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The reaction $X \longrightarrow Y$ shown here follows first-order kinetics. Initially different amounts of X molecules are placed in three equal-volume containers at the same temperature. (a) What are the relative rates of the reaction in these three containers? (b) How would the relative rates be affected if the volume of each container were doubled? (c) What are the relative half-lives of the reactions in (i) to (iii)?

(a) ratio of rates: (i):(ii):(iii) $=4: 3: 6$(b) absolute reaction rates of each would be halved but the relative rates are the same(c) half-life (i) $=$ half-life (ii) $=$ half-life (iii)

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

Carleton College

University of Kentucky

Brown University

Lectures

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In probability theory, the conditional probability of an event A given that another event B has occurred is defined as the probability of A given B, written as P(A|B). It is a function of the probability of B, the probability of A given B, and the probability of B.

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In chemistry, kinetics is the study of the rates of chemical reactions. The rate of a reaction is the change in concentration of a reactant over time. The rate of reaction is dependent on the concentration of the reactants, temperature, and the activation energy of the reaction.

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The reaction $\mathrm{X} \…

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$3 \mathrm{~A} \rightarrow…

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Hello. So today we're going to be looking at a situation where we have a first order reaction of X becoming why. And since this is a first order reaction, the rate law would be that the rate is equal. Teoh a reaction constant times the concentration of X And so we have three containers and one of them contains eight that all three containers were the same. Volume one container contains eight molecules of X. The second one contains six molecules of X, and the third one contains 12 molecules of X. So what would the relative rates be? Well, the rate Peter is determined by the concentration. The K for all of them is the same. So we just have to look at the concentrations, so the ratio would be eight 26 2, 12 But we can simplify that by dividing everything by two to be four, 23 26 Now imagine what would happen if we doubled the volume of each of these containers. Well, what happened would be that the concentration would be halved and so would the rate. But since we're making all three containers bigger, that means that the ratio of their rates will still be the same because this will still be 43 3 to 6 because I'll love their concentrations are changing in the same great ratio. So now let's consider what air there half lifes. While the half life for a first order reaction is given as half, life is equal to the natural log of two over K. So has nothing to do with concentration. All three of them have the same rate constant. So that means that all three of them have the same half life there. Half lifes are all the scene because for a first order reaction, half light does not depends on the concentration.

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