Question

Consider the reaction $X+Y\to$ products. If the initial concentration of $X$ is increased to four times its original value, keeping the concentration of $Y$ constant, the rate of reaction increases fourfold. When the concentration of both $X$ and $Y$ become four times their original values, the rate of reaction becomes sixteen times its original value. The observed rate law is:

• A. $k\left[X{]}^2\right[Y{]}^2$
• B. $k\left[X{]}^1\right[Y{]}^2$
• C. $k\left[X{]}^1\right[Y{]}^1$
• D. $k\left[X{]}^2\right[Y{]}^1$

Answer 1

Answer: (C)

$k\left[X{]}^1\right[Y{]}^1$

$X+Y\to products$
$⟹Rate=k\left[A{]}^x\right[B{]}^y$
$⟹4\times Rate=k[4\times A{]}^x[0\times B{]}^y$

$⟹Rate=k\left[A{]}^x\right[B{]}^y$
$⟹16\times Rate=k[4\times A{]}^x[4\times B{]}^y$

By solving we get value of $x$ and $y=1$.