Answered: Age of a tree/fossils can be measured…

Chemistry: The Molecular Science

5th Edition

ISBN:9781285199047

Author:John W. Moore, Conrad L. Stanitski

Publisher:John W. Moore, Conrad L. Stanitski

Chapter11: Chemical Kinetics: Rates Of Reactions

Section: Chapter Questions

Problem 37QRT: Radioactive gold-198 is used in the diagnosis of liver problems. 198Au decays in a first-order...

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Age of a tree/fossils can be measured by looking at the remaining Carbon-14 in a sample. C-14 has a half-life of 5720 years and this is a first-order reaction. If a piece of wood has converted 88.5% of the carbon-14, then how old is it?

Expert Solution

Step 1

Half life of C-14 = 5720 years

As the reaction follow first order kinetics.,

Rate constant, K = 0.693/t_1/2 = 0.693/5720 years = 1.211 × 10^-4yr^-1

Let the amount of C-14 Intially,A_o = 100 grams

Amount of converted carbon = 88.5 % = 88.5 gram

Amount of carbon remained, A_t = 100 - 88.5 = 11.5 gram

We have to find the time taken,t = ?

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