Answered: ou start with 925 grams of a specific…

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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Question

You start with 925 grams of a specific radioactive isotope. The half life is 73 days. How many milligrams of this isotope remain after exactly one year? Report to 3 significant figures.

Expert Solution

Step 1: Introduction to first order reaction

The radioactive decay follows first-order kinetics.

The integrated rate law for the first-order reaction is -

$K space equals space fraction numerator 2.303 over denominator t end fraction space cross times space log space fraction numerator left square bracket A subscript 0 right square bracket over denominator left square bracket A subscript t right square bracket end fraction$

where K = first-order rate constant

t = time

A₀ = initial amount or initial concentration

A_t = final amount or final concentration.

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