Chp10_IntRateLaws

Chp10_IntRateLaws - A constant half-life inversely...

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Integrated Rate Laws: 1. First order: Differential form: ] [ ] [ A k dt A d R = - = Integrated forms: (i) 0 ] ln[ ] ln[ A kt A t + - = (ii) kt A A t - = 0 ] [ ] [ ln (iii) kt t e A A - = 0 ] [ ] [ These three equations are all the same, just written in different forms. Form (i) suggests that a plot of ln [A]t vs. t is linear with a slope = –k. Equation (ii) form is particularly useful if the concentration of A, [A] is given as a percentage or fraction of the original amount, [A] 0 ! Can you see why? See P. Exp. 10.3 in text. Half-Life for 1 st order rxn ( τ ): At t = τ , [A] τ = [A] 0 / 2 Thus equation (iii) becomes: τ k e A A - = 0 0 ] [ 2 ] [ which, after rearrangement, leads to: k 2 ln = First order rxns/processes are thus characterized by: Exponential decay of concentration with time, [A] vs. t. A plot of ln[A]t vs time is linear with negative slope (equal to –k).
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Unformatted text preview: A constant half-life inversely proportional to the rate constant. 2. Simple Second-Order Rxns: 2 ] [ ] [ A k dt A d =-Leads to an integrated form: kt A A t + = ] [ 1 ] [ 1 and an expression for the half life: ] [ 1 A k = Second-order reactions are characterized by: Plot of 1/[A] vs time is linear with positive slope (equal to rate constant); A half-life that is not constant (increases as [A] falls). This works the other way around: If a plot of ln[A] vs time is linear with negative slope, then the reaction IS first order; if a plot of 1/[A] vs time is linear with positive slope, the reaction is second order....
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Chp10_IntRateLaws - A constant half-life inversely...

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