# For the reaction $A+B \rightarrow C+D$, calculate the value of k for this reaction based on the following data collected in three different experiments:

$\begin{array} {cccc} \text{Experiment} & [A]\; \text{in M} & [B]\; \text{in M} & \text{Initial Rate in Ms}^{-1}\\ 1 & 0.5 & 1.5 & 4.20 \times 10^{-3}\\ 2 & 1.5 & 1.5 & 1.26 \times 10^{-2}\\ 3 & 3.0 & 3.0 & 5.04\times 10^{-2}\\ \end{array}$

$\begin{array}{1 1} 5.6 \times 10^{-3}M^{-1} s^{-1} \\ 5.6 \times 10^{-2}M^{-2} s^{-1} \\ 5.6 \times 10^{-3}M^{-2} s^{-1} \\ 5.6 \times 10^{-2}M^{-1} s^{-1} \end{array}$

Answer: $5.6 \times 10^{-3} M^{-1}s^{-1}$
Given $\begin{array} {cccc} \text{Experiment} & [A]\; \text{in M} & [B]\; \text{in M} & \text{Initial Rate in Ms}^{-1}\\ 1 & 0.5 & 1.5 & 4.20 \times 10^{-3}\\ 2 & 1.5 & 1.5 & 1.26 \times 10^{-2}\\ 3 & 3.0 & 3.0 & 5.04\times 10^{-2}\\ \end{array}$
The rate of the reaction $= k [A]^ x [B]^ y$
Comparing Experiments 1 and 2, With [B] constant, as [A] is tripled, rate is tripled $\rightarrow$ the rate is first order with respect to [A] $\rightarrow$ x = 1
Compare experiments 2 and 3: With [A] and [B] both doubling rate increases by ~4 times $\rightarrow$ Factoring the effect of [A], rate is first order with respect to [B] $\rightarrow$ y = 1
$\Rightarrow$ Rate $= k[A][B]$
To calculate $k$, Insert data from any experiment into the rate equation:
$\Rightarrow 5.04 \times 10^{-2} = k \times 3 \times 3 \rightarrow k = 0.0056 = 5.6 \times 10^{-3} M^{-1}s^{-1}$
edited Jul 25, 2014