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Integrated Rate Law – First Order (25.5)

Integrated Rate Law – First Order (25.5). Differential form of rate equation can be combined with rate law to give a relation between concentration and time First-order reactions (elementary) only involve a single reactant to first-order

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Integrated Rate Law – First Order (25.5)

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  1. Integrated Rate Law – First Order (25.5) • Differential form of rate equation can be combined with rate law to give a relation between concentration and time • First-order reactions (elementary) only involve a single reactant to first-order • Integrated rate law shows the concentration of A decays exponentially with time • Linearized plots can be used to determine order • Natural logarithm is used to get time out of the exponent • If a plot of ln[A] vs. time gives a line, then the reaction is first order and the slope of the line is related to the rate constant • Half-life is a measure of how long it takes for the concentration of reactant to decay to 50% and can also be used to indicate order of reaction • Half-life of first-order reaction is independent of concentration of reaction

  2. Integrated Rate Law – Second Order (25.5) • One type of second-order reaction (elementary) only involves one reactant • Type I second-order reactions show that time is related to the inverse of [A] • The half-life of this reaction is dependent on the initial concentration of reactant • If a plot of 1/[A] vs. time is generated and gives a line, then the reaction is second-order and the slope is related to the rate constant • Another type of second-order reaction involves two reactants (Type II) • This integrated rate law involves concentrations of both reactants • This can be reduced to a Type I rate law if [A]0 = [B]0

  3. Temperature Dependence of Reaction Rates (25.9) • Reaction rates are dependent on temperature and this is expressed through the rate constant • Higher temperatures typically mean faster reaction rates • The preexponential factor (A) in the Arrhenius expression is assumed to be temperature independent (thus a plot of ln k vs. 1/T would be linear) • The activation energy (Ea) is the energy needed for the reactants to overcome the reaction barrier • For reversible reactions, the activation energy changes depending on the direction of the reaction • Catalysts increase reaction rate by lowering the activation energy, thus increasing k • If the Arrhenius expression holds, the activation energy of the reaction can be determined from a linear plot (or a two-point formula) • If a plot of ln k vs. 1/T is linear, the slope is equal to –Ea/R

  4. First-Order Reaction

  5. Second-Order Reaction (Type I)

  6. Activation Energy

  7. Activation Energies for Reversible Reactions

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