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Integrated Rate Laws 02/13/13
AP Chemistry Integrated Rate Laws 02/13/13
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Integrated vs. Differential Rate Laws
Differential Rate Law: A rate law that expresses how the rate depends on the concentration of the reactants. (Often simply called “a rate law.”) Integrated Rate Law: A rate law that expresses how the concentrations depend on time.
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First Order Rate Laws Consider the reaction: aA products
The rate is -∆[A]/ ∆t = k[A]n Since it is often useful to consider the change in concentration in terms of time, the following law is derived from the previous equation by some sort of miracle. ln[A] = -kt + ln[A]0 ln = natural log, k = rate constant, t = time, [A] is at time t, [A]0 is at time 0 (the start of the experiment).
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ln[A] = -kt + ln[A]0 This equation shows how the concentration of A depends on time. If the initial concentration and k are known, the concentration of A at any time can be calculated.
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ln[A] = -kt + ln[A]0 Note that the form of this equation is y = mx + b. y = ln[A] x = t m = -k b = ln[A]0 Therefore, plotting the natural log of concentration vs. time will always produce a straight line for a first order reaction. If the plot is a straight line, the reaction is first order; if the plot is not a straight line, the reaction is not first order.
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ln[A] = -kt + ln[A]0 The integrated rate law can also be expressed in terms of a ratio of [A] and [A]0. ln([A]0/A]) = kt
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First Order Rate Laws Consider 2N2O5(g) 4 NO2(g) + O2(g)
Using this data, verify that the rate law is first order and calculate k. [N2O5] (mol/L) Time (s) 0.1000 0.0707 50 0.0500 100 0.0250 200 0.0125 300 400
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-2 -4 -6 100 200 300 400
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First Order Rate Laws Since the reaction is first order, then the slope of the line is equal to -k = ∆y/ ∆x = ∆(ln[N2O5])/ ∆t Since the first and last points are exactly on the line, we will use them to calculate slope. k = -(slope) = 6.93 x 10-3 s-1
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First Order Rate Law Using the previously obtained data, calculate [N2O5] at 150 seconds after the start of the reaction.
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Half Life of a First Order Reaction
Half Life: the time required for a reactant to reach half its original concentration. ln([A]0/A]) = kt By definition at t =½: [A] = [A]0/2 ln(2) = kt½ t½ = 0.693/k
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Half Life for First Order Reaction
A certain first order reaction has a half-life of 20.0 minutes. Calculate the rate constant for this reaction. How much time is required for this reaction to be 75% complete? ln([A]0/A]) = kt If 75% of the reaction is completed then 25% of the reactants still remain, [A]/[A]0 = .25 and [A]0/[A] = t½ = 0.693/k k=.03465
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Calculate the rate constant. Calculate the half life.
The decomposition of A is first order, and [A] is monitored. The following data are recorded: Calculate the rate constant. Calculate the half life. Calculate [A] when t = 5 min. How long will it take for 90% of A to decompose? T (min) 1 2 4 [A] 0.100 0.0905 0.0819 0.0670
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NH4+(aq) + NO2-(aq) N2(g) + 2H2O(l)
Reaction Rate: Concentration NH4+(aq) + NO2-(aq) N2(g) + 2H2O(l)
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The reaction 2ClO2 (aq) + 2OH- (aq) ClO3- (aq) + ClO2- (aq) + H2O (l) was studied with the following results. Exp [ClO2] [OH-] Rate (M/s) (a) Determine the rate law (b) Calculate the value of the rate law constant
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