A volcanic eruption melts a large chunk of rock, and all gases are expelled. After cooling, argon-40 accumulates from the ongoing decay of potassium-40 (half-life of potassium-40 is 1.25 x 109 yr) in the rock. When a piece of rock is analyzed, it is found to contain 1.38 mmol of potassium-40 and 1.14 mmol of argon-40. How long ago did the rock cool?

Half-life of potassium-40 = 1.25 x 109 year A = The final amount of 40 K left = 1.38 mmol A0 = Initially 40 Ar present = 1.38 +1.14 mmol = 2.52 mmol How long ago did the rock cool = t =?t1/2 = 1.25 × 109 Year We know that rate constant K = 0.693 / t 1/2 K = (0.693 / (1.25 × 109 Year)) = 5.544 × 10-10 Year-1 Also we know that, K = (2.303 / t) log [A0] / [ A ] To calculate time rearranging above equation becomes, t = (2.303 / (5.544 × 10-10)) log (2.52 / 1.14) t = 1.4310 × 109 years Result: t = 1.4310 × 109 years long ago did the rock cool.

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Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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A volcanic eruption melts a large chunk of rock, and all gases are expelled. After cooling, argon-40 accumulates from the ongoing decay of potassium-40 (half-life of potassium-40 is 1.25 x 10⁹ yr) in the rock. When a piece of rock is analyzed, it is found to contain 1.38 mmol of potassium-40 and 1.14 mmol of argon-40. How long ago did the rock cool?

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