The formation of small amounts of nitrogen oxide, NO, in automobile engines is the first step in

step 1 To determine the rate law and the rate constant, we must first determine the order with respect

The formation of small amounts of nitrogen oxide, NO, in...

The formation of small amounts of nitrogen oxide, $\mathrm{NO},$ in automobile engines is the first step in the formation of smog. As noted in Problem 13.63 , nitrogen oxide is readily oxidized to nitrogen dioxide by the reaction $2 \mathrm{NO}(g)+$ $\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$. The following data were collected in a study of the rate of this reaction: What is the rate law for the reaction? Determine the alue of the rate constant with its correct units.

Key Concepts

Rate Law

The rate law is an expression that relates the rate of a chemical reaction to the concentrations of its reactants. It takes the form rate = k[A]^x[B]^y, where k is the rate constant and the exponents x and y are the reaction orders with respect to each reactant. This law is determined experimentally and provides insight into how the speed of the reaction depends on the amount of each reactant present.

Reaction Order

Reaction order refers to the power to which the concentration of a reactant is raised in the rate law. Each reactant has its own order, and the overall order of the reaction is the sum of these individual orders. Reaction orders are not necessarily related to the stoichiometric coefficients in the chemical equation, but instead must be determined through experimentation.

Rate Constant and Units

The rate constant, represented by k in the rate law, is a proportionality factor that is specific to a given reaction at a certain temperature. The units of the rate constant depend on the overall order of the reaction to ensure that the rate is expressed in the proper units (typically concentration per time). For example, for a second-order reaction, the units of k might be M?¹s?¹.

Experimental Determination of Reaction Kinetics

Experimental determination of reaction kinetics involves measuring how the reaction rate varies with changes in reactant concentrations to establish the rate law, determine the orders of reaction, and calculate the rate constant. Techniques include varying one reactant’s concentration at a time while holding others constant and analyzing the data through methods such as the method of initial rates.

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