For the reaction , the rates of reaction are defined as , , and . What is the correct mathematical r — Chemical Kinetics Chemistry Question
Question
For the reaction $2N_2O_5 \rightarrow 4NO_2 + O_2$, the rates of reaction are defined as $-\frac{d[N_2O_5]}{dt} = k_1[N_2O_5]$, $\frac{d[NO_2]}{dt} = k_2[N_2O_5]$, and $\frac{d[O_2]}{dt} = k_3[N_2O_5]$. What is the correct mathematical relationship between $k_1$, $k_2$, and $k_3$?
Answer: B
💡 Solution & Explanation
The rate of reaction 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 given rate expressions yields $\frac{k_1}{2} = \frac{k_2}{4} = k_3$. Multiplying the entire equation by 4 gives $2k_1 = k_2 = 4k_3$.
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