On July $14,1991,$ a train derailment resulted in the spill of

approximately $13,000$ gal of the soil fumigant sodium metham

$($Vapam$)$ to the Sacramento River, $70km$ upstream from Shasta Lake,

California's largest reservoir. The spill killed almost all aquatic life in

the river.

In an aqueous environment, metham $($which is highly soluble$)$

hydrolyzes to form methyl isothiocyanate and $H_{2}S$ as the major

products:

Rate constants for this hydrolysis reaction are $k_a$~~$\frac{300}{Msec}$ and

$k_n^{\text{'}}$~~$1\frac{{10}^{-8}}{sec}.$ Metham also undergoes indirect photolysis to form

methyl isothiocyanate, with a pseudo$-$first$-$order rate constant of

approximately $1\frac{{10}^{-4}}{sec}.$The California Regional Water Quality Control Board urgently

needs your advice, both as to the maximum concentrations of metham

that will be encountered at different points along the Sacramento

River, and as to the total load that will enter Shasta Lake.

a$.$ Calculate the maximum concentration $($in moles per liter$)$ of $N{a}^{+}$

$($which behaves as a conservative tracer$)$ and metham that will be

encountered, both at the town of Dunsmuir downstream

from the spill$)$ and at the point where the Sacramento River reaches

Shasta Lake $(70$ km downstream from the spill$).$

b$.$ How important are the processes of longitudinal dispersion,

hydrolysis, and indirect photolysis in attenuating the peak

concentration of metham between Dunsmuir and Shasta Lake?

Quantify your answer.

c$.$ What are the half$-$lives for hydrolysis and indirect photolysis?

d$.$ How important are these two processes collectively in attenuating

the total load of metham between Dunsmuir and Shasta Lake?

e$.$ Data are currently not available as to the Henry's law constant for

metham. Would you recommend measuring this parameter, or do

you feel that it is reasonable to neglect air$-$water exchange of

metham? Indicate your logic.

f$.$ Estimate the total mass of methyl isothiocyanate $($in moles$)$ that will

be transported into Shasta Lake, ignoring losses from any process

$($such as air$-$water exchange$)$ that might remove this compound

during its transport in the Sacramento River.

The upper reach of the Sacramento River is a small tributary to

Shasta Lake. At the time of the spill, the river had a discharge of

$75,000$ liter $\frac{?}{\text{m}\text{i}\text{n}},$ a mean depth of $0\mathrm{.}3m,$ a pH of $7\mathrm{.}8,$ a mean width

of $1\mathrm{.}2m,$ and a dispersion coefficient of ~~$1\mathrm{.}6{10}^2\frac{m^2}{m}in.$ The

commercial formulation of sodium metham contained $0\mathrm{.}33g$ of

sodium salt of metham per milliliter. The molecular weight of

sodium salt of metham is $129\frac{g}{m}ol.$