Question

clicker question
if increasing the concentration of reactant a by a factor of 2.5 multiplies the rate by a factor of 6.25, the reaction is ______ order in a.
a. zeroth
b. first
c. second
d. third
e. we don’t have enough information to determine the order.
20

Explanation:

Step1: Recall rate - law formula

The rate - law for a reaction with respect to reactant A is $r = k[A]^n$, where $r$ is the rate of the reaction, $k$ is the rate constant, $[A]$ is the concentration of reactant A, and $n$ is the order of the reaction with respect to A.
Let the initial concentration of A be $[A]_1$ and the initial rate be $r_1=k[A]_1^n$. When the concentration of A is increased to $[A]_2 = 2.5[A]_1$, the new rate $r_2=k[A]_2^n=k(2.5[A]_1)^n$.

Step2: Use the given rate - change information

We know that $\frac{r_2}{r_1}=6.25$. Substitute $r_1 = k[A]_1^n$ and $r_2=k(2.5[A]_1)^n$ into $\frac{r_2}{r_1}$:

$$
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Step3: Solve for $n$

Since $2.5^2=6.25$, then $n = 2$.

Answer:

C. Second