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 \( 2k_1 = k_2 = 4k_3 \).