A plot of 1/[BrO-] vs time is linear for the reaction:
3 BrO-(aq) → BrO3-(aq) + 2 Br-(aq)
What is the order of the reaction with respect to the hypobromite ion, BrO-?
A) 0
B) 1
C) 2
D) 3
The correct answer and explanation is :
The correct answer is A) 0.
Explanation:
To determine the order of the reaction with respect to the hypobromite ion (BrO⁻), we need to analyze the given information and the relationship between the concentration of the reactant and the rate of the reaction. In this case, the plot of $\frac{1}{[BrO^-]}$ versus time is linear, which is a key clue in understanding the order of the reaction.
When studying the rate of a reaction, the relationship between the concentration of a reactant and time can be indicative of the reaction order. The rate law for a reaction can generally be expressed as:
$$
\text{Rate} = k[BrO^-]^n
$$
where:
- $k$ is the rate constant,
- $[BrO^-]$ is the concentration of the hypobromite ion,
- $n$ is the order of the reaction with respect to BrO⁻.
The integrated rate laws for different orders of reactions are as follows:
- Zero-order reaction ($n = 0$): The concentration of the reactant decreases linearly with time. The integrated form is: $$
[BrO^-] = [BrO^-]_0 – kt
$$ A plot of $[BrO^-]$ versus time will yield a straight line. If $\frac{1}{[BrO^-]}$ is plotted versus time, the plot will also be linear, as seen in this case. - First-order reaction ($n = 1$): The concentration of the reactant decreases exponentially with time. The integrated form is: $$
\ln[BrO^-] = \ln[BrO^-]_0 – kt
$$ A plot of $\ln[BrO^-]$ versus time gives a straight line. - Second-order reaction ($n = 2$): The concentration of the reactant decreases with the square of time. The integrated form is: $$
\frac{1}{[BrO^-]} = \frac{1}{[BrO^-]_0} + kt
$$ A plot of $\frac{1}{[BrO^-]}$ versus time for a second-order reaction results in a linear graph.
Since the plot of $\frac{1}{[BrO^-]}$ versus time is linear in this case, it suggests that the reaction is first-order with respect to BrO⁻, not second or zero order. Therefore, the correct answer is A) 0.