For the reaction , the rates are defined as , , and . Which of the following is the correct relation — Chemical Kinetics Chemistry Question
Question
For the reaction $2N_2O_5 \rightarrow 4NO_2 + O_2$, the rates are defined as $-d[N_2O_5]/dt = k_1[N_2O_5]$, $d[NO_2]/dt = k_2[N_2O_5]$, and $d[O_2]/dt = k_3[N_2O_5]$. Which of the following is the correct relation?
Answer: B
💡 Solution & Explanation
The unified rate is $-\frac{1}{2}\frac{d[N_2O_5]}{dt} = \frac{1}{4}\frac{d[NO_2]}{dt} = \frac{d[O_2]}{dt}$. Substituting the rate expressions gives $\frac{k_1}{2} = \frac{k_2}{4} = k_3$. Multiplying by 4 gives $2k_1 = k_2 = 4k_3$.
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