The reaction 2A + B₂ → 2AB is an elementary reaction.
For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of 3, the rate of the reaction increases by a factor of ____________. (Round off to the Nearest Integer).

Solution

Chemistry ma’am · 3 steps

Elementary means the stoichiometry is the rate law: squeeze to a third and both concentrations triple.

1. Write the rate law. For an elementary reaction the exponents are the stoichiometric coefficients. So for 2A + B₂ → 2AB the rate is r = k[A]²[B₂], an overall order of 3.
2. Shrink the volume. The amounts of A and B₂ stay the same, and concentration is moles divided by volume. Cutting the volume to one third makes each concentration 3 times larger.

   r₂/r₁ = k(3[A])²(3[B₂])/k[A]²[B₂] = 3² × 3 = 27

3. So. The rate increases by a factor of 27.

The common slip: 9. Cubing the factor is easy to miss: using order 1 gives 3, and using only the [A]² term gives 9, not 27.

The idea to keep. When the volume changes by a factor, every concentration changes by that factor, so the rate changes by the factor raised to the overall order.

Answer from the NTA final answer key. Solution by PrepWiser.