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# Enrichment - Derivation of Integrated Rate Equations - PowerPoint PPT Presentation

Enrichment - Derivation of Integrated Rate Equations. For a first-order reaction, the rate is proportional to the first power of [A]. . Enrichment - Derivation of Integrated Rate Equations.

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Enrichment - Derivation of Integrated Rate Equations

• For a first-order reaction, the rate is proportional to the first power of [A].

• In calculus, the rate is defined as the infinitesimal change of concentration d[A] in an infinitesimally short time dt as the derivative of [A] with respect to time.

• Rearrange the equation so that all of the [A] terms are on the left and all of the t terms are on the right.

• Express the equation in integral form.

• This equation can be evaluated as:

• Which rearranges to the integrated first order rate equation.

• Derive the rate equation for a reaction that is second order in reactant A and second order overall.

• The rate equation is:

• Separate the variables so that the A terms are on the left and the t terms on the right.

• Then integrate the equation over the limits as for the first order reaction.

• Which integrates the second order integrated rate equation.

Enrichment - Derivation of Integrated Rate Equations

• For a zero order reaction the rate expression is:

• Which rearranges to:

• Then we integrate as for the other two cases:

• Which gives the zeroeth order integrated rate equation.

• Plots of the integrated rate equations can help us determine the order of a reaction.

• If the first-order integrated rate equation is rearranged.

• This law of logarithms, ln (x/y) = ln x - ln y, was applied to the first-order integrated rate-equation.