Question

Consider a gaseous reaction $A\left(g\right)+B\left(g\right)\to 3C\left(g\right)$, the rate of the reaction is given by $r=k\left[A\right]{\left[B\right]}^2$. If the volume of the reaction vessel containing these gases is suddenly reduced to $\frac{1}{4}$th of the initial volume, then the rate of the reaction relative to the original rate would be:

• A. 64 times
• B. 16 times
• C. $\frac{64}{3}$ times
• D. $\frac{64}{27}$ times

Answer 1

The correct option is A 64 times

On reducing the volume to ${\frac{1}{4}}^{th}$, the concentration quadruples.
So, $\frac{r\left(\text{new}\right)}{r}=\frac{k\left(4\right[A\left]\right){\left(4\left[B\right]\right)}^2}{k\left[A\right]{\left[B\right]}^2}$
$=\frac{64k\left[A\right][B{]}^2}{k\left[A\right][B{]}^2}=64$