HW 3C
1. What are the four ideas of the kinetic molecular theory?
a. Gases consist of particles that are in random, rapid motion
b. Kinetic energy of the gas is directly proportional to temperature
c. Gases collide with each other and their container with no loss of energy (elastic)
d. Gas particles occupy no volume relative to the overall volume of the container itself
2. Which two of the ideas in #1 are not technically true?
c&d
3. What is the Van der Waal’s equation? What does it correct for?
[P+ a(n/V)2][V-bn] = nRT It corrects for c & d above
4. Which gas in each pair would deviate most from ideality and why?
a. N2 vs. CO CO because it is polar at the same mass
b. CH3OH vs. O2 CH3OH has H-bonds at the same mass
c. Ne vs. Xe They are both non-polar but Xe is bigger so has more London forces
5. Two equal balloons are made; one with Helium and one with Neon. How much faster does
the Helium balloon deflate compared to the Neon? 2.25 times as much
6. SO2 diffuses 1.5 times as fast as an unknown gas. What is the molar weight of the unknown
gas? 144 g/mole
7. If BH3 is put into one end of a tube marked 0 cm and NF3 is put into the other end marked
100 cm, at what distance mark on the tube do they meet? 69.4 cm
8. What is the RMS speed of O2 gas at STP? 461 m/s
9. What is the RMS speed of Rn gas at STP? 175 m/s
10. You have four gas samples:
a. 1 L H2 at STP
b. 1 L of Ar at STP
c. 1 L of H2 at 27 oC and 760 mm Hg
d. 1 L of He at 0 oC and 900 mm Hg
i) Which sample has the most atoms or molecules? Sample D
ii) Which sample has the least atoms or molecules? Sample C
iii) Which sample has the largest mass? Sample B
iv) Which sample has the largest KE? Sample C
11. Five identical balloons are each filled to the same volume at the same temperature and
pressure but are filled with CO2, O2, He, N2, and CH4.
e. Which has the greatest mass? CO2
f. Compare the KEavg of the molecules in each of the balloons. Explain. They are all the
same as they are at the same T
c. Which should deviate most from ideality? Why? All non-polar so CO2 has largest mass
d. All of the balloons decrease in size over time. Which balloon will be the smallest? Why?
He will effuse through the balloon fastest as it is the smallest
12. CO and CO2 are put in separate containers of the same size and the same temperature. The
pressure of CO gas is 2 atm while the pressure of the CO2 gas is 1 atm.
g. Compare the KEavg of the 2 samples. Explain. KE is the same as both are at same T
h. Which gas has a greater RMS speed? Explain why. CO has smaller mass so moves faster
i. Which container contains a greater number of molecules. Justify your answer. CO is at
same conditions but has 2 atm while CO2 has only 1 atm. The extra pressure must be
coming from extra molecules
13. Two containers each have a volume of 1.0 L at 298 K. Container A has 0.10 moles of N 2 (g)
and container B has 0.10 moles of H2 (g). The average kinetic energy of the N2 (g) molecules
is 6.2 x10-21 J. Assume both gases exhibit ideal behavior.
j. Is the pressure in the container of H2 greater than, less than, or equal to the pressure of the
N2? Justify your answer. Pressure should be the same as all conditions are equal
k. What is the average kinetic energy of the H2 (g) molecules. Justify your answer.
6.2x10-21 J because same temperature means it’s the same KE
a. The molecules of which gas, N2 or H2have the greater average speed? Justify. H2 has
greater speed as they are at the same KE so H2 is less massive so moves faster
b. What change could be made that would decrease the average kinetic energy of the N 2
molecules? Justify. Only way to decrease the KEavg is to lower the Temperature.
c. If the volume of the container of H2 was decreased to 0.50 L at 298 K, what effect would
that have on:
i)
The pressure in the container. Justify. Pressure would double by Boyle’s Law
ii)
The average speed of the H2 molecules. Justify. Speed of the molecules
wouldn’t change as temperature hasn’t changed
14. A rigid 5.0 L cylinder contains 24.5 g of N2 and 28.0 g of O2.
l. Calculate the total pressure, in atm, of the gas mixture in the cylinder at 298 K.
24.5g N2 (1 mole/28 g) = 0.875 moles N2
28 g O2 (1 mole/32 g) = 0.875 moles O2
Ptot = nRT/V = (0.875 + 0.875)(0.0821)(298 K)/5 L = 8.56 atm total
m. The temperature of the gas mixture in the cylinder is decreased to 280 K. Calculate:
i) The mole fraction of N2 in the cylinder
XN2= (0.875)/(0.875+0.875) = 0.50
ii) The partial pressure, in atm, of N2 in the cylinder
4.28 atm N2 at 298 K so
(4.28 atm/298 K) = (x atm)/280 K 4.165 atm
n. If the cylinder develops a pinhole-sized leak and the gases begin to escape, would the ratio
of moles of N2/moles of O2 in the cylinder increase, decrease, or remain the same. Justify
your answer. Ratio should decrease as moles N2 will be less as it is moving faster through
the container than O2