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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.

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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 equations1
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 equations2
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 equations3
Enrichment - Derivation of Integrated Rate Equations
  • Express the equation in integral form.
enrichment derivation of integrated rate equations5
Enrichment - Derivation of Integrated Rate Equations
  • Which rearranges to the integrated first order rate equation.
enrichment derivation of integrated rate equations6
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:
enrichment derivation of integrated rate equations7
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.
enrichment derivation of integrated rate equations8
Enrichment - Derivation of Integrated Rate Equations
  • Then integrate the equation over the limits as for the first order reaction.
enrichment derivation of integrated rate equations9
Enrichment - Derivation of Integrated Rate Equations
  • Which integrates the second order integrated rate equation.
enrichment derivation of integrated rate equations10
Enrichment - Derivation of Integrated Rate Equations
  • For a zero order reaction the rate expression is:
enrichment derivation of integrated rate equations12
Enrichment - Derivation of Integrated Rate Equations
  • Then we integrate as for the other two cases:
enrichment derivation of integrated rate equations13
Enrichment - Derivation of Integrated Rate Equations
  • Which gives the zeroeth order integrated rate equation.
enrichment rate equations to determine reaction order
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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