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PS9_08-Solution - Chem 444 B Homework Set#9 Solutions DUE...

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Problem Set #9 -1- Chem 444 B Homework Set #9 - Solutions DUE: Friday, April 11, 2008 1) A 1.0L glass bulb contains 1.0x10 23 H 2 molecules. If the pressure exerted by the gas is 100 kPa… a) what is the temperature (K) of the gas? 3 Solve for T using the ideal gas equation: 100 10 Pa PV T nR × = = 5 1 1.01 10 atm Pa × × ( ) 23 1.0 1.0 10 L molecules × 23 1 6.022 10 mol molecules × × 72.6 0.0821 K L atm mol K = b) what is the root mean square speed of the molecules (m/s)? ( ) 1/ 2 1/2 1/ 2 2 5 2 3 8.314 72.6 3 From Eq. 27.14, 9.06 10 0.002 952 / rms rms J K RT m mol K u kg M s mol u m s = = = × = c) Would the temperature be different if the molecules were O 2 ? Why/Why not? The temperature follows the ideal gas law and does not depend on molecular weight. The parameters P, V and n are given to us in the problem, so the temperature will be the same regardless of the substance used d) Would the root mean square speed be different if the molecules were O 2 ? Why/Why not? The root mean square speed does depend on molecular weight, and is inversely proportional to it (as shown in Eq. 27.14). Therefore, since O 2 is heavier than H 2 , it will have a smaller root mean square speed.
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