Question

Tripling the concentration of a reactant increases the rate of a reaction nine-fold. With this knowledge, answer the following questions:

1. What is the order of the reaction with respect to that reactant?
2. Increasing the concentration of a reactant by a factor of four increases the rate of a reaction four-fold. What is the order of the reaction with respect to that reactant?

Short answer

1. The order of the reaction with respect to that reactant is 2.
2. Increasing the concentration of a reactant by a factor of four increases the rate of a reaction 4-fold. The order of the reaction is 1.

Step-by-step solution

Rate of reaction

\(\begin{aligned}{}{\bf{Rate = }}\,{\bf{k(Reactant}}{{\bf{)}}^{\bf{n}}}\\9{\bf{(Rate) = }}\,{\bf{k(3(reactant)}}{{\bf{)}}^2}\end{aligned}\)

The concentration of the reactant tripled and the rate increased 9-fold, we can conclude that the order with respect to the reactant is 2, since \({3^2}\) = 9.

Rate of reaction

\(\begin{aligned}{}{\bf{Rate = }}\,{\bf{k(Reactant}}{{\bf{)}}^{\bf{n}}}\\4{\bf{(Rate) = }}\,{\bf{k(}}4{\bf{(reactant)}}{{\bf{)}}^1}\end{aligned}\)

The concentration of the reactant and the rate both quadrupled, we can conclude that n=1, and the order with respect to this reactant is 1.