12.3 Rate Laws

Reaction kinetics and rate laws 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 reaction orders 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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  The Rate Law | Introduction to Chemistry View original

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  The Rate Law | Introduction to Chemistry View original

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  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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• Rate law 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###
  • $k$ rate constant depends on temperature and reaction nature
  • $[A]$ and $[B]$ concentrations of reactants A and B
  • $m$ and $[n](https://www.fiveableKeyTerm:n)$ reaction orders for reactants A and B
• Rate law predicts reaction rate based on reactant concentrations
• Helps understand reaction mechanism
• Allows determination of rate-determining step in multi-step reaction

Calculation of reaction rates

• Substitute initial concentrations and rate constant into rate law equation
• Example: For reaction $A + B \rightarrow C$, with rate law $Rate = k[A]^2[B]$
  1. Given $[A]_0 = 0.1 M$, $[B]_0 = 0.2 M$, and $k = 0.5 [M^{-2}s^{-1}](https://www.fiveableKeyTerm:M^{-2}s^{-1})$
  2. Calculate $Rate = (0.5 M^{-2}s^{-1})(0.1 M)^2(0.2 M) = 1 \times 10^{-4} [M s^{-1}](https://www.fiveableKeyTerm:M_s^{-1})$
• 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: $\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$
  • Integrated rate law equations allow for calculation of concentrations at any time t

Determination of reaction orders

• Reaction order exponent in rate law for specific reactant
• Determined experimentally by varying one reactant's concentration while keeping others constant
• Methods for determining reaction order
  • Method of initial rates
    • Measure initial reaction rates at different initial reactant concentrations
    • Compare ratio of rates to ratio of concentrations
  • Graphical method
    • 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 $Rate = k[A]^1[B]^2$
• Determine rate constant by substituting rate, concentrations, and orders into known rate law and solving for $k$

Advanced Kinetics Concepts

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