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Chapter 12: Problem 2

Describe at least two experiments you could perform to determine a rate law.

Short Answer

Expert verified
Two experiments that can be performed to determine a rate law are the Method of Initial Rates and the Integrated Rate Law Experiment. In the Method of Initial Rates, initial reaction rates are compared under different reactant concentrations, providing insights into the order of the reaction and the rate constant. The Integrated Rate Law experiment involves monitoring concentration changes over time and fitting the data to common integrated rate law expressions for zeroth-order, first-order, and second-order reactions. The best fit reveals the reaction order, while the slope of the best-fitted plot allows for the determination of the rate constant.

Step by step solution

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1. Method of Initial Rates Experiment

One common experimental approach to determine a rate law is the method of initial rates. In this method, we monitor the initial rate of reaction under different initial concentrations of reactants. By comparing how the initial rates change as the reactant concentrations are varied, we can deduce the order of the reaction with respect to each reactant and thus determine the rate law. Here's how to perform an initial rates experiment: a. Set up the reaction with different initial concentrations of the reactants, while keeping the other conditions like temperature and pressure constant. b. Monitor the concentration of one of the reactants or products as a function of time, over multiple trials with different initial concentrations. c. Calculate the initial rate of the reaction for each trial, ideally in the early stages of the reaction when the rate is approximately constant. d. Plot the initial rate as a function of the initial concentration(s) of the reactant(s) and find the relationship between them. e. Determine the order of reaction with respect to each reactant, and obtain the rate constant (k) by fitting the data to the rate law expression.
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2. Integrated Rate Law Experiment

Another experimental approach to determine a rate law is using integrated rate laws. Integrated rate laws relate the concentration of reactants or products to the time elapsed during the reaction. By monitoring how the concentrations change over time, we can identify the functional relationship between concentration and time to determine the reaction order and rate constant. Here's how to perform an integrated rate law experiment: a. Set up the reaction under controlled conditions (e.g. constant temperature and pressure). b. Measure the concentration of one of the reactants or products as a function of time (e.g. by using spectrophotometry, titration, or gas collection). c. Plot the concentration data versus time and fit the data to the common integrated rate law expressions for zeroth-order, first-order, and second-order reactions. d. Determine which order provides the best fit to the experimental data (e.g. by evaluating the linearity of the plots). e. From the best-fitted plot, determine the slope, which is related to the rate constant (k) for the reaction and calculate the value of k. By using one (or both) of the described experimental approaches, you can successfully determine the rate law for a given chemical reaction.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Method of Initial Rates
The method of initial rates helps determine the rate law of a chemical reaction by examining how the initial concentrations of reactants affect the initial reaction rate. This method is insightful because it allows chemists to establish the relationship between concentration and rate without confusion from any complex later-stage reaction dynamics.
  • Firstly, the reaction is set up multiple times with differing initial concentrations of reactants, ensuring other experimental conditions such as temperature and pressure remain constant.
  • Through these trials, the initial rate of reaction is measured when the rate remains fairly constant.
  • By analyzing how these initial rates change with concentration, the reaction order for each reactant can be understood.
  • A plot of initial rate against initial concentration will illustrate the relationship, confirming the reaction order and allowing determination of the rate constant through data fitting to the rate law.
Integrated Rate Laws
Integrated rate laws provide a way to connect the concentration of reactants or products directly with time during a reaction. By studying these changes over time, we can discern the reaction order and rate constant in a dynamic context.
  • The experiment begins by maintaining controlled conditions and measuring reactant or product concentration as time progresses.
  • Various techniques like spectrophotometry or titration help track concentration changes.
  • This data is then plotted according to established integrated rate law expressions for different orders: zeroth, first, and second.
  • The plot that offers the most linear fit indicates the reaction order.
  • The slope of this line provides the rate constant, which is crucial for fully understanding the reaction kinetics.
Reaction Order
Understanding the reaction order is pivotal in elucidating how different reactants influence the rate of a chemical reaction. The order is not simply an exponent from the balanced equation, but rather, it is determined experimentally.
  • Each reactant in a reaction can have a different order which collectively gives the overall order.
  • For instance, if a reaction has orders of 1 and 2 for two reactants, its overall order is 3.
  • The reaction order with respect to a reactant shows how a change in concentration affects the rate 鈥� a first-order reaction means the rate doubles if concentration doubles, while a second-order implies the rate quadruples.
This specific knowledge aids in the accurate construction of the rate law and helps predict the effects of concentration changes on the reaction's pace.
Rate Constant
The rate constant, symbolized as \( k \), is a crucial piece of the puzzle when describing a reaction's kinetics. It becomes apparent once the reaction order is established and is vital for quantifying reaction speed.
  • The constant varies with temperature and must be determined experimentally for each different reaction and condition.
  • It is derived from fitting experimental data into the rate law expression.
  • The rate constant's unit changes depending on the total reaction order to keep the rate equation dimensionally consistent.
With the rate constant known, predictions about reaction speeds in varying conditions become feasible.
Kinetic Experiments
Kinetic experiments are fundamental investigations designed to understand the rates of chemical reactions. They provide essential data to develop accurate rate laws.
  • Typically, these experiments involve manipulating concentrations, measuring changes over time, and often controlling variables like temperature or pressure.
  • These controlled experiments are vital for determining the underlying kinetics and are interactive, often involving repeated trials to ensure reliability of data.
  • The analyzed results from kinetic experiments provide insights into the mechanisms driving reactions, timescales, and overall chemistry dynamics.
Performing these experiments carefully with precise measurements paves the way for discovering the detailed reaction pathway and effect of conditions on reaction speed.

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Most popular questions from this chapter

The reaction $$ \left(\mathrm{CH}_{\mathrm{3}}\right)_{3} \mathrm{CBr}+\mathrm{OH}^{-} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}+\mathrm{Br}^{-} $$ in a certain solvent is first order with respect to \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}\) and zero order with respect to \(\mathrm{OH}^{-}\). In several experiments, the rate constant \(k\) was determined at different temperatures. \(\mathrm{A}\) plot of \(\ln (k)\) versus \(1 / T\) was constructed resulting in a straight line with a slope value of \(-1.10 \times 10^{4} \mathrm{~K}\) and \(y\) -intercept of 33.5. Assume \(k\) has units of \(\mathrm{s}^{-1}\). a. Determine the activation energy for this reaction. b. Determine the value of the frequency factor \(A\). c. Calculate the value of \(k\) at \(25^{\circ} \mathrm{C}\).

Consider the general reaction $$ \mathrm{aA}+\mathrm{bB} \longrightarrow \mathrm{cC} $$ and the following average rate data over some time period \(\Delta t\) : $$ \begin{aligned} -\frac{\Delta \mathrm{A}}{\Delta t} &=0.0080 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s} \\ -\frac{\Delta \mathrm{B}}{\Delta t} &=0.0120 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s} \\ \frac{\Delta \mathrm{C}}{\Delta t} &=0.0160 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s} \end{aligned} $$ Determine a set of possible coefficients to balance this general reaction.

Which of the following statement(s) is(are) true? a. The half-life for a zero-order reaction increases as the reaction proceeds. b. A catalyst does not change the value of the rate constant. c. The half-life for a reaction, \(\mathrm{aA} \longrightarrow\) products, that is first order in A increases with increasing \([\mathrm{A}]_{0}\). d. The half-life for a second-order reaction increases as the reaction proceeds.

The activation energy for some reaction $$ \mathrm{X}_{2}(g)+\mathrm{Y}_{2}(g) \longrightarrow 2 \mathrm{XY}(g) $$ is \(167 \mathrm{~kJ} / \mathrm{mol}\), and \(\Delta E\) for the reaction is \(+28 \mathrm{~kJ} / \mathrm{mol}\). What is the activation energy for the decomposition of XY?

One mechanism for the destruction of ozone in the upper atmosphere is $$ \begin{aligned} &\mathrm{O}_{3}(g)+\mathrm{NO}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \\ &\mathrm{NO}_{2}(g)+\mathrm{O}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g) \end{aligned} $$ Overall reaction \(\mathrm{O}_{3}(g)+\mathrm{O}(g) \longrightarrow 2 \mathrm{O}_{2}(g)\) a. Which species is a catalyst? b. Which species is an intermediate? c. \(E_{a}\) for the uncatalyzed reaction $$ \mathrm{O}_{3}(g)+\mathrm{O}(g) \longrightarrow 2 \mathrm{O}_{2}(g) $$ is \(14.0 \mathrm{~kJ} . E_{a}\) for the same reaction when catalyzed is \(11.9 \mathrm{~kJ}\). What is the ratio of the rate constant for the catalyzed reaction to that for the uncatalyzed reaction at \(25^{\circ} \mathrm{C}\) ? Assume that the frequency factor \(A\) is the same for each reaction.
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