AP Chemistry
Unit 3- Homework Problems
Gas Laws and Colligative Properties
STP
1. What is standard pressure for each of the following: atm, mm Hg, Torr, kPa, PSI
1 atm = 760 mm Hg = 760 torr = 101 kPa = 14.7 psi
2. Convert each of the following:
a. 700 mm Hg to atm 0.92 atm
b. 1.5 atm to Torr
1140 Torr
c. 97 kPa to PSI
14.1 psi
d. 750 Torr to mm Hg
750 mm Hg
3. What is a barometer and how does it work? Measures atmospheric pressure. Air pressure
presses down on a pool of mercury that is pushed up an evacuated
4. What pressure is on this open-ended manometer? 810 mm Hg (50 + 760)
50 mm
5. What would the pressure be if #4 was a closed-end vacuum manometer? 50 mm Hg
6. What is standard temperature? 0 oC or 273 K
7. How is the Kelvin scale different from the Celcius and Fahrenheit scale? There are no
negative numbers. Zero on the Kelvin scale is the lowest you can go.
8. Why is the Kelvin scale called the “absolute” scale? Zero on the Kelvin scale is as low as you
can go. Zero means zero.
Pressure and the Atmosphere
1. What is the relationship between altitude and atmospheric pressure? As altitude increases,
pressure decreases.
2. Why does it take longer to cook food in Denver than in Palatine? There is less atmospheric
pressure in Denver due to the high altitude. Thus, it takes less temperature to get water’s
vapor pressure to equal atmospheric pressure. Thus, water boils at a lower temperature and
thus food takes longer to cook.
3. How does a pressure cooker work? Artificially increases atmospheric pressure above 1 atm.
Thus water must get hotter for VP to equal AP. Thus water boils at a higher temperature and
thus food cooks faster.
4. How far under water do you have to go to increase pressure by 1 atm? About 30 feet
5. What are “The Bends”? At very low depths underwater pressure is extremely high. The N2
you normally breathe in air usually goes in and out of the lungs without being absorbed by the
bloodstream. At higher pressures, due to Henry’s Law, the solubility of the gases increases
and thus your bloodstream has N2 gas in it. When you surface, the pressure decreases and the
solubility decreases. Thus you have N2 (g) coming out of your bloodstream. Because your
blood goes everywhere in your body, N2 (g) is bubbling out of your brain, heart, organs, and
anywhere else blood goes. This causes massive problems and could kill you.
Gas Laws
1. A gas is at 10 L and 700 mm Hg. What is the volume at 350 mm Hg? 20 L
2. A gas is at 80 mL and 75 kPa. What is the pressure at 50 mL? 120 kPa
3. A gas is at 2.4 L and 25 oC. What volume is the gas at 50 oC? 2.60 L
4. A gas is at 400 mL and 15 oC. What temperature (oC) will cause the gas to be 100 mL? 72 K
or -201 oC
5. A gas is at 2.3 atm and 0oC. What pressure will cause the gas to be -50 oC? 1.88 atm
6. A gas is at 18 psi and 20 oC. What temperature will cause the gas to be 50 psi? 814 K or 541
o
C
7. A gas has 2.4 moles and 5 L. How many moles will cause the gas to be 8 L? 3.4 moles
8. A gas has 1.7 moles and 350 mL. How many mL will the gas occupy if it is 7.8 moles
instead? 1606 mL
9. A gas has 5.4 L at 800 mm Hg and 20 oC. What volume will the gas occupy if the pressure
drops to 600 mm Hg while the temperature increases to 80 oC? 8.67 L
10. A gas has 650 mL at 15 oC and 3.4 atm. What pressure will the gas be if the volume
increases to 1000 mL while the temperature drops to -20 oC? 1.94 atm
11. A gas has 400 mL at 5 oC and 6.5 psi. What temperature will the gas be if the volume is
dropped to 200 mL while the pressure is increased to 20 psi? 428 K or 155 oC
12. For each of the questions above, state whether the gas law is: Charles’, Gay-Lussac’s,
Boyle’s, Avagadro’s, or Combined.
1. Boyles
2. Boyles
3. Charles
4. Charles
5. Gay-Lussac
6. Gay-Lussac
7. Avagadro’s
8. Avagadro’s
9. Combined
10. Combined
11. Combined
13. Write the Ideal Gas Law. What is the value for R? What are the units of R?
PV = nRT R = 0.0821 Latm/molK
14. What is the pressure on an ideal gas if 0.25 moles of it occupies 3 L at 300 K? 2.05 atm
15. What volume does 50 grams of CO2 occupy if it is at 0oC and 700 mm Hg? 27.65 L
16. How many grams of CH4 are present if 300 mL of it is at 120 kPa and -25 oC? 0.28 grams
17. What is the density of H2 gas at STP? 0.089 g/L
18. What is the density of air (assume 80% N2 and 20% O2) at STP? 1.285 g/L
19. What is the density of Xe gas at 22 oC and 740 mm Hg? 5.27 g/L
20. What is the molecular weight of a gas if 2.3 grams of it occupy 230 mL at a pressure of 750
mm Hg and a temperature of 75 oC? 290 g/mole
21. A gas is 11.8% C, 69.6% Cl and 18.6% F. If 0.107 grams of it fills a 458 mL flask at 25 oC
at a pressure of 21.3 mm Hg, what is the molecular formula of the compound?
Empirical CCl2F = 102 g/mole
MW = 204 so molecular = C2Cl4F2
22. A gas is 25.2% S and 74.8% F. If 0.0955 g are put in an 89 mL flask at 45 oC and a pressure
of 83.8 mm Hg, what is the molecular formula of the gas?
Empirical SF5 = 127.1 g/mole
MW = 254 so molecular = S2F10
23. State Dalton’s Law of Partial Pressures. Ptotal=  Pindividual
24. A container has 0.5 atm of H2, 2.5 atm of He, and 3 atm of O2. What is the Ptotal in the
container? Ptotal = 0.5 + 2.5 + 3 = 6 atm
25. A container has 10 grams of N2, 100 grams of Xe, and 42 grams of Ar. What is the Ptot in
the container if the volume is 4 L and the temperature is 50 oC?
nN2 = 0.357 moles nXe = 0.762 moles
nAr = 1.053 moles
ntotal = 2.17 moles
Ptotal = 14.4 atm
26. A container has 20 grams of O2, 40 grams of CH4, and 10 grams of He at a Ptot of 600 mm
Hg. What is the partial pressure of each gas?
nO2 = 0.625 moles nCH4 = 2.5 moles
nHe = 2.5 moles
ntotal = 5.625 moles
PO2 = (0.625/5.625)* 600 mm Hg = 66.7 mm Hg
PCH4 = (2.5/5.625)* 600 mm Hg = 266.7 mm Hg
PHe = (2.5/5.625)* 600 mm Hg = 266.7 mm Hg
27. Which of the following gases would be nearly impossible to collect over water? Why?
N2, HCl, NH3, Cl2 HCl and NH3 would be nearly impossible to collect over water because
they are soluble in water. They will dissolve in it to make a solution so wouldn’t come out
the other end.
28. Hydrogen gas is collected over water at 15 oC. If the gas was collected at 800 mm Hg
atmospheric pressure, what pressure of H2 gas was collected?
VPH2O at 15 oC = 12.8 mm Hg so PH2 = 800 -12.8 = 787.2 mm Hg
29. Oxygen gas is collected over water at 22 oC. If the gas was collected in a 250 mL container
at 740 mm Hg atmospheric pressure, how many grams of oxygen were collected?
VPH2O at 19.8 mm Hg so PO2 = 740 – 19.8 = 720.2 mm Hg
0.313 grams of O2
Kinetic Molecular Theory
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.
a. Which has the greatest mass? CO2
b. 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.
a. Compare the KEavg of the 2 samples. Explain. KE is the same as both are at same T
b. Which gas has a greater RMS speed? Explain why. CO has smaller mass so moves faster
c. 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
Units of Concentration
1. What are the definitions of each of the following units of concentration (be specific with
solute, solvent, solution, etc.)
a. Molarity M = moles solute/L solution
b. Molality m = moles solute/kg solvent
c. Mole Fraction = moles solute/total moles
d. Mass % (g solute/ total grams) * 100%
e. PPM
g solute/1,000,000 g solvent
or mg/L
f. PPB
g solute/1,000,000,000 g solvent
or mg/kL
2. Convert a 3 m solution of CH3OH to mole fraction. 0.0512 mole fraction
3. Convert a 34% solution of NaCl to molality. 8.81 m
4. Convert a 5.6 PPM solution of Li+ to mass %. 0.00056%
5. You dissolve 25 grams of C10H16O in 350 mL of C2H5OH (density 0.785 g/mL). Calculate the
molality, mole fraction, and mass %.
m = 0.164 moles/0.27475 kg = 0.599 m
mole fraction = (0.164)/(5.97+0.164) = 0.267
mass % = (25)/(25+274.75)*100% = 8.34%
6. Concentrated HCl is 12 M and has a density of 1.18 g/mL. Calculate the molality and mass
% of the HCl in the solution.
m = 12 moles/0.742 kg H2O = 16.2 m
mass % = 438 g/1180 g total = 37.1%
7. Concentrated H2SO4 is 95% acid and has a density of 1.84 g/mL. What is the molality and
molarity of the solution?
m = 0.968 moles/0.005 kg = 194 m
M = 0.968 moles/0.0543 L = 17. M
8. What is the M of a solution that has 2.5 moles of C2H5OH dissolved in 2500 mL of solution?
1M
9. What is the M of a solution that has 100 grams of Na2CO3 dissolved in 475 mL of solution?
1.99 M
10. How many grams of K3PO4 must be dissolved in 250 mL total to make a 0.75 M solution?
39.8 g
11. How many mL are needed to dissolve 35 grams of CaCl2 into a 0.025 M solution? 12,600
mL
12. What is the concentration of each of the ions in each of the following solutions:
a. 0.50 M KI
[K+1] = 0.50 M
[I-1] = 0.50 M
b. 1.25 M Li2SO4 [Li+1] = 2.50 M
[SO4-2] = 1.25 M
c. 0.68 M Na3PO4 [Na+1] = 2.04 M
[PO4-3] = 0.68 M
d. 0.25 M Al2(SO4)3
[Al+3] = 0.50 M
[SO4-2] = 0.75 M
13. If 20 mL of 6 M HCl is diluted to a total volume of 100 mL, what is the new concentration?
1.2 M
14. If 127 mL of 0.125 M H2SO4 needs to be diluted to 0.057 M, what is the new volume? 279
mL
15. If 100 mL of 2.5 M solution A is mixed with 100 mL of 1.6 M solution B, what is the new
concentration of each solution?
Solution A = (2.5 M)(100/200) = 1.25 M
Solution B = (1.6 M)(100/200) = 0.80 M
16. If 57.2 mL of 0.125 M solution A is mixed with 32.9 mL of 0.085 M solution B, what is the
new concentration of each solution?
Solution A = (0.125 M)(57.2/90.1) = 0.0794 M
Solution B = (0.085 M)(32.9/90.1) = 0.0310 M
Saturation Curves
1. What is the solubility of NH4Cl at 40 oC? @50 g NH4Cl/100 g H2O
2. How many grams of KCl will dissolve in 300 g H2O at 80 oC?
solubility @55 g KCl/100 g H2O so 165 g KCl in 300 g H2O
3. A solution has 50 grams of LiCl dissolved in 100 g H2O at 50 oC. Is it saturated, unsaturated,
or supersaturated? Solubility is @95 g/100 g H2O so unsaturated
4. 500 grams of H2O were made into a saturated solution of NaNO3 at 80oC. The solution was
then cooled to 20 oC. How many grams of NaNO3 ppt out of solution? 150 g/100 g H2O at
80oC to 90 g/100 g H2O at 20 oC so difference of 60 g/100 g H2O so 300 g in 500 g H2O ppt
out
5. On the graph above, draw in a line which represents the solubility of gases such as CO2. The
blue line above represents gases as the higher the temperature, the lower the solubility of
gases.
Colligative Properties
1. Two beakers of equal volume are placed in a room. Beaker A contains pure water and beaker
B contains saltwater. After a day of evaporation, which has more liquid in it and why?
Beaker B has saltwater so has a lower VP so will have more liquid left
2. If 35 grams of C2H4(OH)2 is dissolved in 500 g of water, what is the vapor pressure of the
water? The water is at 32 oC and the pure vapor pressure of water at 32 oC is 35.7 mm Hg.
0.565 moles C2H4(OH)2 and 27.778 moles of H2O
XH2O = 27.778/(27.778+0.565) = 0.98
VPH2O = (0.98)(35.7 mm Hg) = 34.9 mm Hg
3. If 105 g of I2 is dissolved in 325 g of CCl4 at 65 oC. Given that the pure vapor pressure of
CCl4 at this temperature is 531 mm Hg, what is the vapor pressure of the solution?
0.414 moles I2 and 2.110 moles of CCl4
XCCl4 = 2.110/(0.414+2.110) = 0.836
VPCCl4 = (0.836)(531 mm Hg) = 444 mm Hg
4. What is the boiling point of a solution of 15 g of non-ionizing (NH2)2CO in 500 g H2O? The
Kbp of water is 0.5 oC/m.
0.25 moles/0.5 kg = 0.5 m
T = kmi = (0.5 oC/m)(0.5 m)(1) = 0.25 so new boiling point is 100.25 oC
5. A solution of C3H5(OH)3 in 735 g of water (Kbp H2O is 0.5 oC/m) has a boiling point of 104.4
o
C. What is the molality of the glycerol in the solution? What is the mass% of the glycerol?
T = kmi 4.4 oC = (0.5 oC/m)(x m)(1) x = 8.8 m
Mass % = 809.6 g/1809.6 *100% = 44.7%
6. A bottle of wine is 11% C2H5OH in water. If the bottle is chilled to -20 oC, will the wine
freeze? Kfp water is -1.86 oC/m.
11 g C2H5OH & 89 g H2O so m = 0.239 moles C2H5OH/0.089 kg = 2.69 m
T = kmi = (-1.86 oC/m)(2.69 m)(1) = -5 oC so new freezing point is -5 oC
so the wine will freeze
7. You dissolve 15 g sugar (C12H22O11) in 225 g of water (Kfp = -1.86 oC/m). What is the
freezing point of the solution?
15 g sugar/342 g/mole = 0.0439 moles in 0.225 kg so
m = 0.195 m
o
o
T = kmi = (-1.86 C/m)(0.195 m)(1) = -0.36 C so new freezing point is -0.36 oC
8. You dissolve 20 grams of Na2SO4 in 150 grams of water (Kfp = -1.86 oC/m). Knowing that
Na2SO4 ionizes completely in water, what is the new freezing point of the water?
20 g Na2SO4/142.1 g/mole = 0.141 moles in 0.150 kg so m = 0.938 m
T = kmi = (-1.86 oC/m)(0.938 m)(3) = -5.24 oC so new freezing point is -5.24 oC
9. List the following solutions in order of increasing melting point:
a. 0.1 m sugar
b. 0.1 m NaCl
c. 0.08 m CaCl2
d. 0.04 m Na2CO3
0.08 m CaCl2 < 0.1 m NaCl < 0.04 m Na2CO3 < 0.1 m sugar
10. List the following solutions in order of decreasing freezing point:
a. 0.20 m C2H4(OH)2
b. 0.12 m K2SO4
c. 0.10 m MgCl2
d. 0.12 m KBr
0.20 m > 0.12 m KBr > 0.10 m MgCl2 > 0.12 m K2SO4
11. A 0.7549 g sample of CxHyOz burns to make 1.9061 g CO2 and 0.3370 g H2O. Also, in a
different experiment, a 0.5246 gram sample was dissolved in 10 g of lauric acid and the
freezing point was lowered by 1.68 oC.
a. What is the empirical formula of the substance?
1.9061 g CO2 *(1mole/44 g CO2) = 0.0433 moles C
0.3370 g H2O *(1 mole/18 g H2O)(2 moles H/mole H2O) = 0.0374 moles H
0.0433 moles C *(12 g/mole) = 0.5198 g C
0.0374 moles H *(1 g/mole) = 0.0374 g H
0.7549 g CHO – 0.5198 g C – 0.0374 g H = 0.1977 g O
0.1977 g O/ 16 g/mole = 0.01236 mole O
So empirical is C7H6O2
b. If Kf of lauric acid is 3.90 oC/m, calculate the molar mass of the substance.
122 g/mole
c. What is the molecular formula of the substance? C7H6O2
12. A substance is found to be 65.6% C and 9.4% H and 25% O. In a different experiment, 1.57
g of the compound were dissolved in 16.08 g of camphor and it was observed that the freezing
point of camphor was 15.2 oC lower than pure camphor.
a. What is the empirical formula of the compound?
65.6 g C (1 mole/12 g) = 5.47 moles C
25 g O (1 mole/16 g) = 1.56 moles O
9.4 g H (1 mole/1 g) = 9.4 moles H
So empirical is C7H12O2
b. If Kf of camphor is 40 oC/m, calculate the molar mass of the substance.
256 g/mole
c. What is the molecular formula of the substance?
C14H24O4
Combination Problems
1. Two containers each have a volume of 1.0 L at 298 K. Container A has 0.10 moles of N2 (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.
a. 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
b. 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
c. 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
d. What change could be made that would decrease the average kinetic energy of the N2
molecules? Justify. Only way to decrease the KEavg is to lower the Temperature.
e. 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
2. A rigid 5.0 L cylinder contains 24.5 g of N2 and 28.0 g of O2.
a. Calculate the total pressure, in atm, of the gas mixture in the cylinder at 298 K.
24.5 g 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
b. 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
c. 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
3. Concentrated sulfuric acid (18.4 M H2SO4) has a density of 1.84 g/mL. After dilution with
water to 5.2 M, the solution has a density of 1.38 g/mL.
a. Calculate the volume of concentrated acid needed to make 1.0 L of 5.2 M H2SO4
(18.4 M)(X L) = (5.2 M)(1 L)
0.283 L of 5.2 M needed
b. Determine the mass % of H2SO4 in the original concentrated solution.
1805 g H2SO4/1840 g solution *100% = 98.1%
c. Calculate the volume of 5.2 M H2SO4 that can be completely neutralized with 10.5 g of
NaHCO3.
H2SO4 + 2 NaHCO3  2 H2CO3 + Na2SO4
10.5 g NaHCO3 *(1mole/84 g) = 0.125 moles NaHCO3
0.125 moles NaHCO3 * (1 mole H2SO4/2 NaHCO3) = 0.0625 moles H2SO4
0.0625 moles (1 L/5.2 moles) = 0.0120 L or 120 mL
d. What is the molality of the 5.2 M H2SO4 solution?
5.2 moles/0.8699 kg H2O = 5.978 m