### Word equation

**diammonium sulfide + nitric acid → ammonium nitrate + hydrogen sulfide**

### Input interpretation

* (NH4)2S + HNO3 → NH4NO3 + H2S*

** Diammonium sulfide nitric acid ammonium nitrate hydrogen sulfide**

### Balanced equation

Balance the chemical equation algebraically:

* (NH4)2S + HNO3 → NH4NO3 + H2S*

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

* c1(NH4)2S + c2 HNO3 → c3NH4NO3 + c4H2S*

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

*H: 8c1 + c2= 4c3 + 2c4 *

*N: 2c1+ c2 = 2c3 *

*S: c1 = c4*

*O: 3c2 = 3c3*

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=2*

* c3 = 2 c4=1*

Substitute the coefficients into the chemical reaction to obtain the balanced

equation:

**Answer:**

* (NH4)2S + HNO3 → NH4NO3 + H2S*