If one molecule of the product C is formed from one molecule of the reactant A and one molecule of the reactant B, and the initial concentrations of A and B have a common value [A]=[B]= $a$ moles/L, then [C]= $a^2kt/(akt+1)$, where $k$ is a constant.

(a) Find the rate of reaction at time $t$.
(b) If $x=$[C], what is $dx/dt$ in terms of $a,k,$ and $x$?
(c) What happens to the concentration as $t \to \infty$?
(d) What happens to the rate of reaction as $t \to \infty$?
(What do the results mean in (c) and (d) in practical terms?)

(a)
(b)
(c)
(d)