How to Perform Kinetics calculations with differential and integrated rate laws

How to Perform Kinetics calculations with differential and integrated rate laws

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L ECTURE 2: K INETICS C ALCULATIONS U SING THE D IFFERENTIAL AND I NTERGRATED R ATE L AWS How to do the famous kinetic calculations, applied to 0th, 1st and 2nd order reactions In this lecture you will learn to do the following Determine reaction order from units Determine reaction order from method of initial rates Calculate “k” from rate equation Convert how fast (differential rate equation) into how much (integrated rate equation) using calculus Use integrated rate law to find half lives Use integrated rate law to find extent of reaction First we review the differential rate equation and define the pieces of the rate law: Δ [R ] = rate = [R] x A exp [-Ea/RT] = k [R ] x Δ t rate constant, k Rate From S l o p e r a t e l a w Note that there are four physical parameters in the rate law that determine the rate of reaction: 1. [ ] x concentration and order of reactants and products 2. Ea activation energy 3. T temperature the three factors making up k, the rate constant 4. A pre-exponential factor We will save learning to do calculations involving parameters 2-4 for Lecture 3 when we learn about kinetic theory and concentrate for now on the concentration term, [R ], and how the order of reaction, x. [ R ] x
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Order of Reaction In the rate equation: rate = k [R ] x , x is the order of reaction in the function that describes how concentration affects rate. Example of reaction order: 2 N 2 O 5 ----> 4NO 2 + O 2 rate = k[N 2 O 5 ] This reaction is first order in [N 2 O 5 ] and first order overall . Example of reaction order: 2 N O + O 2 ----> 2NO rate = k[NO][O 2 ] This reaction is first order in NO and in O 2 and second order overall. We will look at three examples of reaction order in this lecture. order rate equation effect of concentration on rate 0 rate = k[R] 0 = k none 1 rate = k[R] 1 rate increases linearly with concentration 2 rate = k[R] 2 rate increases as the square of the concentration Example 1: 0 th order x = 0 so Rate = k [R] 0 = k This means that rate is independent of concentration [R] as is shown below. Note that no matter what the concentration, the slope does not change. 0 th order [ ] t
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1 st order x = 1 Rate = k [R] 1 This means that rate varies with concentration [R] and as we saw in class, follows an exponential function—very fast initial rates and then, at longer times, a very small slope. Example 3: 2 nd order x = 2 Rate = k [R] 2 This means that rate varies with concentration [R] 2 and is most commonly associated with bimolecular collision reactions— what you would traditionally think of as the way a reaction happens Æ A collides with B and makes a product. A+B Æ P. This kind of reaction is actually less likely than you might think, as we will learn when we get to kinetic theory. [ ] t
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How to Perform Kinetics calculations with differential and integrated rate laws

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