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AP Chemistry 2.4 Chemical Reaction Rates 8 Views


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Description:

Time to calculate some half-life. And no, you can't only half-pay attention.

Language:
English Language

Transcript

00:04

And here’s your Shmoop du jour, brought to you by carbon dating, the Match.com for

00:09

scientists. We guarantee we’ll find you someone you’ll [Scientist using a tablet for match.com]

00:11

have chemistry with. Okay, here’s today’s question:

00:14

Half-life is a measure of the time it takes for half a sample to decay. Radiometric carbon

00:19

dating uses the half-life of carbon-14 to estimate the age of a carbon-containing objects.

00:24

What is the rate constant for a first-order reaction that has a half-life of 56.0 seconds?

00:30

And here are your potential answers:

00:33

So what is “half-life,” aside from the portion of your time you spend on Netflix? [Woman with feet up watching TV]

00:39

For the sake of this problem, “half-life” is the amount of time it takes for something

00:42

to decrease to half its initial value. As the problem tells us, in chemistry, “half-life”

00:47

often means how long it takes for half of a radioactive sample to decay, but it can [Sample decays and clock ticks]

00:52

also refer to how long it takes for half of some species to be consumed in a regular chemical

00:56

reaction. In this problem, we know that some species [Woman zaps magic stick to a man on stage and he disappears]

00:59

is disappearing following a first-order rate law, and half of it is gone after 56.0 seconds.

01:05

To find the rate constant, we have to remember the equation for half-life: [Girl using calculator]

01:09

t½ = 0.693/k, where k is the first-order rate constant.

01:18

If you don’t remember this equation, you can figure it out by starting with the rate

01:21

law and solving a first order ordinary differential equation.

01:25

That is, if you want to make life way harder for yourself. [Boy studying at his desk]

01:27

Might just want to take the plunge and memorize. So, we need to take this equation and plug

01:32

in the value of the half-life, t½ or half-life= 56.0 seconds. Solving

01:38

for k, we find that the rate constant equals 0.0124 per second.

01:42

So that means that A is the correct answer. Now quick, head over to CarbonDating.com before [Scientist using tablet]

01:46

you have your half-life – we mean mid-life – crisis.

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