Question

Question #1d00a

Answer 1

Here's how to think about it.

Since a plot of `1/P_"A"` vs. `t` is linear, the reaction is second-order in `"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 `"A"` represents the pressure of the gas.

The slope of the plot of `1/"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 `"A"_0`, you can calculate the half-life.

If `"A"_0` = 150 ppbv, 10 % of `"A"_0` = 15.0 ppbv.

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