Chapter 12, Problem 63A

Interpretation Introduction

Interpretation: To calculate the total number of liters of gas.

Concept Introduction: A mole is $6.02\times {10}^{23}$ atoms/molecules. The SI unit for the amount of substance is a mole and it is represented by “mol”.

The coefficients are the numbers that are written in front of the chemical formula/symbol in order to balance a chemical reaction.

Answer to Problem 63A

The total number of liters of nitrogen gas is $63.80\text{ L}$ .

Explanation of Solution

The given chemical reaction is depicted as follows:

  ${\text{2NH}}_4{\text{NO}}_3\left(s\right)\to 2{\text{ N}}_2\left(g\right)+4{\text{ H}}_2\text{O}\left(l\right)+{\text{O}}_2\left(g\right)$

The decomposition of two moles of ammonium nitrate it yields two moles of nitrogen, four moles of water, and one mole of oxygen.

The amount of ammonium nitrate is $228\text{ g }$ . At STP, 1 mol of the gas has molar volume 22.4 L.

Calculation for the total number of liters of nitrogen gas is as follows:

  $\text{228 }\cancel{{\text{g NH}}_4{\text{NO}}_{\text{3}}}\times \frac{1\cancel{{\text{mol NH}}_4{\text{NO}}_{\text{3}}}}{\text{80}\text{.04 }\cancel{{\text{g NH}}_4{\text{NO}}_{\text{3}}}}\times \frac{\text{ 2}\cancel{{\text{mol N}}_2}}{2\cancel{{\text{mol NH}}_4{\text{NO}}_{\text{3}}}}\times \frac{22.4{\text{ L N}}_2}{1\cancel{{\text{mol N}}_2}}=63.80{\text{ L N}}_2$

Conclusion

Thus, the total number of liters of nitrogen gas is $63.80\text{ L}$ .