Question

The rate law of a reaction can only be determined from experiment. Two experimental procedures for determining rate laws were outlined in Chapter 12. What are the two procedures and how are they used to determine the rate laws?

Short answer

The two experimental procedures for determining rate laws are the Initial Rates Method and the Integrated Rate Laws Method. The Initial Rates Method involves measuring the initial rate of a reaction under different initial concentrations of reactants and comparing these rates to deduce the order of the reaction with respect to each reactant. Steps include varying reactant concentrations, measuring initial rates, analyzing the data for a relationship, determining reaction orders, and expressing the overall rate law. The Integrated Rate Laws Method involves measuring how concentrations of reactants or products change over time, allowing us to determine the rate law by finding how a reactant's concentration affects the time it takes for the reaction to reach a certain point. Steps include choosing a measurable reactant or product, setting up an experiment, monitoring concentrations at time intervals, plotting the data against time, comparing the curve to theoretical curves, determining reaction orders, and constructing a rate law equation.

Step-by-step solution

Procedure 1: Initial Rates Method

This method involves measuring the initial rate of a reaction under different initial concentrations of reactants. By comparing how the initial rate changes with changes in concentration, we can determine the order of the reaction with respect to each reactant. To use the initial rates method, follow these steps: 1. Set up a series of experiments where you vary the initial concentration of one reactant, keeping the concentration of other reactants constant. 2. Measure the initial rate of the reaction for each experiment. 3. Analyze the data and find the relationship between the initial rate and the initial concentration of the reactant. 4. Determine the order of the reaction with respect to the varying reactant based on the observed relationship. 5. Repeat steps 1-4 for each reactant in the reaction. 6. Use the determined orders for each reactant to express the overall rate law for the reaction.

Procedure 2: Integrated Rate Laws Method

This method involves measuring how concentrations of reactants or products change during a reaction over time. This allows us to determine the rate law by finding how the concentration of a reactant affects the time it takes for the reaction to reach a certain point. To use the integrated rate laws method, follow these steps: 1. Choose a reactant or product whose concentration can be easily measured over time. 2. Set up a single experiment with known initial concentrations of reactants. 3. Monitor the concentration of the chosen reactant or product at different time intervals during the reaction. 4. Plot the concentration data against time and determine the shape of the curve. 5. Compare the curve to theoretical curves for zeroth-order, first-order, and second-order reactions. 6. Determine the order of the reaction with respect to the chosen reactant or product based on the curve shape that best fits the experimental data. 7. Use the determined order to construct a rate law equation for the reaction. These two procedures allow us to determine rate laws for reactions experimentally by observing how initial rates or concentrations change over time. By understanding the relationship between concentrations and the rates of reactions, we can establish the rate law equation for a given reaction.

Key concepts

Initial Rates Method

The initial rates method is a straightforward experimental technique used to determine the rate law of a chemical reaction. It focuses on analyzing how the initial rate of a reaction changes with varying concentrations of reactants.

Here's how it works:

• Start by preparing several reaction mixtures where the concentration of one reactant is altered while others are kept constant.
• Measure the initial rate of the reaction for each mixture. The initial rate is typically the rate at the start of the reaction, minimizing complications from product formation.
• Next, analyze the changes in the initial rate as the concentration of the reactant varies. This involves examining the relationship between rate and concentration.
• If the rate doubles as the concentration doubles, the reaction is first order with respect to that reactant. If the rate quadruples, the reaction is second order, and so on.
• Repeat this process for each reactant to find the order of reaction concerning each.

After determining the order for each reactant, you can write the rate law as an equation. This method is popular because it provides immediate insights without requiring extensive time series data collection.

Integrated Rate Laws

Integrated rate laws provide a powerful tool for analyzing how reactant concentrations change over time. This method is particularly useful for more complex reactions where initial rates might be challenging to measure reliably.

To use integrated rate laws, you start by tracking a single reactant or product's concentration over time.
Here's the approach:

• Conduct a reaction, maintaining initial conditions that are well-defined.
• Systematically measure the concentration of your chosen reactant or product at intervals as the reaction proceeds.
• Plot these concentrations against time to see the reaction's progression.
• The plot's shape reveals the order of the reaction when compared to known plots for zeroth-, first-, and second-order reactions.
• A linear plot indicates a zeroth-order reaction, a logarithmic plot indicates a first-order reaction, and a hyperbolic plot suggests a second-order reaction.

Based on which theoretical curve the data fits, you can derive the integrated rate equation. This method elegantly ties together time, concentration, and reaction order to construct a detailed rate law.

Reaction Order

Understanding the concept of reaction order is crucial to mastering chemical kinetics. Reaction order defines how the rate of a chemical reaction is affected by the concentration of its reactants. It's determined experimentally and tells us how changes in concentration influence reaction speed.

Here's a closer look at what reaction order entails:

• Zero Order: The rate is constant and independent of the concentration of reactants. Doubling the concentration doesn’t change the rate.
• First Order: The rate is directly proportional to the concentration of one reactant. Doubling the concentration doubles the reaction rate.
• Second Order: The rate is proportional to the square of a reactant's concentration. Doubling the concentration quadruples the rate.

For complex reactions involving multiple reactants, the overall order is the sum of the individual orders with respect to each reactant.

Determining the reaction order helps predict how the reaction will proceed under various conditions, providing valuable insights into reaction mechanisms and kinetics.

Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the speed or rate at which chemical reactions occur. It's an essential field as it helps scientists understand not only how fast reactions proceed but also the factors influencing these speeds.

Key points about chemical kinetics include:

• Kinetics typically involves measuring changes in concentrations over time, under varying temperature and pressure conditions.
• Kinetics also investigates the effect of catalysts in speeding up reactions without undergoing permanent chemical change themselves.
• The field is crucial for optimizing industrial processes, predicting reaction behavior, and developing new chemical products.
• Through kinetic studies, scientists can elucidate reaction mechanisms, revealing the step-by-step pathway that a reaction follows to convert reactants to products.

Knowledge gained from kinetics allows chemists to manipulate conditions favorably to achieve the desired reaction speed and yield, which is especially important in fields such as pharmacology and environmental chemistry.