The rate equation for the reaction $$2A + B \rightarrow C$$ is found to be: rate $$= k[A][B]$$. The correct statement in relation to this reaction is that the

1. Reaction and Rate Law Profile:

The chemical equation and its experimentally determined rate law are given as:

$$\text{2A} + \text{B} \rightarrow \text{C}$$

$$\text{Rate} = k[\text{A}][\text{B}]$$

From the exponents in the rate law equation, the reaction is of first order with respect to reactant $$\text{A}$$, first order with respect to reactant $$\text{B}$$, and has an overall reaction order of $$1 + 1 = 2$$ (second order).

Option-by-Option Analysis:

• Option A: The unit of $$k$$ must be $$\text{s}^{-1}$$

  The unit for a second-order rate constant ($$k$$) is given by the general formula $$\text{M}^{1-n}\text{s}^{-1}$$ (where $$n$$ is the overall order):

  $$\text{Unit of } k = \text{M}^{1-2}\text{s}^{-1} = \text{M}^{-1}\text{s}^{-1} = \text{L mol}^{-1}\text{s}^{-1}$$

  The unit $$\text{s}^{-1}$$ is strictly for a first-order reaction.

  Result: INCORRECT




• Option B: The value of $$k$$ is independent of the initial concentration of $$\text{A}$$ and $$\text{B}$$

  The rate constant ($$k$$) is a fundamental proportionality constant characteristic of a specific chemical reaction. Its value depends strictly on external parameters such as temperature and the presence of a catalyst. It does not change with varying initial concentrations of the reactants.

  Result: CORRECT




• Option C: The rate of formation of $$\text{C}$$ is twice the rate of disappearance of $$\text{A}$$

  According to the stoichiometry of the balanced chemical equation, the relative rates are related as follows:

  $$\text{Rate of reaction} = -\frac{1}{2}\frac{d[\text{A}]}{dt} = +\frac{d[\text{C}]}{dt}$$

  $$\implies \frac{d[\text{C}]}{dt} = -\frac{1}{2}\frac{d[\text{A}]}{dt}$$

  This means the rate of formation of $$\text{C}$$ is actually half the rate of disappearance of $$\text{A}$$.

  Result: INCORRECT




• Option D: $$t_{1/2}$$ is a constant

  For a second-order reaction, the half-life ($$t_{1/2}$$) depends inversely on the initial concentration of the reactant ($$t_{1/2} = \frac{1}{k[A]_0}$$). It is only a constant for first-order reactions.

  Result: INCORRECT

Conclusion:

The value of the rate constant $$k$$ is a temperature-dependent parameter and remains completely unaffected by changes in the starting concentrations of the reactants.

Answer: Option B — values of $$k$$ is independent of the initial concentration of $$\text{A}$$ and $$\text{B}$$