Glossary

3.2 Initial rates method

3 min read•july 22, 2024

Chemical kinetics studies how fast reactions happen. The is a key tool for figuring out reaction rates and orders. It helps us understand how changing reactant amounts affects reaction speed.

By measuring initial rates with different reactant concentrations, we can determine the rate law. This tells us how each reactant influences the overall reaction rate. Understanding these relationships is crucial for predicting and controlling chemical reactions.

Initial Rates Method

Initial rates method fundamentals

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  • Experimental approach determines rate law and for each reactant in a chemical reaction
  • Measures initial reaction rate for a series of experiments with varying initial concentrations of reactants
  • Rate law relates reaction rate to concentrations of reactants raised to their respective reaction orders
    • Rate law: Rate=k[A]m[B]nRate = k[A]^m[B]^n, where kk is , [A][A] and [B][B] are reactant concentrations, and mm and nn are reaction orders
  • Reaction orders for each reactant determined by comparing ratios of initial rates and corresponding reactant concentrations between experiments
    • First-order reaction: doubling concentration of reactant doubles initial rate
    • Second-order reaction: doubling concentration quadruples initial rate
  • Overall order of reaction is sum of individual reaction orders for each reactant

Analysis of initial rates data

  • Set up table with columns for experiment number, initial concentrations of reactants, and initial rate
  • Perform experiments with varying initial concentrations of reactants, keeping all other factors constant (temperature, pressure)
  • Measure initial rate for each experiment and record data in table
  • Compare ratios of initial rates and corresponding reactant concentrations between experiments to determine reaction order for each reactant
    • If ratio of initial rates equals ratio of reactant concentrations raised to a power, that power is reaction order for that reactant
  • Write rate law equation using determined reaction orders and generic rate constant, kk

Rate constant and order calculations

  1. Determine reaction orders using initial rates method
  2. Rearrange rate law equation to solve for rate constant, kk
    • k=Rate[A]m[B]nk = \frac{Rate}{[A]^m[B]^n}
  3. Substitute initial rate and reactant concentrations from any experiment into rearranged equation to calculate rate constant
  4. Rate constant units depend on overall order of reaction
    • First-order reaction: kk units are s−1s^{-1}
    • Second-order reaction with single reactant: kk units are M−1s−1M^{-1}s^{-1}
  5. Reaction order for each reactant determined by comparing ratios of initial rates and corresponding reactant concentrations between experiments

Mechanism determination using initial rates

  • Initial rates method helps distinguish between different proposed reaction mechanisms by comparing experimentally determined rate law with rate laws predicted by each mechanism
  • Each proposed mechanism has unique rate-determining step, which is slowest step in
  • Rate law for overall reaction determined by rate-determining step
  • Derive rate law for each proposed mechanism and compare to experimentally determined rate law to identify most likely mechanism
    • If experimental rate law matches rate law predicted by particular mechanism, that mechanism more likely to be correct
  • If experimental rate law does not match any proposed mechanisms, suggests actual mechanism may be more complex or alternative mechanisms not yet considered

Key Terms to Review (15)

Activation Energy: Activation energy is the minimum amount of energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to be transformed into products, linking the concepts of kinetics and thermodynamics in the context of chemical reactions.
First-order reactions: First-order reactions are chemical reactions where the rate depends linearly on the concentration of one reactant. This means that if the concentration of that reactant changes, the rate of reaction will change proportionally. Understanding first-order reactions is crucial as they relate to concepts like the Arrhenius equation, which helps explain how temperature and activation energy influence reaction rates, as well as methods for determining initial rates and various factors that can affect these rates.
Half-life: Half-life is the time required for half of the reactant to be consumed in a chemical reaction, providing a measure of the rate at which a reaction occurs. This concept is crucial in understanding how quickly substances degrade or react, especially in applications such as pharmaceuticals and environmental science, where it helps predict the behavior of drugs and pollutants over time.
Heterogeneous catalyst: A heterogeneous catalyst is a substance that increases the rate of a chemical reaction while remaining in a different phase from the reactants, typically solid catalysts in liquid or gas reactions. These catalysts provide an active surface area where the reactants can adsorb, facilitating their transformation into products without being consumed in the process. This type of catalysis is essential in various industrial processes, enhancing reaction rates and selectivity.
Homogeneous catalyst: A homogeneous catalyst is a catalyst that exists in the same phase as the reactants in a chemical reaction, typically in a solution. This type of catalyst facilitates a reaction by providing an alternative reaction pathway with a lower activation energy, thus increasing the reaction rate while being consumed in the process. The uniformity in phase allows for better interaction between the catalyst and reactants, impacting various aspects of chemical kinetics.
Initial rates method: The initial rates method is a technique used in chemical kinetics to determine the rate law of a reaction by measuring the initial reaction rates at varying concentrations of reactants. This approach allows chemists to establish how the rate of a reaction depends on the concentration of reactants and, in turn, helps identify the order of the reaction with respect to each reactant. By analyzing the changes in reaction rates, this method is essential for understanding gas-phase reaction kinetics and is often employed in various experimental methods for rate law determination.
Integrated Rate Laws: Integrated rate laws express the relationship between the concentration of reactants and time for a chemical reaction. They help in determining how the concentration of reactants changes over time, allowing scientists to predict the behavior of reactions in various environments, such as gas-phase reactions, and during consecutive reactions. Understanding integrated rate laws is essential for calculating half-lives and analyzing data graphically or through initial rates methods.
Method of initial rates: The method of initial rates is a technique used to determine the rate law and reaction order by measuring the initial rate of reaction for different initial concentrations of reactants. This method allows for the calculation of how the rate changes with varying concentrations, helping to establish the relationship between concentration and rate, which is key to understanding differential rate laws and overall reaction kinetics.
Product formation: Product formation refers to the process by which reactants are converted into products during a chemical reaction. This process is crucial in understanding how quickly a reaction occurs and how the concentrations of reactants and products change over time, which is essential for analyzing reaction kinetics.
Rate Constant: The rate constant is a proportionality factor in the rate law that quantifies the speed of a chemical reaction at a given temperature. It connects the concentration of reactants to the reaction rate, showing how quickly the reaction proceeds. The value of the rate constant is influenced by factors such as temperature, activation energy, and the presence of catalysts, making it a key element in understanding reaction kinetics and dynamics.
Reactant concentration: Reactant concentration refers to the amount of a substance present in a given volume of solution or reaction mixture, which significantly influences the rate at which chemical reactions occur. Higher reactant concentrations typically lead to more frequent collisions between molecules, thus increasing the rate of reaction. Understanding how concentration affects reaction rates is crucial for predicting the behavior of chemical systems and is foundational in analyzing rate laws and reaction orders.
Reaction mechanism: A reaction mechanism is a detailed step-by-step description of the process by which reactants are transformed into products during a chemical reaction. This concept connects the rates of reactions with the molecular events that occur, providing insight into how and why certain factors affect reaction dynamics and outcomes.
Reaction Order: Reaction order is the power to which the concentration of a reactant is raised in the rate law expression for a chemical reaction, indicating how the rate of reaction depends on the concentration of reactants. This concept helps in understanding how different conditions affect the speed of a reaction, and it is essential for analyzing data from kinetic experiments and designing reactors.
Second-order reactions: Second-order reactions are chemical reactions whose rate is dependent on the concentration of two reactants or the square of the concentration of one reactant. This means that if you double the concentration of one reactant, the reaction rate quadruples, reflecting a more complex interaction than first-order reactions. Understanding second-order reactions is crucial for grasping how factors like temperature and activation energy influence reaction rates, as described by the Arrhenius equation, and how initial concentrations affect reaction rates in practical scenarios.
Zero-order reactions: Zero-order reactions are chemical reactions that do not depend on the concentration of the reactants; instead, their rate remains constant over time. This means that the reaction proceeds at a steady rate, regardless of how much reactant is present. Such reactions often occur in scenarios where a reactant is saturated, limiting the effect of its concentration on the rate, and this characteristic directly influences the determination of initial rates and the factors affecting reaction rates.
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