The rate expression for the reaction A(g)+B(g) →C(g)is rate =kCA2CB1/2. What changes in the initial concentrations of A and B will cause the rate of reaction to increase by a factor of eight?

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The rate expression for the reaction $A_{(g)} + B_{(g)}$ $\to C_{(g)}$ is rate $= {kC}_{A}^{2} C_{B}^{1 / 2}$ . What changes in the initial concentrations of A and B will cause the rate of reaction to increase by a factor of eight?

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$C_{A} \times 2; C_{B} \times 2$

$C_{A} \times 1; C_{B} \times 4$

$C_{A} \times 2; C_{B} \times 4$

answer is B.

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Detailed Solution

$A_{(g)} + B_{(g)}$ $\to C_{(g)}$

$rate = {KC}_{A}^{2} C_{B}^{1 / 2} Increase = 8 In the case of C_{A} \times 2 and C_{B} \times 2, we can say that \begin{aligned} k & = {(2 C_{A})}^{2} \times (4 CB)^{1 / 2} \\ = [2^{2} C_{A}^{2}] \times [4^{1 / 2} C_{B}^{1 / 2}] \\ k & = 4 \times 2 \times C_{A}^{2} C_{B}^{1 / 2} \\ = 8 C_{A}^{2} C_{B}^{1 / 2} \end{aligned} B : C_{A} \times 2; C_{B} \times 4$