91Ó°ÊÓ

The rate law is an essential concept in chemical kinetics. It describes the relationship between the rate of a chemical reaction and the concentration of the reactants. In a reaction, the rate law can be expressed in general form 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 the orders of the reaction with respect to each reactant. For the given exercise, which involves the reaction \(2 \mathrm{NO}(g) + 2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g) + 2 \mathrm{H}_{2} \mathrm{O}(g)\), the rate law is first order in \(\mathrm{H}_{2}\) and second order in \(\mathrm{NO}\). Thus, the rate law expression becomes \(rate = k [\mathrm{NO}]^2 [\mathrm{H}_{2}]^1\). This informs us how changes in the concentrations of \(\mathrm{NO}\) and \(\mathrm{H}_{2}\) will affect the reaction rate.

The reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. Understanding how to calculate the reaction rate is critical in chemical kinetics. In our exercise, we use the rate law to determine how fast the reaction progresses under given conditions. By plugging the concentrations of \(\mathrm{NO}\) and \(\mathrm{H}_{2}\) into the rate law, we can calculate the reaction rate.

• With \(\mathrm{NO}\) at 0.035 M and \(\mathrm{H}_{2}\) at 0.015 M, we find that the reaction rate is 5.355 M\,s^{-1}
• When \(\mathrm{NO}\) is increased to 0.10 M and \(\mathrm{H}_{2}\) is 0.010 M, the reaction rate changes to 60.0 M\,s^{-1}

This clearly illustrates how variations in reactant concentrations impact the reaction rate.

The rate constant, symbolized as \(k\), is a crucial factor in the rate law equation. It provides the proportionality between the reaction rate and the concentrations of reactants raised to their respective orders. The value of \(k\) is specific to a particular reaction at a certain temperature, illustrating its dependence on conditions like temperature. In this exercise, the rate constant \(k\) is given as \(6.0 \times 10^{4} \mathrm{M}^{-2} \mathrm{~s}^{-1}\) at 1000 K. The units of the rate constant can vary depending on the reaction order, reflecting the need to multiply the concentration terms to yield a rate with units of concentration per time. The given value of \(k\) allows us to compute the reaction rate by applying it in conjunction with the reactant concentrations in the rate law expression.

The order of a reaction with respect to a particular reactant denotes the power to which the concentration of that reactant is raised in the rate law. The overall order of a reaction is the sum of the orders with respect to each reactant. For the reaction provided in the task, it is second order overall because it is first order in \(\mathrm{H}_{2}\) and second order in \(\mathrm{NO}\).

• First Order: Indicates a direct proportionality, i.e., if the concentration doubles, so does the reaction rate.
• Second Order: The rate is proportional to the square of the concentration; doubling the concentration quadruples the rate.

Knowing the order of a reaction helps predict how changing concentrations will alter the reaction speed, which is vital for both experimental kinetics and industrial application. In this exercise, understanding that the reaction is more sensitive to changes in \([\mathrm{NO}]\) due to its higher order, explains why an increase in \([\mathrm{NO}]\) causes a significant increase in the reaction rate.