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A topic from the subject of Kinetics in Chemistry.

  • 1 year ago
  • 6 min read

Rate Laws and Rate Constants

In chemistry, the rate law expresses the relationship between the rate of a reaction and the concentrations of the reactants. It's an experimentally determined equation, not derived directly from the stoichiometry of the balanced reaction equation.

Rate Law Expression

A general rate law is written as:

Rate = k[A]m[B]n

Where:

  • Rate represents the speed at which the reaction proceeds (often expressed as the change in concentration per unit time).
  • k is the rate constant. It's a proportionality constant specific to the reaction at a given temperature. A larger k indicates a faster reaction.
  • [A] and [B] represent the molar concentrations of reactants A and B.
  • m and n are the reaction orders with respect to reactants A and B, respectively. These are exponents determined experimentally and are not necessarily equal to the stoichiometric coefficients in the balanced equation.

Rate Constant (k)

The rate constant (k) is a crucial factor in the rate law. Its value depends on several factors:

  • Temperature: Increasing temperature generally increases the rate constant, and thus the reaction rate.
  • Catalyst: Catalysts increase the rate constant by providing an alternative reaction pathway with lower activation energy.
  • Nature of Reactants: The inherent reactivity of the reactants influences the rate constant.

The units of k depend on the overall order of the reaction (m + n in the example above).

Reaction Order

The reaction order (m and n in the example) describes how the rate of the reaction changes with the concentration of each reactant. It's an experimentally determined value, and can be:

  • Zero-order: The rate is independent of the concentration of the reactant (m or n = 0).
  • First-order: The rate is directly proportional to the concentration of the reactant (m or n = 1).
  • Second-order: The rate is proportional to the square of the concentration of the reactant (m or n = 2).
  • and so on...

The overall reaction order is the sum of the individual orders (m + n).

Determining Rate Laws

Rate laws are typically determined experimentally, often using methods like the initial rates method or integrated rate laws.

Rate Laws and Rate Constants
Overview

Rate laws describe the relationship between the concentration of reactants and the rate of a chemical reaction. Rate constants are numerical values that quantify the rate of a reaction.

Key Points

Reaction order: The sum of the exponents of the concentration terms in the rate law is the order of the reaction.

Rate constant: The proportionality constant in the rate law that depends on temperature and other factors.

Integrated rate laws: Express the relationship between concentration and time.

Half-life: The time required for the concentration of a reactant to decrease by half.

Arrhenius equation: Relates the rate constant to temperature and the activation energy.

Main Concepts

Concentration dependence: The rate of a reaction is proportional to the concentrations of the reactants raised to their respective orders. This relationship is expressed mathematically in the rate law: Rate = k[A]m[B]n, where k is the rate constant, [A] and [B] are the concentrations of reactants, and m and n are the reaction orders with respect to A and B respectively.

Temperature dependence: The rate constant increases with temperature, following the Arrhenius equation: k = Ae-Ea/RT, where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

Predicting reaction rates: Rate laws allow us to predict the rate of a reaction if the concentrations of the reactants and the rate constant are known.

Applications: Rate laws are used in chemical engineering, medicine, and other fields to design processes and optimize reactions. For example, understanding rate laws is crucial for designing efficient industrial chemical processes or for studying the kinetics of drug metabolism in the body.

Experiment: Determining the Rate Law and Rate Constant for a Chemical Reaction
Objective

To experimentally determine the rate law and rate constant for the following reaction:

2A + B → C
Materials
  • Sodium thiosulfate solution (Na2S2O3)
  • Iodine solution (I2)
  • Hydrochloric acid (HCl)
  • Sodium hydroxide (NaOH)
  • Starch solution
  • Burette
  • Pipette
  • Stopwatch
Procedure
  1. Prepare the reaction mixture: In a test tube, combine the following solutions:
    • 10 mL of Na2S2O3 solution
    • 5 mL of I2 solution
    • 5 mL of HCl solution
  2. Start the reaction: Add 2 drops of starch solution to the reaction mixture. This will turn the solution a deep blue color.
  3. Titrate the reaction mixture: Using a burette, add NaOH solution dropwise to the reaction mixture until the blue color disappears. Record the volume of NaOH solution used.
  4. Repeat steps 1-3 for different initial concentrations of A, B, and HCl. By varying the initial concentrations, you can determine the order of the reaction with respect to each reactant.
Key Procedures
  • Use a clean burette and pipette. This is essential for accurate measurements.
  • The starch solution acts as an indicator for the reaction endpoint.
  • Determine the order of the reaction experimentally. This involves varying the initial concentrations of the reactants and observing the effect on the reaction rate.
Data Analysis
  1. Calculate the initial rate of reaction. The initial rate of reaction can be determined from the change in concentration of a reactant or product over a short time interval at the beginning of the reaction. More sophisticated methods may involve plotting concentration vs time and determining the initial slope.
  2. Determine the order of the reaction with respect to each reactant. This is typically done by the method of initial rates. Multiple experiments are run with different initial concentrations of each reactant, while holding others constant. The order with respect to each reactant can be determined by comparing the effect on the initial rate of changing its concentration.
  3. Calculate the rate constant. Once the order of the reaction with respect to each reactant is known, the rate constant (k) can be calculated using the rate law equation and the data from one of the experiments.
Significance

This experiment allows students to experimentally determine the rate law and rate constant for a chemical reaction. This knowledge is important for understanding the kinetics of chemical reactions and for predicting the reaction rate under different conditions.

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