Chapter 20, Problem 80IAE

The half-life for the first-order decomposition of nitramide, ${\text{NH}}_{\text{2}}{\text{NO}}_{\text{2}}\left(\text{aq}\right)\to {\text{N}}_{\text{2}}\text{O}\left(\text{g}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{l}\right)$ , is 123 min at $15°\text{C}$ , If 165 mL of a 0.105 M ${\text{NH}}_{\text{2}}{\text{NO}}_{\text{2}}$ solution is allowed to decompose, how long must the reaction proceed to yield 50.0 mL of ${\text{N}}_2\text{O}\left(g\right)$ collected over water at $15°\text{C}$ and a baometric pressure of 756 mmHg? (The vapor pressure of water at $15°\text{C}$ is 12.8 mmHg.)