Question

In a reaction, A + B $\rightarrow$ Product, rate is doubled when the concentration of B is doubled and rate increases by a factor of 8 when the concentrations of both the reactants (A and B) are doubled. Rate law for the reaction can be written as

• A. rate = K[A]$[B]^2$
• B. rate = K$[A]^2 [B]^2$
• C. rate = $k[A][B]$
• D. rate = k$[A]^2$[B]

Answer 1

The Correct Option is D

To determine the rate law for the given reaction A + B \rightarrow \text{Product}, we need to analyze how the rate changes with respect to changes in concentrations of the reactants, A and B.

Given:

1. The rate is doubled when the concentration of B is doubled.
2. The rate increases by a factor of 8 when the concentrations of both A and B are doubled.

We start with the general form of the rate law:

\text{rate} = k[A]^m[B]^n

We analyze the given conditions to determine the values of m and n:

1. Doubling B: The rate doubles when B is doubled. Mathematically, this can be represented as:

If [B] is doubled, the rate becomes k[A]^m(2[B])^n = 2 \times k[A]^m[B]^n

When we simplify, we get:

(2^n) = 2 \Rightarrow n = 1

2. Doubling both A and B: The rate increases by a factor of 8. This gives us:

If both [A] and [B] are doubled, then:

k(2[A])^m(2[B])^n = 8 \times k[A]^m[B]^n

Substitute n = 1 into the equation:

(2^m)(2^1) = 8 \Rightarrow 2^m \times 2 = 8 \Rightarrow 2^m = 4 \Rightarrow m = 2

Thus, the rate law becomes:

\text{rate} = k[A]^2[B]^1

Now, comparing with the given options, the correct rate law is:

rate = k$[A]^2$[B]

Conclusion: By analyzing the effect of concentration changes on the reaction rate, we conclude that the correct rate law is \text{rate} = k[A]^2[B], which matches the given correct answer option.