This question is about treating nerve agent poisoning

Nerve agents bind to and inhibit an enzyme called

acetylcholinesterase $($AChE$).$ The inhibited AChE can no longer

hydrolyse a key neurotransmitter, which leads to paralysis and

ultimately death.

One of the main treatments for nerve agent poisoning is a group

of chemicals containing the oxime functional group $(C=$NOH$).$

These reactivate the inhibited AChE by removing the bound nerve

agent. An important reactivator is the salt $2-$pyridine aldoxime

methyl chloride $($PAM$).$

$($a$)($i$)$ Calculate the molar mass of PAM.

$($ii$)$ An adult poisoned by a nerve agent requires an hourly dose of $3\mathrm{.}00$mmol of PAM

for every kilogram of body mass. Calculate the mass of PAM required for an $80kg$

person over a $24-$hour treatment period.

Nerve agents work very quickly. Kinetic studies of oximes treatments are an important area of

study. The rate of reactivation of inhibited AChE by PAM is shown below.

$($b$)($i$)$ Give the approximate order of reaction with respect to PAM at concentrations of

PAM below $0\mathrm{.}0002mold{m}^{-3}.$

$($ii$)$ Give the approximate order of reaction with respect to PAM at concentrations of

PAM above $0\mathrm{.}0008mold{m}^{-3}.$

The following two$-$step mechanism was proposed to explain these results:

AChE$-$I $+$ PAM $longrightarro{w}^{K_c}$ AChE$-I-$PAM $longrightarro{w}^{k_2}$ AChE $+I-$PAM

where AChE$-$I is the inhibited AChE, AChE$-$I$-$PAM is a complex of the inhibited AChE and

PAM, and I$-$PAM is PAM with the nerve agent attached.

$($c$)K_c$ is the equilibrium constant for the the first step. Write an expression for $K_c.$

Based on this model, the following expression can be derived for the observed first$-$order rate

constant with respect to the concentration of inhibited AChE $(\{$:$k_{\text{o}\text{b}\text{s}})$ :

$k_{\text{o}\text{b}\text{s}}=\frac{k_2[\text{P}\text{A}\text{M}]}{[PAM]+\frac{1}{K_c}}$

$k_{\frac{?}{abs}}$ is the observed rate constant

$K_c$ is the equilibrium constant for the the first step

$k_2$ is the rate constant for the second step

A graph of $\frac{1}{k_{\text{o}\text{b}\text{s}}}$ was plotted against $\frac{1}{{[}^{\text{P}\text{A}\text{M}}]}$ :

$($d$)($i$)$ Calculate $k_2.$

$($ii$)$ Calculate $K_c.$

Another important research area is developing more effective AChE reactivators for treating

nerve agent poisoning. One new group of reactivators was developed using

$($E$)-1,4-$dibromobut$-2-$ene as a starting material.

$($e$)$ Draw the structure of $(E)-1,4-$dibromobut$-2-$ene.

This group of reactivators was synthesised via a $2-$step pathway, using a series of related

reagents:

$($E$)-$

$($f$)$ How many different reactivators could be made with the above set of reagents?

The most potent reactivator $Y$ had $12$ signals in its ${?}^{13}C$ NMR and was obtained from

intermediate $x$ that had $8$ signals in its ${?}^{13}C$ NMR$.$

$($g$)$ Draw the structures of $x$ and $Y.$