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12.3 Rate Laws

2 min read•june 25, 2024

Reaction kinetics and are crucial for understanding how fast chemical reactions occur. They provide a mathematical framework to predict reaction speeds based on reactant concentrations, helping chemists control and optimize chemical processes.

Rate laws describe the relationship between reaction rate and reactant concentrations. By determining and rate constants, chemists can calculate reaction rates, predict concentration changes over time, and gain insights into reaction mechanisms and rate-determining steps.

Reaction Kinetics and Rate Laws

Components of rate laws

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Top images from around the web for Components of rate laws

  • Rate Laws for Elementary Steps | Introduction to Chemistry View original

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  • The Rate Law | Introduction to Chemistry View original

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  • mathematical equation relates reaction rate to reactant concentrations
  • Determines how reaction rate depends on each reactant's concentration
  • General form: Rate = ###[k](https://www.fiveableKeyTerm:K)[[A]](https://www.fiveableKeyTerm:[A])^[m](https://www.fiveableKeyTerm:M)[[B]](https://www.fiveableKeyTerm:[B])^n_0###
    • kk depends on temperature and reaction nature
    • [A][A] and [B][B] concentrations of reactants A and B
    • mm and [n](https://www.fiveableKeyTerm:n)[n](https://www.fiveableKeyTerm:n) reaction orders for reactants A and B
  • Rate law predicts reaction rate based on reactant concentrations
  • Helps understand
  • Allows determination of in multi-step reaction

Calculation of reaction rates

  • Substitute initial concentrations and into rate law equation
  • Example: For reaction A+B→CA + B \rightarrow C, with rate law Rate=k[A]2[B]Rate = k[A]^2[B]
    1. Given [A]0=0.1M[A]_0 = 0.1 M, [B]0=0.2M[B]_0 = 0.2 M, and k=0.5[M−2s−1](https://www.fiveableKeyTerm:M−2s−1)k = 0.5 [M^{-2}s^{-1}](https://www.fiveableKeyTerm:M^{-2}s^{-1})
    2. Calculate Rate=(0.5M−2s−1)(0.1M)2(0.2M)=1×10−4[Ms−1](https://www.fiveableKeyTerm:Ms−1)Rate = (0.5 M^{-2}s^{-1})(0.1 M)^2(0.2 M) = 1 \times 10^{-4} [M s^{-1}](https://www.fiveableKeyTerm:M_s^{-1})
  • Predict concentration changes over time by integrating rate law
    • First-order reactions: [[A]_t = [A]_0 e^{-kt}](https://www.fiveableKeyTerm:[A]_t_=_[A]_0_e^{-kt})
    • Second-order reactions: 1[A]t=1[A]0+kt\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt
    • equations allow for calculation of concentrations at any time t

Determination of reaction orders

  • exponent in rate law for specific reactant
  • Determined experimentally by varying one reactant's concentration while keeping others constant
  • Methods for determining reaction order
      • Measure initial reaction rates at different initial reactant concentrations
      • Compare ratio of rates to ratio of concentrations
      • Plot natural logarithm of reaction rate vs natural logarithm of reactant concentration
      • Slope of line equals reaction order
  • Construct rate laws by combining determined reaction orders for each reactant
    • Example: If reaction is first-order in A and second-order in B, rate law is Rate=k[A]1[B]2Rate = k[A]^1[B]^2
  • Determine rate constant by substituting rate, concentrations, and orders into known rate law and solving for kk

Advanced Kinetics Concepts

  • : time required for reactant concentration to decrease by half
  • : rate is independent of reactant concentration
  • : series of elementary steps that describe how a reaction occurs at the molecular level
    • Helps explain observed rate law and identify rate-determining step

Key Terms to Review (30)

[A]: [A] refers to the mathematical relationship between the rate of a chemical reaction and the concentrations of the reactants involved. It is a fundamental concept in the study of chemical kinetics and is crucial for understanding the factors that influence the speed of a reaction.
[A]_t = [A]_0 e^{-kt}: [A]_t = [A]_0 e^{-kt} is an equation that describes the concentration of a reactant (A) at a given time (t) in a first-order chemical reaction. It relates the initial concentration of the reactant ([A]_0) to its concentration at time t ([A]_t) and the rate constant (k) of the reaction.
[B]: [B] is a key concept in the context of 12.3 Rate Laws, which describes the relationship between the concentration of reactants and the rate of a chemical reaction. It is a crucial factor in determining the overall rate of a reaction and understanding how reaction conditions can be manipulated to control the reaction rate.
1/[A]_t = 1/[A]_0 + kt: This equation represents the relationship between the concentration of a reactant (A) at time t, the initial concentration of the reactant, and the rate constant (k) in the context of a first-order reaction. It is a fundamental expression in the study of reaction kinetics and rate laws.
Graphical Method: The graphical method is a technique used to visually represent and analyze the relationship between variables in chemical kinetics, particularly in the context of rate laws. It involves plotting experimental data on a graph to determine the order of a reaction and the rate constant.
Half-life: Half-life is the time required for half of the radioactive nuclei in a sample to decay. It is a characteristic property of each radioactive isotope.
Half-life: Half-life is the time it takes for a radioactive substance to decay to half of its original amount. It is a fundamental concept in nuclear chemistry that describes the exponential decay of radioactive isotopes and is crucial for understanding the behavior of radioactive materials.
Integrated Rate Law: The integrated rate law is a mathematical expression that describes the relationship between the concentration of a reactant and the time elapsed during a chemical reaction. It allows for the determination of the order of a reaction and the rate constant, providing a quantitative understanding of the reaction kinetics.
Integrated rate laws: Integrated rate laws describe the concentration of reactants as a function of time. They are derived from differential rate laws and are used to determine reaction order and rate constants.
K: K is a variable used to represent various constants and parameters in the context of chemical processes and principles. It is a versatile term that appears in multiple areas of chemistry, including the study of gas behavior, reaction kinetics, chemical equilibrium, and thermodynamics.
K[A]^m[B]^n: k[A]^m[B]^n is a mathematical expression used to represent the rate law in chemical kinetics. The rate law describes the relationship between the reaction rate and the concentrations of the reactants involved in the reaction.
M: M is a widely used term in chemistry that represents various important concepts, including molarity, stoichiometry, effusion and diffusion, rate laws, and precipitation and dissolution. This versatile term is crucial for understanding and applying fundamental chemical principles across multiple topics in the field of chemistry.
M s^{-1}: M s^{-1} is a unit used to express the rate of change, specifically the rate of a chemical reaction. It represents the change in the amount or concentration of a substance per unit of time, with 'M' denoting the unit of measurement for the substance (typically moles per liter) and 's^{-1}' representing the inverse of time (per second).
M^{-2}s^{-1}: $M^{-2}s^{-1}$ is a unit of measurement that represents the inverse square of a quantity per unit of time. This term is commonly used in the context of rate laws, which describe the relationship between the concentration of reactants and the rate of a chemical reaction. The exponent $-2$ indicates that the quantity being measured is inversely proportional to the square of the unit, while the exponent $-1$ on the time unit (seconds) suggests that the quantity is measured per unit of time.
Method of initial rates: The method of initial rates is a technique used to determine the rate law of a chemical reaction by measuring the initial rate of reaction for different starting concentrations of reactants. This method allows for the determination of the order of reaction with respect to each reactant.
Method of Initial Rates: The method of initial rates is a technique used in chemical kinetics to determine the rate law and rate constant for a chemical reaction. It involves measuring the initial rate of a reaction at different initial concentrations of the reactants to establish the relationship between the rate and the concentrations of the reactants.
N: The variable 'n' is a fundamental unit used in various contexts in chemistry, representing the amount or quantity of a substance. It is a key parameter in understanding stoichiometric relationships, gas laws, and reaction kinetics.
Overall reaction order: Overall reaction order is the sum of the exponents of the concentration terms in a rate law equation. It indicates how the rate of reaction depends on the concentration of reactants.
Rate constant: The rate constant, often denoted as $k$, is a proportionality factor in the rate equation that relates the reaction rate to the concentration of reactants. Its value is specific to a particular reaction and changes with temperature.
Rate Constant: The rate constant is a measure of the speed or rate at which a chemical reaction occurs. It is a fundamental parameter that describes the intrinsic reactivity of the reactants and the reaction mechanism, and it is an essential component in understanding and predicting the kinetics of chemical processes.
Rate equations: Rate equations are mathematical expressions that describe the rate of a chemical reaction as a function of the concentration of reactants. They help determine the speed at which reactants convert to products.
Rate Law: The rate law is an equation that describes the relationship between the rate of a chemical reaction and the concentrations of the reactants. It is a fundamental concept in chemical kinetics that helps quantify and predict the speed of a reaction under specific conditions.
Rate laws: Rate laws express the relationship between the rate of a chemical reaction and the concentration of its reactants. They are typically written in the form: $rate = k[A]^m[B]^n$, where $k$ is the rate constant, and $[A]$ and $[B]$ are the concentrations of reactants.
Rate-Determining Step: The rate-determining step is the slowest elementary step in a reaction mechanism that controls the overall rate of the chemical reaction. It is the step that limits the speed at which the reaction can proceed and is the crucial factor in determining the reaction rate.
Reaction mechanism: A reaction mechanism describes the step-by-step sequence of elementary reactions by which overall chemical change occurs. It provides detailed information on the intermediates, transition states, and energy changes throughout the process.
Reaction Mechanism: A reaction mechanism is the step-by-step sequence of elementary reactions that describes how reactants are transformed into products during a chemical reaction. It provides a detailed understanding of the pathways and intermediates involved in the overall chemical process.
Reaction Order: Reaction order is a measure of how the rate of a chemical reaction changes with the concentrations of the reactants. It describes the relationship between the rate of a reaction and the concentrations of the reactants involved, providing insights into the mechanism of the reaction.
Reaction orders: Reaction orders indicate the power to which the concentration of a reactant is raised in the rate law expression. They help determine how changes in concentration affect the reaction rate.
Zero-Order Reaction: A zero-order reaction is a chemical reaction where the rate of the reaction is independent of the concentration of the reactants. In other words, the reaction rate remains constant regardless of how much of the reactants are present.
π* antibonding molecular orbital: A π* antibonding molecular orbital is a type of molecular orbital formed when atomic orbitals combine in such a way that their electron density resides outside the internuclear axis, leading to decreased stability of the molecule. It is characterized by having a higher energy level than the original atomic orbitals.
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Glossary
Glossary
12.4 Integrated Rate Laws