Back to Library

(AI-Powered Suggestions)

Related Topics

A topic from the subject of Kinetics in Chemistry.

  • 11 months ago
  • 6 min read

Rate Equations and Order of Reactions

The rate of a chemical reaction describes how quickly reactants are converted into products. The rate equation, also known as the rate law, expresses the relationship between the reaction rate and the concentrations of reactants. It has the general form:

Rate = k[A]m[B]n

Where:

  • Rate is the speed of the reaction.
  • k is the rate constant (a proportionality constant specific to the reaction and temperature).
  • [A] and [B] are the concentrations of reactants A and B.
  • m and n are the orders of the reaction with respect to reactants A and B, respectively. These are experimentally determined and are not necessarily equal to the stoichiometric coefficients in the balanced chemical equation.

Order of Reaction

The overall order of a reaction is the sum of the individual orders (m + n in the example above). Reactions can be:

  • Zero-order: The rate is independent of the concentration of reactants (m + n = 0).
  • First-order: The rate is directly proportional to the concentration of one reactant (m or n = 1, the other is 0).
  • Second-order: The rate is proportional to the square of the concentration of one reactant (m or n = 2) or the product of the concentrations of two reactants (m = 1 and n = 1).
  • Higher-order reactions: Reactions with orders greater than two are also possible but less common.

Determining the Rate Equation

The rate equation cannot be determined from the stoichiometry of the balanced chemical equation alone. It must be determined experimentally, often by varying the concentrations of reactants and observing the effect on the reaction rate.

Rate Constant (k)

The rate constant, k, is temperature-dependent and is often described by the Arrhenius equation. A larger value of k indicates a faster reaction rate at a given temperature.

Rate Equations and Order of Reactions
Key Points
  • Rate equations express the relationship between the concentration(s) of reactants and the rate of a reaction.
  • The order of a reaction with respect to a reactant is the exponent of its concentration term in the rate equation. The overall order of a reaction is the sum of the individual orders with respect to each reactant.
  • Rate equations are determined experimentally, not from the stoichiometry of the balanced chemical equation.
Main Concepts

The rate of a chemical reaction describes how quickly reactants are consumed and products are formed. It's typically expressed as the change in concentration per unit time (e.g., mol L-1 s-1). The rate equation (also known as the rate law) mathematically links the reaction rate to the concentrations of reactants. This equation is always determined experimentally.

The order of a reaction provides crucial information about the reaction mechanism. It indicates how the rate depends on the concentration of each reactant. For example, a first-order reaction's rate is directly proportional to the concentration of one reactant, while a second-order reaction might depend on the square of one reactant's concentration or the product of the concentrations of two reactants. Higher-order reactions are also possible, though less common.

Understanding the order of reaction allows us to predict how the reactant concentrations will change over time and to determine the reaction mechanism. Different reaction mechanisms have different rate equations and orders.

Examples

Example 1: A simple second-order reaction

Consider the reaction between hydrogen and iodine:

$$H_2(g) + I_2(g) \rightarrow 2HI(g)$$

The experimentally determined rate equation is:

$$rate = k[H_2][I_2]$$

where k is the rate constant. The reaction is first-order with respect to H2, first-order with respect to I2, and second-order overall (1 + 1 = 2).

Example 2: A first-order reaction

The decomposition of nitrogen dioxide:

$$2NO_2(g) \rightarrow 2NO(g) + O_2(g)$$

has a rate equation of:

$$rate = k[NO_2]^2$$

This reaction is second-order overall and second-order with respect to NO2.

Note that the overall order of a reaction is not necessarily related to the stoichiometric coefficients in the balanced chemical equation.

Rate Equations and Order of Reactions Experiment

Objective: To determine the order of reaction and rate constant for a chemical reaction.

Materials:

  • Sodium thiosulfate solution (Na2S2O3)
  • Hydrochloric acid solution (HCl)
  • Potassium iodide solution (KI)
  • Starch solution
  • Buret
  • Pipette
  • Stopwatch
  • Test tubes
  • Conical flasks (or other suitable vessels for mixing)
  • Graduated cylinders (for accurate volume measurements)

Procedure:

  1. Prepare a series of test tubes (or conical flasks) containing varying concentrations of Na2S2O3 and a fixed, known concentration of HCl. Keep the total volume consistent across all test tubes/flasks.
  2. To each test tube/flask, add a fixed, known amount of KI solution.
  3. Add a few drops of starch solution to each test tube/flask as an indicator. The starch will react with iodine (produced in the reaction) to form a dark blue-black complex.
  4. For each test tube/flask, simultaneously add the remaining reactant (either Na2S2O3 or HCl, depending on which is being varied). Start the stopwatch immediately.
  5. Record the time it takes for the solution to turn a dark blue-black color. This indicates the completion of a specific extent of reaction (e.g., consumption of a certain amount of thiosulfate). The time is inversely proportional to the reaction rate.
  6. Repeat steps 1-5 for different concentrations of Na2S2O3 (keeping HCl concentration constant) to determine the order with respect to Na2S2O3. Then repeat with varying HCl concentrations (keeping Na2S2O3 constant) to determine the order with respect to HCl.

Data Analysis:

  • Calculate the initial rate of the reaction for each test tube/flask. The rate is inversely proportional to the time taken for the color change: Rate ∝ 1/time. (Note: This assumes the change in concentration is the same in each trial. If a spectrophotometer is used to track the concentration change over time, a more precise rate determination can be done.)
  • Plot the initial rate of the reaction against the initial concentration of Na2S2O3 (keeping HCl concentration constant). If the graph is linear, the order with respect to Na2S2O3 is 1. If the graph is a curve, the order is not 1. Similar analysis can determine the order with respect to HCl.
  • Determine the order of reaction with respect to each reactant from the graphs (linear or non-linear relationship) and calculate the rate constant (k) using the rate equation. The rate equation will take the form: Rate = k[Na2S2O3]m[HCl]n, where 'm' and 'n' are the orders with respect to Na2S2O3 and HCl respectively.
  • The overall order of reaction is the sum of the orders of reaction with respect to each reactant (m + n).

Significance:

  • This experiment allows students to experimentally determine the order of a reaction and the rate constant.
  • Understanding reaction orders and rate constants is essential for understanding the kinetics and mechanisms of chemical reactions.
  • It has applications in various fields, such as pharmaceutical development, environmental chemistry, and chemical engineering.

Share on: