Question

Given below are two statements:
Statement I : The rate law for the reaction $\text{A + B} \rightarrow \text{C}$ is rate$({r}) = k[{A}]^2[{B}]$. When the concentration of both A and B is doubled, the reaction rate is increased x'' times. **Statement II** : ![Graph](https://images.collegedunia.com/public/qa/images/content/2024_11_20/image_21d322ba1732091224935.png) The figure is showing the variation in concentration against time plot'' for a ``y'' order reaction. The value of $x + y$ is _________.

Answer 1

Step 1: Analyze Statement I The rate law is:

$r = k[A]^2[B].$

When the concentrations of $A$ and $B$ are doubled:

$r' = k[2A]^2[2B] = k(2^2)[A]^2(2)[B].$

$r' = 8k[A]^2[B].$

Thus, $r' = 8r$, so $x = 8$.

Step 2: Analyze Statement II From the figure, the concentration decreases linearly with time. A linear decrease in concentration indicates a zero-order reaction ($y = 0$).

Final Step: Calculate $x + y$

$x + y = 8 + 0 = 8.$

Final Answer: 8.