Page 210 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 13] KINETIC MOLECULAR THEORY 199

masses of molecules could be prepared with the naturally occurring mixture. Naturally occurring fluorine
exists 100% as 19 F, and molecules of its gaseous compound with uranium, UF 6 , will have two different
masses, corresponding to 235 UF 6 and 238 UF 6 . Uranium has been separated into its isotopes by repeated
effusion of UF 6 through towers of porous dividers. Each process enriches the individual isotopes a little, and
very many repetitions are required to get relatively pure isotopes.

13.9. Calculate the ratio of rates of effusion of 238 UF 6 and 235 UF 6 . Fluorine is 100% 19 F.
Ans. The masses of the molecules are 352 and 349 amu. The relative rates of effusion are

352
= 1.004
349
The molecules of 235 UF 6 will travel on average 1.004 times as fast as those of 238 UF 6 .
13.10. List the different molecular masses possible in UCl 3 with 238 U and 235 U as well as 35 Cl and 37 Cl.
35
35
Ans. 238 U( Cl) 3 343 amu 235 U( Cl) 3 340 amu
35
37
37
238 U( Cl) 2 ( Cl) 345 amu 235 U( Cl) 2 ( Cl) 342 amu
35
238 35 37 347 amu 235 35 37 344 amu
U( Cl)( Cl) 2 U( Cl)( Cl) 2
238 37 349 amu 235 37 346 amu
U( Cl) 3 U( Cl) 3
2
1
13.11. What possible complications would there be in trying to separate hydrogen into H and H by gaseous
diffusion?
1
2
2
1
Ans. Hydrogen occurs as diatomic molecules, and it would be easy to separate H 2 , H H, and H 2 , but not
2
the individual atoms. There would be very little H 2 since the heavy isotope accounts for only 0.015% of
naturally occurring hydrogen atoms.
Supplementary Problems
Total volume of gas molecules
13.12. (a) Is the ratio
Volume of gas sample
smaller for a given sample of gas at constant pressure at 300 K or at 400 K? (b) Will the gas exhibit more ideal
behavior at 300 K or at 400 K?
Ans. (a) The ratio is smaller at 400 K. The volume of the molecules themselves does not change appreciably
between the two temperatures, but the gas volume changes according to Charles’ law.
(b) Since the gas volume is larger at 400 K, the gas molecules are farther apart at that temperature and
exhibit lower intermolecular forces. The gas is therefore more ideal at the higher temperature.

Total volume of gas molecules
13.13. (a) Is the ratio
Volume of gas sample
smaller for a given sample of gas at constant temperature at 1.00 atm or at 2.00 atm? (b) Will the gas exhibit more
ideal behavior at 1.00 atm or at 2.00 atm?
Ans. (a) The ratio is smaller at 1.00 atm. The volume of the molecules themselves does not change appreciably
between the two pressures, but the gas volume changes according to Boyle’slaw.
(b) Since the gas volume is larger at 1.00 atm, the gas molecules are farther apart at that temperature, and
exhibit lower intermolecular forces. The gas is therefore more ideal at the lower pressure.

13.14. (a) Calculate the average kinetic energy of O 2 molecules at 1.00 atm and 300 K. (b) Does the pressure matter?
(c) Does the identity of the gas matter?
3
Ans. (a) KE = kT = 1.5[1.38 × 10 −23 J/(molecule·K)](300 K) = 6.21 × 10 −21 J
2
(b) and (c) The pressure and the identity of the gas do not matter.