A reaction between reactants A and B follows the rate law:
Rate = k [A]2[B]1
Arrange, under the given conditions, the rate of the reaction in increasing order :
A. Concentration of only reactant A is doubled .
B. Concentration of only reactant B is doubled.
C. Concentration of reactant A is tripled and that of reactant B is halved.
D. Concentration of reactant A is halved and that of reactant B is doubled.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → D, B, A, C
The rate law shows how strongly the rate depends on each reactant. For Rate = k[A]x[B]y, suppose [A] is multiplied by a factor a and [B] by a factor b. The rate is then multiplied by:
\( \displaystyle \frac{\text{New rate}}{\text{Old rate}}=a^{x}\times b^{y} \)
Here x = 2 and y = 1, so the rate changes by a factor of a2 × b.
Applying this to each change:
\( \displaystyle \text{(A)}\ [A]\ \text{doubled}:\ 2^{2}\times1=4 \)
\( \displaystyle \text{(B)}\ [B]\ \text{doubled}:\ 1^{2}\times2=2 \)
\( \displaystyle \text{(C)}\ [A]\ \text{tripled},\ [B]\ \text{halved}:\ 3^{2}\times\frac{1}{2}=\frac{9}{2}=4.5 \)
\( \displaystyle \text{(D)}\ [A]\ \text{halved},\ [B]\ \text{doubled}:\ \left(\frac{1}{2}\right)^{2}\times2=\frac{2}{4}=0.5 \)
Shortcut: (D) is the only change that lowers the rate, and (C) gives the largest increase. Only Option (1) starts with (D) and ends with (C).