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Enrichment - Derivation of Integrated Rate EquationsPowerPoint Presentation

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].

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

- 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

- Express the equation in integral form.

Enrichment - Derivation of Integrated Rate Equations

- This equation can be evaluated as:

Enrichment - Derivation of Integrated Rate Equations

- Which rearranges to the integrated first order rate equation.

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 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 Equations

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

Enrichment - Derivation of Integrated Rate Equations

- Which integrates the second order integrated rate equation.

Enrichment - Derivation of Integrated Rate Equations

- For a zero order reaction the rate expression is:

Enrichment - Derivation of Integrated Rate Equations

- Which rearranges to:

Enrichment - Derivation of Integrated Rate Equations

- Then we integrate as for the other two cases:

Enrichment - Derivation of Integrated Rate Equations

- Which gives the zeroeth order integrated rate equation.

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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