Chapter 11, Problem 9STP

Interpretation Introduction

Interpretation:

The number of moles of nitrogen gas released needs to be determined when 18.0 moles of dinitrogen tetroxide is consumed in the reaction.

Concept introduction:

The ratio of mass of substance to its molar mass is said to be number of moles of that substance.

The ratio of amount of any two compounds involved in a chemical reaction in terms of mole is said to be mole ratio, and used as a conversion factor between reactants and products.

Answer to Problem 9STP

The number of moles of nitrogen gas release is $\text{27}{\text{.0 mol of N}}_{\text{2}}\left(\text{g}\right)$ when 18.0 moles of dinitrogen tetroxide is consumed in the reaction.

Explanation of Solution

The complete balanced equation is:

${\left({\text{CH}}_{\text{3}}\right)}_{\text{2}}{\text{N}}_{\text{2}}{\text{H}}_{\text{2}}\left(\text{l}\right){\text{ + 2N}}_2{\text{O}}_4\left(\text{l}\right)\to 3{\text{N}}_{\text{2}}\left(\text{g}\right){\text{ + 4H}}_{\text{2}}\text{O}\left(\text{g}\right)+{\text{ 2CO}}_{\text{2}}\text{(g)}$

From the balanced chemical reaction, the mole ratio of dinitrogen tetroxide, ${\text{N}}_{\text{2}}{\text{O}}_{\text{4}}\text{(l)}$ and nitrogen gas, ${\text{N}}_{\text{2}}\left(\text{g}\right)$ is 2:3 that means 2 moles of ${\text{N}}_{\text{2}}{\text{O}}_{\text{4}}\text{(l)}$ produces 3 moles of ${\text{N}}_{\text{2}}\left(\text{g}\right)$. So, the mole ratio that enables to calculate the number of moles of ${\text{N}}_{\text{2}}\left(\text{g}\right)$ released from 18.0 moles of ${\text{N}}_{\text{2}}{\text{O}}_{\text{4}}\text{(l)}$ is:

$\text{18}{\text{.0 mol of N}}_{\text{2}}{\text{O}}_{\text{4}}\text{(l)×}\frac{{\text{3 mol of N}}_{\text{2}}\left(\text{g}\right)}{{\text{2 mol of N}}_{\text{2}}{\text{O}}_{\text{4}}\text{(l)}}\text{ = 27}{\text{.0 mol of N}}_{\text{2}}\left(\text{g}\right)$

Hence, the number of moles of nitrogen gas release is $\text{27}{\text{.0 mol of N}}_{\text{2}}\left(\text{g}\right)$ when 18.0 moles of dinitrogen tetroxide is consumed in the reaction.