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Enrichment - Derivation of Integrated Rate Equations

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

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

  2. 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.

  3. 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.

  4. Enrichment - Derivation of Integrated Rate Equations • Express the equation in integral form.

  5. Enrichment - Derivation of Integrated Rate Equations • This equation can be evaluated as:

  6. Enrichment - Derivation of Integrated Rate Equations • Which rearranges to the integrated first order rate equation.

  7. 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:

  8. 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.

  9. Enrichment - Derivation of Integrated Rate Equations • Then integrate the equation over the limits as for the first order reaction.

  10. Enrichment - Derivation of Integrated Rate Equations • Which integrates the second order integrated rate equation.

  11. Enrichment - Derivation of Integrated Rate Equations • For a zero order reaction the rate expression is:

  12. Enrichment - Derivation of Integrated Rate Equations • Which rearranges to:

  13. Enrichment - Derivation of Integrated Rate Equations • Then we integrate as for the other two cases:

  14. Enrichment - Derivation of Integrated Rate Equations • Which gives the zeroeth order integrated rate equation.

  15. 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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