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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].
![Enrichment - Derivation of Integrated Rate Equations For a first-order reaction, the rate is proportional to the first power of [A].](http://images.slideplayer.com./16/5113595/slides/slide_1.jpg "Enrichment - Derivation of Integrated Rate Equations For a first-order reaction, the rate is proportional to the first power of [A].")
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Enrichment - Derivation of Integrated Rate Equations 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.
![Enrichment - Derivation of Integrated Rate Equations 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.](http://images.slideplayer.com./16/5113595/slides/slide_2.jpg "Enrichment - Derivation of Integrated Rate Equations 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.")
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Enrichment - Derivation of Integrated Rate Equations Rearrange the equation so that all of the [A] terms are on the left and all of the t terms are on the right.
![Enrichment - Derivation of Integrated Rate Equations Rearrange the equation so that all of the [A] terms are on the left and all of the t terms are on the right.](http://images.slideplayer.com./16/5113595/slides/slide_3.jpg "Enrichment - Derivation of Integrated Rate Equations Rearrange the equation so that all of the [A] terms are on the left and all of the t terms are on the right.")
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Enrichment - Derivation of Integrated Rate Equations Express the equation in integral form.
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Enrichment - Derivation of Integrated Rate Equations This equation can be evaluated as:
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Enrichment - Derivation of Integrated Rate Equations Which rearranges to the integrated first order rate equation.
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Enrichment - Derivation of Integrated Rate Equations Derive the rate equation for a reaction that is second order in reactant A and second order overall. The rate equation is:
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Enrichment - Derivation of Integrated Rate Equations Separate the variables so that the A terms are on the left and the t terms on the right.
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Enrichment - Derivation of Integrated Rate Equations Then integrate the equation over the limits as for the first order reaction.
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Enrichment - Derivation of Integrated Rate Equations Which integrates the second order integrated rate equation.
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Enrichment - Derivation of Integrated Rate Equations For a zero order reaction the rate expression is:
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Enrichment - Derivation of Integrated Rate Equations Which rearranges to:
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Enrichment - Derivation of Integrated Rate Equations Then we integrate as for the other two cases:
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Enrichment - Derivation of Integrated Rate Equations Which gives the zeroeth order integrated rate equation.
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Enrichment - Rate Equations to Determine Reaction Order 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.
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![Slide 1 of 61 14-4 Zero-Order Reactions A → products R rxn = k [A] 0 R rxn = k [k] = mol L -1 s -1.](/16/5022734/big_thumb.jpg "Slide 1 of 61 14-4 Zero-Order Reactions A → products R rxn = k [A] 0 R rxn = k [k] = mol L -1 s -1.>")
