Question

For the gaseous reaction $\text{N}_2\text{O}_5 \rightarrow 2\text{NO}_2 + \frac{1}{2}\text{O}_2$, the rate can be expressed as follows: 

The correct relation between $K_1, K_2$ and $K_3$ is

• A. $k_1 = 2k_2 = 4k_3$
• B. $2k_1 = k_2 = 4k_3$
• C. $2k_1 = 3k_2 = 4k_3$
• D. $4k_1 = 2k_2 = k_3$

Hint:

In kinetic studies, relate the rate constants to the stoichiometric coefficients in the rate expressions.

Answer 1

The Correct Option is B

The rate of disappearance of $\text{N}_2\text{O}_5$ is $-\frac{d[\text{N}_2\text{O}_5]}{dt} = k_1[\text{N}_2\text{O}_5]$,
the formation of $\text{NO}_2$ is $\frac{d[\text{NO}_2]}{dt} = 2k_1[\text{N}_2\text{O}_5]$,
and the formation of $\text{O}_2$ is $\frac{d[\text{O}_2]}{dt} = \frac{1}{2}k_1[\text{N}_2\text{O}_5]$.
Balancing the coefficients, we find $2k_1 = k_2 = 4k_3$.