## Q. 14.4.3

The gas phase decomposition of dinitrogen pentaoxide at 335 K is first order in N$_{2}$O$_{5}$.
$N_{2}O_{5}(g) S → NO_{2}(g) + ½ O_{2}$(g)
During one experiment it was found that the N$_{2}$O$_{5}$ concentration dropped from 0.249 M at the beginning of the experiment to 0.0496 M in 230 seconds. What is the value of the rate constant for the reaction at this temperature?

## Verified Solution

You are asked to determine the rate constant for a reaction.
You are given the balanced equation for the reaction, the order of the reaction with respect to the reactant, the initial concentration of the reactant, and the concentration of the reactant after a known amount of time has passed.

Use the first order integrated rate equation.

$ln\frac{\left[\text{N}_{2}\text{O}_{5}\right]_{t} }{\left[\text{N}_{2}\text{O}_{5}\right]_{o}}$ = -kt                $\left[\text{N}_{2}\text{O}_{5}\right]_{t}$ = 0.0496 M

$\left[\text{N}_{2}\text{O}_{5}\right]_{o}$ = 0.249 M              t = 230 seconds

$ln\left(\frac{0.0496\text{ M}}{0.249\text{ M}} \right)$ = -k(230 s)

-1.61=-k(230 s)

k = 7.02 × 10$^{-3}$ s$^{-1}$