# An elementary reaction, $2 A + C \rightarrow D$ , is second order in $A$ and first order in $C$. The rate of this reaction is $2.5 \times 10 ^{-1}1\; M/s$ when the concentrations of $A$ and $C$ are all $3.00\; mM$. What is the rate constant for the reaction?

$\begin{array}{1 1} 0.0926 \times 10^8 \; M^{-2}s^{-1} \\ 2.5 \times 10^8 \; M^{-2}s^{-1} \\ 0.2779 \times 10^8 \; M^{-2}s^{-1} \\ 0.8333 \times 10^8 \; M^{-2}s^{-1}\end{array}$

Answer: $0.0926 \times 10^8 \; M^{-2}s^{-1}$
The rate law for the reaction is rate $= k [A]^2[C]$
Given $[A] = [C] = 3.00\;mM$, and rate $= 2.5 \times 10 ^{-1}1\; M/s$, $k = \large\frac{2.5 \times 10^{-1}} {(3.0 \times 10^3)^2 \times 3.0 \times 10^3}$
$\Rightarrow k = 0.0926 \times 10^8 \; M^{-2}s^{-1}$
answered Jul 24, 2014