### Word equation

* ammonia + water → ammonium hydroxide*

### Input interpretation

* NH3 + H2O → NH4OH*

** Ammonia water ammonium hydroxide**

### Balanced equation

Balance the chemical equation algebraically:

* NH3 + H2O → NH4OH*

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

* c1NH3 + c2H2O → c3 NH4OH*

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

*H: 3c1+ 2c2 = 5c3*

*N: c1 = c3*

*O: c2 = c3*

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=1*

Substitute the coefficients into the chemical reaction to obtain the balanced

equation:

**Answer:**

* NH3 + H2O → NH4OH*