College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.3 - Integer Exponents and Scientific Notation - P.3 Exercises: 53

Answer

$4.03*10^{27}$ molecules

Work Step by Step

First, we calculate the volume of the room: $\mathrm{Volume}=\mathrm{depth}*\mathrm{width}*\mathrm{height}=5 \mathrm{m}*10\mathrm{m}*3\mathrm{m}=150 \mathrm{m}^3$ To convert to liters, we multiply by 1000: $150\mathrm{m}^3*1000 \mathrm{liters/m^3}=150000 \mathrm{liters}$ Finally, we use the fact that each 22.4 liters in volume contains an Avogadro's number of molecules: $150000\mathrm{liters}\frac{6.02*10^{23}\mathrm{molecules}}{22.4\mathrm{liters}}\approx4.03*10^{27}$ molecules
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