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Chapter 14: Problem 7

Explain what is meant by the rate law of a reaction.

Short Answer

Expert verified
The rate law of a reaction is a mathematical equation that relates the rate of a chemical reaction to the concentrations of its reactants. It is empirically determined and usually takes the form of 'Rate = k \([A]^m \times [B]^n\)'. The rate law models how a reaction will proceed over time, enabling control over reaction rates and gaining insights about the reaction mechanism and the effect of temperature.

Step by step solution

01

Define the rate law

The rate law of a reaction is a mathematical expression that illustrates the relationship between the rate at which a chemical reaction proceeds and the concentration of the reactants. As such, the rate law is a crucial component in determining the kinetics, or speed, of a chemical reaction.
02

Explain the construction of a rate law

Rate laws are determined experimentally and are usually of the form 'Rate = k \([A]^m \times [B]^n\)', where 'Rate' denotes the rate of the reaction, 'k' denotes the rate constant for the reaction, '[A]' and '[B]' denotes the concentrations of the reactants and 'm' and 'n' denote the orders of the reaction with respect to the reactants A and B respectively. The overall order of reaction is the sum of individual orders (m + n). The orders of reaction represent the effect of reactant concentrations on the rate of reaction and can be 0, 1, 2 or sometimes fractions.
03

Discuss the significance of the rate law

The rate law is significant because it allows scientists to model how a reaction will proceed over time. This has practical importance in a wide array of fields, from designing industrial processes to understanding biological systems. By controlling the concentrations of reactants, the rate of a reaction can be manipulated. Additionally, from the rate constant, the rate law also allows information about the reaction mechanism and the effect of temperature on reaction rate to be obtained.

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Most popular questions from this chapter

Consider this elementary step: $$ X+2 Y \longrightarrow X Y_{2} $$ (a) Write a rate law for this reaction. (b) If the initial rate of formation of \(\mathrm{XY}_{2}\) is \(3.8 \times 10^{-3} \mathrm{M} / \mathrm{s}\) and the initial concentrations of \(X\) and \(Y\) are \(0.26 M\) and \(0.88 M\), what is the rate constant of the reaction?

The rate of the reaction $$ \begin{aligned} \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(a q) &+\mathrm{H}_{2} \mathrm{O}(l) \\ \longrightarrow & \mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) \end{aligned} $$ shows first-order characteristics-that is, rate \(=\) \(k\left[\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}\right]\) - even though this is a second- order reaction (first order in \(\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}\) and first order in \(\mathrm{H}_{2} \mathrm{O}\) ). Explain.

Many reactions involving heterogeneous catalysts are zero order; that is, rate \(=k\). An example is the decomposition of phosphine \(\left(\mathrm{PH}_{3}\right)\) over tungsten (W): $$ 4 \mathrm{PH}_{3}(g) \longrightarrow \mathrm{P}_{4}(g)+6 \mathrm{H}_{2}(g) $$ It is found that the reaction is independent of \(\left[\mathrm{PH}_{3}\right]\) as long as phosphine's pressure is sufficiently high \((\geq 1 \mathrm{~atm}) .\) Explain.

The thermal decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) obeys firstorder kinetics. At \(45^{\circ} \mathrm{C}\), a plot of \(\ln \left[\mathrm{N}_{2} \mathrm{O}_{5}\right]\) versus \(t\) gives a slope of \(-6.18 \times 10^{-4} \mathrm{~min}^{-1}\). What is the half-life of the reaction?

Use the Arrhenius equation to show why the rate constant of a reaction (a) decreases with increasing activation energy and (b) increases with increasing temperature.
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