# For the elementary reaction "2 A <-> B", the forward and backward rate constants are k1 and k2 respectively. Then the rate of disappearance of A is equal to: (A) k1[A]^2 - k2[B] (B) 2k1[A]^2 + 2k2[B] (C) 2k1[A]^2 - 2k2[B] (D) [2k1 - k2][A]

## Question

For the elementary reaction $2 \mathrm{~A} \rightleftharpoons \mathrm{B}$, the forward and backward rate constants are $k_1$ and $k_2$ respectively. Then the rate of disappearance of A is equal to:

(A) $k_1[\mathrm{~A}]^{2}-k_2[B]$

(B) $2k_1[A]^{2}+2k_2[B]$

(C) $2k_1[A]^{2}-2k_2[B]$

(D) $\left[2k_1-k_2\right][A]$

✨ Free AI Tools for You

Powered by Chatterbot AI

## Answer

The correct answer is **Option C**:
$$
2k_1[A]^2 - 2k_2[B]
$$

### Explanation:

The rate of an elementary reaction $$2A \rightleftharpoons B$$ with forward and reverse rate constants $ k_1 $ and $ k_2 $ respectively, follows the formula for the rate of change of concentration of reactants and products based on their stoichiometric coefficients.

For reactant $ A $, which has a stoichiometric coefficient of 2 in the balanced chemical equation, the **rate of disappearance** can be given by:

$$ -\frac{1}{2} \frac{d[A]}{dt} = k_1[A]^2 - k_2[B] $$

Multiplying both sides of the equation by 2 to get the actual rate of disappearance of $ A $ gives:

$$ -\frac{d[A]}{dt} = 2k_1[A]^2 - 2k_2[B] $$

This is expressed as the reaction proceeds, thus reflecting the concentration changes in the reagents.

Therefore, the rate of disappearance of $ A $ is:

$$ 2k_1[A]^2 - 2k_2[B] $$

Thus, the correct choice is **(C)**.

India's 1^{st} AI Doubt Solver for CBSE, JEE, and NEET

and then it's just ₹212 a month