For the decomposition of nitrous oxide N2O →N2+ 0.5O2, the rate equation is given by−𝑟𝑁2𝑂 = 𝑘1[𝑁2𝑂]21 + 𝑘2[𝑁2𝑂]Propose a mechanism for the reaction and derive the above expression
Question
For the decomposition of nitrous oxide N2O →N2+ 0.5O2, the rate equation is given by−𝑟𝑁2𝑂 = 𝑘1[𝑁2𝑂]21 + 𝑘2[𝑁2𝑂]Propose a mechanism for the reaction and derive the above expression
Solution
The proposed mechanism for the decomposition of nitrous oxide (N2O) can be a two-step process:
Step 1: N2O ↔ N2 + O (slow, rate-determining step) Step 2: O + N2O → N2 + O2 (fast)
The rate of the reaction is determined by the slowest step, which is the first step in this case. Therefore, the rate equation for the first step is:
Rate = k1[N2O]
However, this equation does not match the given rate equation. To derive the given rate equation, we need to consider the second step as well.
In the second step, the concentration of O is not known. However, we can express it in terms of N2O using the equilibrium constant (K) for the first step:
K = [N2][O]/[N2O] => [O] = K[N2O]/[N2]
Substituting [O] into the rate equation for the second step gives:
Rate = k2N2O = k2K[N2O]^2/[N2]
Adding the rate equations for the first and second steps gives the overall rate equation:
Rate = k1[N2O] + k2K[N2O]^2/[N2]
This equation matches the given rate equation if we let k1 = k1 and k2K/[N2] = k2. Therefore, the proposed mechanism is consistent with the given rate equation.
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