The reaction (nitrogen monoxide reacts with hydrogen gas to form nitrogen gas and water vapor) is believed to take place in three steps, the first of which is the fast reversable dimerization of NO to form N2O2, and the last of which is the reaction N2O + H2 -> N2 + H2O. (i) what is the (slow) second step? (ii) Show, using the stead-state approximation, that the mechanism is consistant with the obseved rate law. (iii) Why is it only approximatily true that the reaction is first-order in H2?
To answer these questions, let's break down each part:
(i) The slow second step: In a reaction mechanism, the slow step typically determines the overall rate of the reaction. From the given information, we know that the first step is the fast reversible dimerization of NO to form N2O2, and the last step is the reaction of N2O and H2 to form N2 and H2O. Since the reaction is believed to take place in three steps, the slow second step must involve the formation or consumption of intermediate species. However, without additional information, it is not possible to directly determine the exact nature of the slow second step.
(ii) Using the steady-state approximation: The steady-state approximation is a common approach to simplify complex reaction mechanisms. It assumes that the concentration of the intermediate species remains constant during the reaction. To show that the mechanism is consistent with the observed rate law, we need to consider the rate-determining step and derive the rate law expression.
Given that the last step is the reaction N2O + H2 -> N2 + H2O, we can assume this step to be the rate-determining step. The rate law for this step can be written as:
Rate = k * [N2O] * [H2]
To apply the steady-state approximation, we assume that the rate of formation of the intermediate species N2O2 (from the fast step) is equal to its rate of consumption in the slow second step. This allows us to express [N2O2] in terms of the concentrations of other species involved in the reaction.
(iii) Approximation of first-order reaction with H2: The statement that the reaction is approximately first-order in H2 suggests that the rate of the overall reaction is primarily dependent on the concentration of H2. However, since the given information does not provide further details, we cannot definitively explain why this is true without additional information about the reaction mechanism or experimental data.
In summary, while we can determine the rate law expression using the steady-state approximation and understand the slow second step, the exact nature of the slow step and the reasoning behind the approximate first-order behavior of H2 require additional information or data.