In remote regions, one major source of ${?}^{*}OH$ is the photolysis of ozone, which first forms the

high$-$energy reactive oxygen atom, $O{(}^{1}D)$ :

$O_3+hvO{(}^{1}D)+O_2$

Tropospheric $O{(}^{1}D),$ which is at steady state because of its short lifetime, has two main fates:

reaction with gas$-$phase water $(R3)$ or deactivation by collision with a molecule other than water

$($R$4)$ to form the less reactive $O$ atom, $O{(}^{3}P),$ which reforms ozone $($R$5).$ These elementary

reactions are:

$O{(}^{1}D)+H_{2}O{2}^{*}OH$

$O{(}^{1}D)+MO{(}^{3}P)+M$

$O{(}^{3}P)+O_2{O}_3$

$k_3=2\mathrm{.}0{10}^{-10}c{m}^{3}ml{c}^{-1}{s}^{-1}$

$k_4=3\mathrm{.}0{10}^{-10}c{m}^{3}ml{c}^{-1}{s}^{-1}$

Assume that $M$ in $R4$ can be any molecule except for $H_{2}O.$ Answer the following questions

assuming an atmospheric pressure of $1$atm,$T=25C,$ an ozone mixing ratio of $40ppbv,$ and a

relative humidity of $100\%,$ unless noted otherwise.

a$.$ If the $O{(}^{1}D)$ concentration is $4\mathrm{.}0{10}^{-3}mlcc{m}^{-3},$ what is the rate of ${?}^{*}OH$ formation from $R3?$

b$.$ The activation energy for $R3$ is $-0\mathrm{.}74kJmo{l}^{-1}($Dunlea and Ravishankara, $2004).$ What is

the value of the rate constant $k_3$ at $-20C?($Note $-$ answer the rest of the questions using the

standard temperature of $25C.)$

c$.$ What is the lifetime of $O{(}^{1}D)$ with respect to $R3?$

d$.$ What is the overall lifetime of $O{(}^{1}D)$ in this system $($i$.$e$.,$ considering both R$3$ and R$4)?$

e$.$ If $R3$ and $R4$ are the only sinks of $O{(}^{1}D),$ what fraction of this species goes down each

pathway?

f$.$ Make a plot that shows the fraction of $O{(}^{1}D)$ that goes down path $R3$ as a function of $RH,$

from $0$ to $100\%.$ Use a spreadsheet or program for this question. Include a copy of your

spreadsheet $($neat and concise$)$ at the end of your assignment. Your graph should have a title

and axis labels with units.