ShmoopTube

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

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

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

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

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

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

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And here are your potential answers:

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

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

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

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

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

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

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

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

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

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

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law and solving a first order ordinary differential equation.

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

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

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

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

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

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

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