Chemistry: Molecular Approach (4th Edition)

Published by Pearson
ISBN 10: 0134112830
ISBN 13: 978-0-13411-283-1

Chapter 20 - Exercises - Page 973: 48

Answer

$1.3\,\mu g$

Work Step by Step

$t=24\,h+9\,h= 33\,h$ $N_{0}=1.5\,\mu g$ $t_{1/2}=8\,days=8\times 24\,h=192\,h $ $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{192\,h}=3.609375\times10^{-3}\,h^{-1}$ Recall: $\ln \frac{N_{t}}{N_{0}}=-kt$ $\implies \ln \frac{N_{t}}{1.5\,\mu g}=-3.609375\times10^{-3}\,h^{-1}\times33\,h=-0.11911$ $\implies \frac{N_{t}}{1.5\,\mu g}=e^{-0.11911}=0.88771$ $\implies N_{t}=1.5\,\mu g\times0.88771=1.3\,\mu g$
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