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Define half-life. Write the equation relating the half-life of a first-order reaction to the rate constant.

$$t=\frac{\ln 2}{k}$$

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

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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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Define half-life. Write th…

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Write the equations relati…

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Define the half-life of a …

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What does the term half-li…

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What is the approximate ha…

so Ah, half life. You may have heard maybe in the context of, um, atomic decay. So we know that things like for pretty much every type of Adam we know that it decays over time. So the way that we do some sort of carbon dating is that we know how long it takes for carbon to decay. And we can use basically the level of decay in different fossils or different substances in order to determine how much time has passed. Um, since that thing was alive so ah, half life is the time it takes for 1/2 of a total substance to decompose. So for carbon, we know the carbons, half life and the nice thing about the carbons half life is it's constant. So the main thing that you need to know for in AP chemistry course is that a first order reaction has a constant half life. Oh, constant half life. This is really important because there are several problems where it will show you some data and you have to realize that the half light is constant. So we can see that if we start with 100 after 1/2 life, we would have 50 molecule or you can say 100 Adams of whatever after 1/2 left were 50 after another half life, we have 25 and after another half life, we'd have 12.5 and you get the idea. And so the first order reaction, um, equation for 1/2 life is G 1/2. So that's how we write half life in kind of fancy equation ways. T 1/2 equals 0.693 over K. And so this is specifically for a first order reaction. This wouldn't work for any other type of reaction, but we can see that a dozen depend on the concentration any of our reactant. So as long as you have that, um, that rate constant you can solve for your half life and also advice first, if they tell you the half life you can now go back and solve for the rate constant if, and only if again. This is a really important point. You are looking at a first order reaction for ah second order reaction or a zero order reaction. We have a different equation for 1/2 life

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