Question

In a reaction with two reactants, two trials are performed. In both trials, the concentration of reactant $A$ is held constant.
If the concentration of reactant $B$ is doubled and the rate of the reaction increases by a factor of eight, what can be concluded from the reaction?

• A. The order of reactant $B$ in the overall rate law is $3$
• B. The order of reactant $A$ in the overall rate law is $1$
• C. The order of reactant $B$ in the overall rate law is $2$
• D. The order of reactant $B$ in the overall rate law is $1$
• E. The order of reactant $A$ in the overall rate law is $3$

Answer 1

The correct option is A The order of reactant $B$ in the overall rate law is $3$

Let rate law be, $R=k{\left[A\right]}^x[B{]}^y⟶\left(i\right)$
$\therefore 8R=k{\left[A\right]}^x[2B{]}^y⟶\left(ii\right)$

Dividing (i) & (ii), $\frac{1}{8}={\left(\frac{1}{2}\right)}^y$
$\therefore y=3$

Rate$=k{\left[A\right]}^x[B{]}^3$

Therefore, the order of reactant $B$ in the overall rate law is 3.

Therefore, option $\left(A\right)$ is the correct answer.