For a reaction 2A_2+ B_2→ 2A_2B The reactant A will be consumed at:

The correct answer is Option (3) → double the rate at which B is consumed.

For the given reaction:

    \( \displaystyle \ce{2A2 + B2 -> 2A2B} \)

    \( \displaystyle \text{Rate} = -\frac{1}{2}\frac{d[\ce{A2}]}{dt} = -\frac{d[\ce{B2}]}{dt} = \frac{1}{2}\frac{d[\ce{A2B}]}{dt} \)

Multiplying the first two terms by 2:

    \( \displaystyle -\frac{d[\ce{A2}]}{dt} = 2\left(-\frac{d[\ce{B2}]}{dt}\right) \)

Two molecules of \( \ce{A2} \) react with every molecule of \( \ce{B2} \), so A (as \( \ce{A2} \)) is consumed at double the rate at which B is consumed.

Why the other options are incorrect

• Option (1) half the rate that B is consumed. — Incorrect. This inverts the ratio; \( \ce{A2} \) has the larger coefficient, so it is used up faster, not slower.

• Option (2) same rate at which B is consumed. — Incorrect. Equal rates would need equal coefficients, as in \( \ce{Hg + Cl2 -> HgCl2} \); here the coefficients are 2 and 1.

• Option (4) double the rate at which \(A_2B\) is formed. — Incorrect. \( \ce{A2} \) and \( \ce{A2B} \) both have the coefficient 2, so \( \ce{A2} \) is consumed at the same rate at which \( \ce{A2B} \) is formed.

NCERT (2026-27 edition):
Rate of a Chemical Reaction – “… For expressing the rate of such a reaction where stoichiometric coefficients of reactants or products are not equal to one, rate of disappearance of any of the reactants or the rate of appearance of products is divided by their respective stoichiometric coefficients. Since rate of consumption of HI is twice the rate of formation of H₂ or I₂, to make them equal, the term Δ[HI] is divided by 2.”