Question

The following data are for the reaction $A+B\to products$ :
Conc. A Conc. B Initial Rate
(M) (M) ($mol{L}^{-1}{s}^{-1}$)
0.1 0.1 $4.0\times {10}^{-4}$
0.2 0.2 $1.6\times {10}^{-3}$
0.5 0.1 $2.0\times {10}^{-3}$
0.5 0.5 $1.0\times {10}^{-2}$
(i) What is the order with respect to A and B for the reaction?
(ii) Calculate the rate constant.
(iii) Determine the reaction rate when the concentrations of A and B are 0.2 M and 0.35 M, respectively.

• A. (i) $rate=\left[A\right]\left[B\right];$ (ii) $k=4\times {10}^{-2}{M}^{-1}{S}^{-1}$ (iii) $rate=2.8\times {10}^{-3}M.s^{-1}$
• B. (i) $rate=\left[A{]}^2\right[B];$ (ii) $k=8\times {10}^{-4}{M}^{-1}{S}^{-1}$ (iii) $rate=2.8\times {10}^{-3}M.s^{-1}$
• C. (i) $rate=\left[A\right][B{]}^2;$ (ii) $k=8\times {10}^{-4}{M}^{-1}{S}^{-1}$ (iii) $rate=2.8\times {10}^{-3}M.s^{-1}$
• D. None of these

Answer 1

Answer: (A)

(i) $rate=\left[A\right]\left[B\right];$ (ii) $k=4\times {10}^{-2}{M}^{-1}{S}^{-1}$ (iii) $rate=2.8\times {10}^{-3}M.s^{-1}$

(i) the order with respect to A and B for the reaction $Rate=K\left[A{]}^x\right[B^{]}y$

From the first and third experiments, [B] is held constant and [A] is increased by factor 5.

$\frac{\left[0.1{]}^x\right[0.1{]}^y}{\left[0.5{]}^x\right[0.1{]}^y}=\frac{[4.0\times {10}^{-4}]}{[20\times {10}^{-4}]}$

$\Rightarrow x=1$

The result is that the rate goes up by same factor of 5. Conclusion: First order in A.

From the third and fourth experiments, [A] is held constant and [B] is increased by factor 5.

$\frac{\left[0.5{]}^x\right[0.1{]}^y}{\left[0.5{]}^x\right[0.5{]}^y}=\frac{[2.0\times {10}^{-3}]}{[10\times {10}^{-3}]}$

$\Rightarrow y=1$

The result is that the rate goes up by a factor of 5. Conclusion: First order in [B]

$rate=k\left[A\right]\left[B\right]$

(ii) The rate constant $k=\frac{Rate}{\left[A\right]\left[B\right]}$

From experiment 1, $k=\frac{4.0\times {10}^{-4}}{\left[0.1\right]\left[0.1\right]}=4\times {10}^{-2}{M}^{-1}{s}^{-1}$

(iii) The reaction rate when the concentrations of A and B are 0.2 M and 0.35 M, respectively

$Rate=k\left[A\right]\left[B\right]=4\times {10}^{-2}\times \left[0.2\right]\left[0.35\right]=2.8\times {10}^{-3}$