# Question 1d00a

Sep 15, 2016

Here's how to think about it.

Since a plot of $\frac{1}{P} _ \text{A}$ vs. $t$ is linear, the reaction is second-order in $\text{A}$.

Therefore, you use the equations for a second-order reaction.

The integrated rate law for a second order reaction is

color(blue)(bar(ul(|color(white)(a/a) 1/"A"_t = kt + 1/"A"_0color(white)(a/a)|)))" "

where $\text{A}$ represents the pressure of the gas.

The slope of the plot of $\frac{1}{\text{A}} _ t$ vs $t$ is $k$.

For a second order reaction,

color(blue)(bar(ul(|color(white)(a/a) t_½ = 1/(k"A"_0) color(white)(a/a)|)))" "#

Since you now know the values of $k$ and ${\text{A}}_{0}$, you can calculate the half-life.

If ${\text{A}}_{0}$ = 150 ppbv, 10 % of ${\text{A}}_{0}$ = 15.0 ppbv.

Insert these values into the integrated rate law and solve for $t$.