Which of the following expression is correct for the rate of reaction…

The correct answer is Option (3) → \(\frac{\Delta [Br^-]}{\Delta t} = \frac{5}{6}\frac{\Delta [H^+]}{\Delta t}\)

When the stoichiometric coefficients are not all 1, the rate of reaction is written by dividing the rate of change of each concentration by its coefficient, so that one value describes the whole reaction (minus sign for reactants, plus for products).

Equating the Br^– and \( \ce{H^{+}} \) terms of the rate expression:

    \( \displaystyle -\frac{1}{5}\frac{\Delta[\ce{Br-}]}{\Delta t} = -\frac{1}{6}\frac{\Delta[\ce{H+}]}{\Delta t} \)

    \( \displaystyle \frac{\Delta[\ce{Br-}]}{\Delta t} = \frac{5}{6}\frac{\Delta[\ce{H+}]}{\Delta t} \)

Shortcut: Br^– and \( \ce{H^{+}} \) are used up in the ratio 5 : 6, so Br^– disappears 5/6 as fast as \( \ce{H^{+}} \).

Note 1: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.

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. … Similarly, for the reaction”

    \( \ce{5Br^-(aq) + BrO3^-(aq) + 6H^+(aq) -> 3Br2(aq) + 3H2O(l)} \)

    \( \displaystyle \text{Rate} = -\frac{1}{5}\frac{\Delta[\ce{Br-}]}{\Delta t} = -\frac{\Delta[\ce{BrO3-}]}{\Delta t} = -\frac{1}{6}\frac{\Delta[\ce{H+}]}{\Delta t} = \frac{1}{3}\frac{\Delta[\ce{Br2}]}{\Delta t} = \frac{1}{3}\frac{\Delta[\ce{H2O}]}{\Delta t} \)

Note 2: The same/similar question has been asked in different years by NTA as per the details given below: