Answer to Question #266725 in Physical Chemistry for Jugo

Question

What would the rate constant of the reaction be given the following set of

experiments?

A + B → C + D

Experiment [A] (M) [B] (M) Initial Rate (M/s)

1 0.040 0.040 2.2x10-4

2 0.040 0.080 4.4x10-4

3 0.080 0.080 8.8 x 10

-4

Answer 1

Interpreting the values in the tables and aligning them

$\begin{matrix} Exp&A(m)&B(m) & initial\>rate\\ 1&0.040&0.040&2.2×10^{-4}\\ 2&0.040&0.080&4.4×10^{-4}\\ 3&0.080&0.080&8.8×10^{-4} \end{matrix}$

Working

$\frac{Rate\,2}{Rate\>1}=\frac{4.4×10^{-4}}{2.2×10^{-4}}=\frac{k(0.04)^x(0.08)^y}{k(0.04)^x(0.04)^y}$

$2=2^y\quad\implies y=1$

$\frac{Rate\>3}{Rate\>2}=\frac{8.8×10^{-4}}{4.4×10^{-4}}=\frac{k(0.080)^x(0.080)^y}{k(0.040)^x(0.080)^y}$

$2=2^x\quad \implies x=1$

Substituting data for trial 1,

$2.2×10^{-4}=k(0.04)^1(0.04)^1$

$K=0.1375\>M^{-1}s^{-1}$