13.1 The rate of a reaction

Chemical Kinetics

  • Definition: Chemical kinetics is the area of chemistry focused on the rates or speeds at which chemical reactions occur.

  • Kinetic Energy: Refers to the energy associated with the motion of an object.

  • Reaction Rate: Defined as the change in concentration of a reactant or product with time (units: M/s).

Rate of a Reaction

  • Learning Objective (LO):

    • Evaluate the average rate of a reaction using provided data.

    • Infer the instantaneous rate of a reaction from a graph.

    • Use the stoichiometry of a reaction to express the rate in terms of reactants or products.

Definitions and Key Concepts

  • Thermodynamics vs. Kinetics:

    • Thermodynamics: Determines if a reaction can take place.

    • Kinetics: Measures how fast a reaction proceeds.

  • Average Rate: The average change in concentration over a specified time period.

  • Instantaneous Rate: The rate of change in concentration at a specific moment in time.

Expressing Reaction Rates

  • For a reaction A → B:

    • Rate = -Δ[A]/Δt

    • Rate = Δ[B]/Δt

    • Note: [A] decreases with time, making Δ[A] negative.

Graphical Representation of Reaction Rates

  • Figure 11.1: Shows the progress of reaction A → B over a period of 60 seconds. The transition shows A decreasing and B increasing.

  • Figure 11.2: Demonstrates the rate of reaction A → B, plotting the decrease in A and increase in B over time. The concentrations change from pure A to a mixture and finally to products.

    • At approximately 20-30 seconds, concentrations of A and B are equal.

Reaction of Molecular Bromine with Formic Acid

  • Reaction Equation:

    • Br2(aq) + HCOOH(aq) → 2Br^-(aq) + 2H^+(aq) + CO2(g)

  • A visual color change occurs during the reaction as bromine, initially red-brown, loses color to become colorless, indicating a decrease in concentration.

Measuring Rates of Reaction

  • To calculate the average rate:

    [ ext{average rate} = \frac{[Br_2]{final} - [Br_2]{initial}}{t_{final} - t_{initial}} ]

  • Instantaneous rates can be determined by calculating the slope of the tangent to the curve on a concentration vs. time graph.

  • Table 11.1: Displays rates of the bromine-formic acid reaction over time, showing the relationship between concentration change and time.

Rate Constant (k)

  • The rate is directly proportional to bromine concentration:

    • Rate = k[Br2]

  • The rate constant (k) represents the proportionality between the rate of reaction and the concentration of reactants. Its unit is s^-1, indicating that it is independent of reactant concentration.

Stoichiometry and Rate Expressions

  • Example Reaction:

    • A typical stoichiometric expression relates the rate to changes in reactant and product concentrations.

  • Practice Exercise: Given a reaction, write rate expressions for the disappearance of reactants and the appearance of products.

Instantaneous and Average Rates

  • Distinctions:

    • Instantaneous Rate: Defined as the rate of change at a specific moment in time.

    • Average Rate: Measured over an extended time interval.

  • Rate of Reaction Calculations: Derived from concentration vs. time graphs, where the average rate is indicated by the slope between two points and instantaneous rate by the slope of the tangent.

Additional Practice Problems

  1. Calculate instantaneous rates based on given concentration/time graphs.

  2. Write the average rate expressions for various reactions based on stoichiometry.

  3. Apply knowledge of physical changes during reactions to predict behavior under varying conditions.