The reaction 2NO1g2 + 2 H21g2S N21g2 + 2 H2O1g2 is first order in H2 and second order in NO. Write the rate law, and specify the units of the rate constant.

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insert step 1> Identify the order of the reaction with respect to each reactant. The reaction is first order in H_2 and second order in NO.

insert step 2> Write the general form of the rate law for the reaction. The rate law is expressed as: rate = k [NO]^m [H_2]^n, where k is the rate constant, m is the order with respect to NO, and n is the order with respect to H_2.

insert step 3> Substitute the given orders into the rate law. Since the reaction is second order in NO and first order in H_2, the rate law becomes: rate = k [NO]^2 [H_2]^1.

insert step 4> Determine the overall order of the reaction by adding the exponents of the concentration terms in the rate law. The overall order is 2 (for NO) + 1 (for H_2) = 3.

insert step 5> Specify the units of the rate constant k. For a reaction of overall order n, the units of k are typically (L^(n-1) mol^(1-n) s^(-1)). For this third-order reaction, the units of k are L^2 mol^(-2) s^(-1).

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Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as Rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are the concentrations of the reactants, and m and n are their respective orders. For the given reaction, the rate law can be written based on the specified orders of the reactants.

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Rate Law Fundamentals

Order of Reaction

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It indicates how the rate of reaction is affected by changes in concentration. In this case, the reaction is first order in H2 and second order in NO, meaning that the rate is directly proportional to the concentration of H2 and proportional to the square of the concentration of NO.

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Average Bond Order

Units of the Rate Constant (k)

The units of the rate constant depend on the overall order of the reaction. For a reaction that is first order in one reactant and second order in another, the overall order is three. The units of k can be derived from the rate law, where the rate is typically expressed in mol/L·s. Thus, for a third-order reaction, the units of k would be L^2/(mol^2·s).

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