + aluminum hydroxide**

## Input interpretation

**Al(N** ** + ****H****2****O**** →**** HN****O****3**** + Al(OH****)****3**

** ****Aluminum nitrate ****water ****nitric** **acid aluminum hydroxide**

## Balanced equation

Balance the chemical equation algebraically:

** Al(N****O****3****)****3**** + ****H****2****O**** →**** HN****O****3**** + Al(OH****)****3**

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

** ****c****1****Al(N****O****3****)****3** ** + ****c****2****H****2****O ****→ ****c****3**** HN****O****3**** + ****c****4****Al(OH****)****3**

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

** Al: ****c****1****= ****c****4**

** N: 3****c****1****= ****c****3**

** O: 9 ****c****1**** + ****c****2**** =**** 3****c****3****+ 3****c****4**

** H: 2****c****2****= ****c****3****+ 3****c****4**

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:

**c****1**** = 1**

**c****2****=3**

**c****3****=3 **

**c****4****=1**

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

**Answer:**

** Al(N****O****3****)****3**** + ****3H****2****O**** →**** 3 HN****O****3**** + Al(OH****)****3**