Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 14 - The Ideal Gas Law and Kinetic Theory - Problems - Page 386: 56

Answer

1.4

Work Step by Step

Here we use the equation $KE_{Avg}=\frac{1}{2}mv_{rms}^{2}$ to find the ratio of the diffusion rates for the two types of atoms at a fixed temperature. $KE_{Avg}=\frac{1}{2}mv_{rms}^{2}$ $v_{rms}=\sqrt {\frac{2KE_{Avg}}{m}}$ We also know that, $KE_{Avg}=\frac{3}{2}kT$ Therefore, for a fixed temperature average kinetic energy is equal. The ratio of the = $\frac{R_{A}}{R_{B}}=\frac{v_{rms,A}}{v_{rms,B}}=\frac{\sqrt {\frac{2KE_{Avg}}{m_{A}}}}{\sqrt {\frac{2KE_{Avg}}{m_{B}}}}=\sqrt {\frac{m_{B}}{m_{A}}}$ diffusion rates Let's plug known values into this equation. $$\frac{R_{A}}{R_{B}}=\sqrt {\frac{2\space u}{1\space u}}=1.4$$
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