AP Chem Kinetics integrated rate laws, half life

Remember order of reaction? Rate = k[A] m [B] n Overall reaction order = m+ n Remember that rate has units of mol L -1 s -1 (M/s)

Two types of rate laws Differential rate law- what we did so far – Shows how the rate of reaction is dependent on concentration (m and n) – Uses initial rates of reaction occurring at varying conc. and sees how the rate changes due to conc. Integrated rate law – Shows how conc. depends on time – Conc. are measured at various times and data is plotted. We see how integrated rate law fits the data (gives us a straight line)

Why do I need to integrate???? The slope of this graph isn’t that useful in predicting concentrations of reactants over long periods of time I can find average rate from entire graph (not super accurate) Or using tangent I can find Instantaneous rate But it would be nice if I had a graph with a linear relationship so at any point on graph I can find conc. or time or make predictions I want to integrate rate to make a linear graph so I have a constant rate. I can then use y=mx+b to make find conc. of reactants at various times Want straight line so we can use y=mx+b to predict information Not all graphs give us a straight line slope so we may need to manipulate to get in y=mx+b form. Zero order, 1 st order, 2 nd order graphs are predictable tangent

Zero order reactions A rxn that is zero order has a rate law in which exponents of all reactants are zero Equation: Rate =k This type of reaction doesn’t depend on concentration of any reactant. The rate is constant. Slope =  [A]  T Rate = k The slope is negative …therefore Slope of line = -k The graph is already linear- I don’t need to manipulate the data to “integrate” the rate

Integrate the zero rate law (to get y= mx +b FORM) y = mx +b FORM [A] t = -kt +[A] 0

1 st order Reaction (probably most impt b/c also deal with ½ life of rxn) Any rate law when the sum of the exponents is a first order reaction Equation: rate = k[A] So as reaction progresses, the amount of A decreases and the rate decreases

Integrate data to linearize graph… so we can have it in y=mx+b form Can use to get info at any point Can find avg rate, instaneous rate, This one is an integrated graph f or 1 st order rxn. Plot ln[A] vs time

Integrated first order law y = mx+ b ln[A] t = -kt + ln[A] 0 kt = ln ( [A] 0 /[A] t )

Integrated rate law example A certain first order reaction has a rate constant of 4.5 x s -1. How much of 50.0 x molar sample will be left after 75.0s?

Integrated rate law example 2 The decomposition of a M sample of N 2 O 5 is first order and has a k of 6.93x10 -3 s -1. What will the concentration of N 2 O after 150s have passed?

2 nd order reactions Equation: rate = k[A] 2 or k[A][B] Integrated: 1/[A] t = kt + 1/[A] 0 Slope = +k

Recap order Rate lawIntegrated rate lawStraight line plot O Rate = k [A] t = -kt +[A] 0 [A] vs t 1 Rate = k[A] ln[A] t = -kt +ln[A] 0 ln[A] vs t 2 Rate = k[A] 2 1/[A] t = kt + 1/[A] 0 1/ln[A] vs t

Stop video here Re-Start at 19:35 to finish ½ life part of PowerPoint

Last Topic in Kinetics Half – life = amount of time it takes for half the sample to decay (if talking about radioactivity) or be consumed by the reaction (reaction rates) Radioactivity is not on ap test so we will only talk about ½ life as it pertains to reaction rates

½ life only applies to 1 st order reactions 1 st order reactions Notice the graph is before integrated form Half life = t 1/2 t 1/2 =0.693/k

Example 1 What is the half life of a reaction that has a first order rate constant of 2.6 x s -1 ?

Example 3 In the first order reaction D products its is found that 90% of the original amount of reactant D decomposes in 140 minutes. Find the half of the decomposition reaction.