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:

The figure is showing ``the variation in concentration against time plot'' for a ``y'' order reaction. The value of $x + y$ is _________.

Answer 1

Correct Answer: 8

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.