$3.$ Nitric oxide, NO$($g$)$ reacts with chlorine gas, Cl$2($g$),$ in the reaction $2$NO$($g$)+$ Cl$2($g$)2$NOCl$($g$)$

Initial rates of reaction are determined for various combinations of initial concentrations of reactants and recorded below;

Trial

Initial $[$NO$]$

$($mol$/$L$)$

Initial $[$Cl$2]$

$($mol$/$L$)$

Rate of production of NOCl $($mol$/$L$.$s$)$

$1$

$0\mathrm{.}10$

$0\mathrm{.}10$

$1\mathrm{.}8$ x $10-2$

$2$

$0\mathrm{.}10$

$0\mathrm{.}20$

$3\mathrm{.}6$ x $10-2$

$3$

$0\mathrm{.}20$

$0\mathrm{.}20$

$1\mathrm{.}43$ x $10-1$

a$)$ What is the rate law equation for the reaction?

b$)$ What is the rate$-$determining step?

c$)$ Calculate a value for the rate constant, including units.

d$)$ Calculate the expected rate of reaction if the initial concentrations of NO and Cl$2$ gases were $0\mathrm{.}30$ and $0\mathrm{.}40$ mol$/$L$,$ respectively.