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

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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 La tm mol K = b) what is the root mean square speed of the molecules (m/s)? 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 Ms mol um 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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Problem Set #9 -2- 2) At an altitude of 15 km the temperature is 217K and the pressure is 12.1 kPa. a) What is the mean free path of N 2 molecules (in nm)? () ( ) ( ) 23 1 2 3 25 8.314 217 From Eq. 27.51, 2 2 6.022 10 0.45 12.1 10 3.89 10 A J K RT mol K l NP m o l n m P a J l σ ⎛⎞ ⎜⎟ ⎝⎠ == ×× 2 nm Pa 1 Pa × 1 J 3 / m 9 10 1 nm m × 3 389 nm = b) How many collisions per second does an N 2 molecule make? 1/2 23 27 2 5 2 9 from the equation between 27.50 and 27.51 8 1.38 10 / 217 8 is given by Eq. 27.42, 28 1.66 10 / 1.64 10 405 / 405 / 1.04 389 10 A B A u l z JK K kT uu m amu kg amu m um s s u ms z lm π = × = × 91 10 s 3) (McQ&S, 27-23) 2 2 0 /2 0 2 0 From problem 27-21, ( ) We find probabilities by integrating over the speeds of interest. .. To solve this integral, let ; 2 B B mu k T B mu k T B u BB m F u du ue du m pu u ue du mu mu xd x d u = ≥= −− 2 0 0 Now replace the x and solve for the limits of integration. ..
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This homework help was uploaded on 04/13/2008 for the course CHEM 444 taught by Professor Jameslis during the Spring '08 term at University of Illinois at Urbana–Champaign.

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

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