## Word equation

Aluminum sulfate + ammonia + water → aluminum hydroxide + ammonium sulfate

## Input interpretation

** Al2(SO4)3 + 2NH3 + 6H2O → 2Al(OH)3 + (NH4)2SO4**

Aluminum sulfate, ammonia, water, aluminum hydroxide, ammonium sulfate

## Balanced equation

To balance the chemical equation algebraically, we first add stoichiometric coefficients (c) to the reactants and products:

*c1 Al2(SO4)3 + c2 NH3 + c3 H2O → c4 Al(OH)3 + c5 (NH4)2SO4*

Then, we set the number of atoms in the reactants equal to the number of atoms in the products for aluminum, oxygen, sulfur, hydrogen, and nitrogen:

** Al: **2c1 = 2c4

** O: **12c1 + 6c3 = 6c4 + 4c5

** S: **3c1 = c5

** H: **2c2 + 6c3 = 6c4 + 8c5

** N: **2c2 = 2c5

Since the coefficients are relative quantities and underdetermined, we choose a coefficient to set arbitrarily. To keep the coefficients small, we typically set one coefficient to one. For example, we can set c1 = 1 and solve the system of equations for the remaining coefficients:

c1 = 1

c2 = 6

c3 = 6

c4 = 2

c5 = 3

Substituting the coefficients into the chemical reaction yields the balanced equation:

**Al2(SO4)3 + 2NH3 + 6H2O → 2Al(OH)3 + (NH4)2SO4**