Chemical Kinetics - Integrated rate law for first order reaction

  • First order reactions
  • Rate law expression for first order reactions
  • Integrated rate law for first order reactions
  • Derivation of integrated rate law
  • Example: Decomposition of hydrogen peroxide
    • Balanced chemical equation
    • Determining the rate law expression
    • Deriving the integrated rate law
  • Half-life of a first order reaction
  • Determining the half-life using the integrated rate law
  • Example: Radioactive decay of a substance
    • Balanced nuclear equation
    • Determining the rate law expression
    • Deriving the integrated rate law
  • Plotting a graph of concentration vs. time
  1. First order reactions
  • Definition of first order reactions
  • Examples of first order reactions in everyday life
  • Importance of studying first order reactions in chemistry
  • Relationship between reactant concentration and reaction rate in first order reactions
  • Rate constant for first order reactions
  1. Rate law expression for first order reactions
  • General form of rate law expression: rate = k[A]
  • Explanation of rate (r) and rate constant (k)
  • Relationship between rate constant and reaction rate
  • Units of rate constant (k)
  • Determination of the rate law expression experimentally
  1. Integrated rate law for first order reactions
  • Definition of integrated rate law
  • Purpose of integrated rate law
  • Types of integrated rate laws (zero order, first order, second order)
  • Focus on integrated rate law for first order reactions
  1. Derivation of integrated rate law for first order reactions
  • Deriving the integrated rate law using calculus
  • Assumptions made during the derivation process
  • Final form of the integrated rate law for first order reactions
  • Equation representing the relationship between reactant concentration and time
  • Use of integrated rate law in determining reaction kinetics
  1. Example: Decomposition of hydrogen peroxide
  • Balanced chemical equation for decomposition of hydrogen peroxide
  • Determining the rate law expression for the reaction
  • Experimentally measured rate data for different concentrations of hydrogen peroxide
  • Substituting values into the integrated rate law equation
  • Calculating the rate constant (k) and reaction order (n)
  1. Half-life of a first order reaction
  • Definition of half-life
  • Relationship between half-life and the rate constant (k)
  • Use of half-life in determining the reaction order
  • Importance of half-life in understanding reaction kinetics
  • Calculation of half-life using the integrated rate law equation
  1. Determining the half-life using the integrated rate law
  • Deriving an expression for half-life from the integrated rate law equation
  • Substituting values into the half-life equation
  • Example calculation of half-life for a first order reaction
  • Impact of reactant concentration on the half-life of a reaction
  • Application of half-life in predicting reaction progress
  1. Example: Radioactive decay of a substance
  • Balanced nuclear equation for radioactive decay
  • Determining the rate law expression for radioactive decay
  • Experimental data for the decay of a radioactive substance
  • Using the integrated rate law equation to calculate the rate constant (k)
  • Determining the half-life of the radioactive substance
  1. Plotting a graph of concentration vs. time
  • Importance of graphical representation in kinetics
  • Plotting a concentration vs. time graph for a first order reaction
  • Interpretation of the graph in terms of reaction rate and reaction progress
  • Relationship between the slope of the graph and the rate constant (k)
  • Analyzing the graph to determine the reaction order
  1. Summary
  • Recap of key concepts covered in the lecture
  • Understanding first order reactions and rate law expression
  • Importance of integrated rate law and its derivation
  • Applications of half-life in reaction kinetics
  • Graphical representation and interpretation of concentration vs. time graphs
  1. Half-life equation for first order reactions
  • The half-life (t1/2) of a first order reaction can be determined using the integrated rate law equation for first order reactions.
  • The equation for calculating the half-life is: t1/2 = (0.693 / k)
  • In this equation, k represents the rate constant of the reaction.
  1. Example calculation of half-life for a first order reaction
  • Suppose we have a first order reaction with a rate constant (k) of 0.05 s^-1.
  • To calculate the half-life, we can use the equation: t1/2 = (0.693 / k)
  • Substituting the value of k in the equation, we get: t1/2 = (0.693 / 0.05) = 13.86 seconds.
  • Therefore, the half-life of the reaction is approximately 13.86 seconds.
  1. Impact of reactant concentration on the half-life of a reaction
  • The half-life of a reaction is independent of the initial concentration of the reactant.
  • Regardless of the starting concentration, the time it takes for the concentration to decrease by half remains the same.
  • This is a characteristic of first order reactions and is a unique property of exponential decay.
  1. Application of half-life in predicting reaction progress
  • The half-life can be used to predict the progress of a first order reaction.
  • By knowing the half-life and the initial concentration, we can determine how much time it will take for the concentration of the reactant to reach a certain level.
  • This information is useful in various fields, such as medicine, environmental studies, and industrial processes.
  1. Example: Radioactive decay of a substance
  • Radioactive decay is a first order reaction that involves the spontaneous breakdown of unstable atomic nuclei.
  • The rate law expression for radioactive decay is: rate = k[A]
  • In this equation, A represents the radioactive substance and k is the rate constant.
  • The integrated rate law equation for radioactive decay is: ln(A / A0) = -kt
  • A0 represents the initial concentration of the radioactive substance, t is the time, and ln denotes the natural logarithm.
  1. Determining the rate constant (k) for radioactive decay
  • To determine the rate constant (k) for radioactive decay, experimental data is needed.
  • The measured values of reactant concentration (A) at different times (t) can be used to calculate the rate constant.
  • By rearranging the integrated rate law equation and substituting values, the rate constant can be determined.
  • Understanding the rate constant is important for predicting the decay rate of radioactive substances.
  1. Determining the half-life of a radioactive substance
  • The half-life of a radioactive substance can be determined using the rate constant (k) calculated from experimental data.
  • The half-life equation for radioactive decay is: t1/2 = (0.693 / k)
  • By substituting the value of k into the equation, the half-life of the radioactive substance can be calculated.
  • This information is crucial for various applications, such as medical imaging, radioactive dating, and nuclear power.
  1. Plotting a concentration vs. time graph
  • Graphical representation is a useful tool in studying reaction kinetics.
  • A concentration vs. time graph provides visual information about the change in reactant concentration over time.
  • For a first order reaction, the graph shows an exponential decay curve.
  • The slope of the graph is related to the rate constant (k) of the reaction.
  1. Interpreting a concentration vs. time graph
  • The slope of a concentration vs. time graph for a first order reaction represents the rate constant (k) of the reaction.
  • The steeper the slope, the larger the rate constant and the faster the reactant is being consumed.
  • The graph also provides information about the reaction progress, as the concentration decreases over time.
  • The initial concentration and time can be used to calculate the half-life of the reaction.
  1. Conclusion
  • In this lecture, we have studied the integrated rate law for first order reactions.
  • We have derived the integrated rate law equation and learned how to determine the rate constant (k).
  • The concept of half-life and its calculation for first order reactions has been explained.
  • Graphical representation in the form of concentration vs. time graphs provides valuable insights into reaction kinetics.
  • Understanding these concepts is important for predicting reaction progress and analyzing reaction rates in various fields.