UNIT 6: Gas Laws Review Sheet KEY
1.
Terms and Equations to Know:
a. Dalton’s Law: Ptotal = P1 + P2 + P3 …;
♦ Total Pressure = Sum of the partial pressures and each pressure exerts a separate pressure
independent of the other gases
b. Boyle’s Law: P1 × V1 = P2 × V2
♦ Volume and pressure of a gas are inversely proportional
c. Charles’ Law: V1 / T1 = V2 / T2
♦ Volume and temperature of a gas are directly proportional
d. Combined Gas Law: P1 × V1 = P2 × V2
T1
T2
e. Gay-Lussac’s Law: P1 = P2
T1 T2
♦ Temperature and pressure of a gas are directly proportional
f.
Graham’s Law:
𝑹𝒂𝒕𝒆 𝑨
=√
𝑹𝒂𝒕𝒆 𝑩
𝑴𝒐𝒍𝒂𝒓 𝑴𝒂𝒔𝒔 𝑩
𝑴𝒐𝒍𝒂𝒓 𝑴𝒂𝒔𝒔 𝑨
♦
2.
3.
The ratio of the rate of diffusion of two gases is inversely proportional to the square root of their
masses
g. The Three Common States of Matter in Terms of Particle Motion:
♦ Gas: particles move randomly and independent of one another
Liquid: particles vibrate around a moving point
Solid: particles vibrate about a fixed point
h. Plasma and give two examples:
♦ State of matter consisting of free electrons and positive ions- no atoms in plasma state; most common
form of matter
Examples: lightning, neon signs, aurora borealis
i. Pressure and five units discussed in class:
♦ Force per unit area (P = F/A)
It results from the collision of molecules with the walls of a container
Units are: KPa, mmHg, torr, atm, and psi
j. Barometer:
♦ Instrument used to measure atmospheric pressure
k. Kinetic Energy:
♦ Energy associated with movement
K.E. = ½ mass × (velocity)2 = ½ mv2
l. Temperature and two units discussed in class:
♦ Temperature is a measure of the average kinetic energy of the particles of a substance
Units are °C and K
m. Kinetic Theory:
♦ “Matter consists of small moving particles that collide elastically”
n. Absolute Zero:
♦ The temperature where all molecular motion ceases
It is 0K and -273°C (No temperature is lower than this)
What does STP stand for and what are its numerical values (i.e., give five for pressure and 2 for temperature):
♦ Standard Temperature and Pressure
Pressure units are 101.3 KPa, 760 mmHg, 760 torr, 1 atm, and 14.7 psi
Temperature units are 0°C and 273 K
What are the three assumptions of the Kinetic Theory?
♦ (1) all matter consists of small particles
(2) these particles are in constant motion
(3) collisions between particles are perfectly elastic
GAS LAW PROBLEMS:
1. Convert the following temperatures from Celsius to Kelvin and Kelvin to Celsius:
a. 22°C
(22 + 273) = 295 K
d. 220 K (220 – 273) = -53°C
b. 444°C (444 + 273) = 717 K
e. 390 K (390 – 273) = -117°C
c. -60°C (-60 + 273) = 213 K
f. 20 K
(20 – 273) = -253°C
2. Convert the following pressure units to the indicated pressure units:
a. 2 atm = 1520 mmHg
d. 1520 mmHg = 202.3 KPa
b. 55 KPa = 412.5 torr
e. 755 mmHg = .993 atm
c. 315 torr = 315 mmHg
3. A gas occupies a volume of 100 cubic meters at 2.5 atm. What volume will it occupy at a pressure of 1.25 atm if
the temperature remains constant?
♦ P1 × V1 = P2 × V2
(2.5 atm) × (100 cm3) = (1.25 atm) × (V2)
250 = 1.25 V2
V2 = 200 cm3
4. A gas occupies a volume of 5340 cm3 at a temperature of 20°C. Calculate the volume that this gas will
occupy at 60°C if the pressure is held constant (must convert to Kelvin first).
𝑽𝟏
𝑽𝟐
𝟓𝟑𝟒𝟎
𝑽𝟐
♦
=
=
𝑻
𝑻
𝟐𝟗𝟑 𝑲
𝟑𝟑𝟑 𝑲
𝟏
𝟐
1778220 = 293 V2
V2 = 6069 cm3
5. A gas occupies a volume of 500 cm3 at 150 KPa. What volume will it occupy at standard pressure if the
temperature remains constant?
♦
P1 × V1 = P2 × V2
(150 KPa) × (500 cm3) = (101.3 KPa) × (V2)
75000 = 101.3 V2
V2 = 740.4 cm3
6. A sample of gas occupies 200 cm3 at STP. Calculate the volume this same amount of gas would occupy
at a pressure of .75 atm and a temperature of 10°C.
♦
P1 × V1 = P2 × V2
T1
T2
(1atm)(200 cm3) = (.75 atm)(V2)
273 K
283 K
3
V2 = 276 cm
7. A gas occupies a volume of 100 dm3 at 3 atm and 0°C. If the temperature increases to 546 K, what is
the new pressure if the volume remains constant?
𝑷𝟏
𝑷
♦
= 𝑻𝟐
𝑻
𝟏
𝟐
3 atm = P2 atm
273 K
546 K
P2 = 6 atm
8. There is a mixture of three gases in a closed container. Gas A exerts a pressure of 15 psi, Gas B a
pressure of 6.5 psi, and the total pressure is 25.7 psi. What is the partial pressure of Gas C?
♦
Ptotal = PA + PB + PC
25.7 psi = 15 psi + 6.5 psi + PC
25.7 psi = 21.5 + PC
PC = 4.2 psi
9. A large gas balloon sits at the surface of the sea. After being lowered 40 ft under the surface, the gas
balloon has its temperature drop to one-third of its original surface temperature and its pressure has
quadrupled. What effect will this have on its volume?
♦
P1 × V1 = P2 × V2
T1
T2
(1atm)( 1L) = (4 atm)(V2)
1K
1/3 K
V2 = .083 Volume will decrease by 1/12
10. The pressure of a sample of helium in a 2.00L container is 2.5 atm. What is the new pressure if the
sample is placed in a 6.00L container?
♦
P1 × V1 = P2 × V2
(2.5 atm) × (2.00 L) = (P2 atm) × (6.00L)
5.00 = 6.00 P2
P2 =.833 atm
11. What is the volume that 24 grams of CO occupies at STP?
♦
24 grams × 1 Mole × 22.4 L = 19.2 L
1
28 g
1 Mole
12. Calculate the volume that 2.54 Moles of CO2 occupies at STP?
♦
2.54 Moles × 22.4 Liters = 56.9 L
1
1 Mole
13. The pressure of a gas in a tank is 1.75 atm at 25°C. If the temperature rises to 85°C what will the
pressure be?
𝑷𝟏
𝑷
♦
= 𝑻𝟐
𝑻
𝟏
𝟐
1.75 atm = P2 atm
298 K
358 K
P2 = 2.10 atm
14. A gas occupies a volume of 200 dm3 at 1500 mmHg and 0°C. If the temperature increases to 450 K,
what is the new pressure if the volume remains constant?
𝑷𝟏
𝑷
♦
= 𝑻𝟐
𝑻
𝟏
𝟐
1500 mmHg
273 K
=
P2 mmHg
450 K
P2 = 2472 mmHg
15. Which of the following gases would diffuse most rapidly: N2, O2, He, Cl2?
♦ He (smallest molar mass)
16. What is the ratio of the rate of diffusion of H2 to He?
♦
𝑹𝒂𝒕𝒆 𝑨
𝑴𝒐𝒍𝒂𝒓 𝑴𝒂𝒔𝒔 𝑩
= √𝑴𝒐𝒍𝒂𝒓 𝑴𝒂𝒔𝒔 𝑨
𝑹𝒂𝒕𝒆 𝑩
𝑹𝒂𝒕𝒆𝑯𝒚𝒅𝒓𝒐𝒈𝒆𝒏
𝑹𝒂𝒕𝒆𝑯𝒆𝒍𝒊𝒖𝒎
𝟒.𝟎𝟎 𝒈
= √𝟐.𝟎𝟎 𝒈 = 1.41
Ideal Gas Law, Gas Stoichiometry and the Combined Gas Law
1. Calculate the volume in liters of 3.60 moles of nitrogen gas (N2) will occupy at STP?
♦ 𝑷𝑽 = 𝒏𝑹𝑻
STP = 273 K and 101.3 KPa
(101.3 KPa) (V) = (3.60 M) (8.3145) (273K)
101.3 V = 8171.49
101.3
101.3
V = 80.7 L
2. How many moles of gas will an 11.5 liter container hold at -20 degrees Celsius and a pressure of 1.18 atm.
♦ 𝑷𝑽 = 𝒏𝑹𝑻
(1.18 atm) (11.5 L) = (x M) (0.0821) (253K)
13.57 = 20.7713 x
20.7713
20.7713
n = .653 Moles
3. Calculate the temperature of a gas if 4.5 moles of it occupies a volume of 1.85 L at 1.23 atm.
♦ 𝑷𝑽 = 𝒏𝑹𝑻
(1.23 atm) (1.85 L) = (4.5 M) (0.0821) (T)
2.276 = .36945 T
.36945
.36945
n = 6.16 K
4. Calculate the pressure in KPa exerted by a gas if .83 moles occupies 8.5 L at 150K.
♦ 𝑷𝑽 = 𝒏𝑹𝑻
(P) (8.5 L) = (.83 M) (8.3145) (150K)
8.5 P = 1035.155
8.5
8.5
P = 121.8 KPa
5. What is the molecular mass of a gas if .150 L have a mass of .922 g at 99° C and 107 KPa?
♦
𝑴𝑴 =
(𝒈𝒓𝒂𝒎𝒔)(𝑹)(𝑻)
(𝑷)(𝑽)
MM = (.922 g) (8.3145) (372 K)
(107 KPa) (.150 L)
MM = 2851.74
16.05
MM = 177.68 g
6. Using the equation S + O2  SO2, calculate the number of liters of SO2 produced if 86 grams of sulfur are burned
in oxygen.
♦ S + O2  SO2 (Mass to Volume Problem)
1. Convert grams of S to moles
86 grams / 32.1 grams = 2.679 M
2. Mole Ratio
S = 1 = 2.679M  x = 2.679 M
SO2 1
xM
3. Convert moles to liters
2.679 Moles × 22.4 L = 60.01 Liters
7. From the reaction 3 Zn + 2 H3PO4  Zn3(PO4)2 + 3 H2 calculate the number of grams of H3PO4 that must be
reacted to produce 166 liters of H2.
♦ 3 Zn + 2 H3PO4  Zn3(PO4)2 + 3 H2 (Volume to Mass Problem)
1. Converts of liters of H2 to moles
166 L / 22.4 L = 7.41 M
2. Mole Ratio
H2 = 3 = 7.41M  x = 4.94 M
H3PO4 2 x M
3. Convert moles to grams
4.94 Moles × 98 grams = 484.12 grams
8. Propane burns in oxygen to produce carbon dioxide and water. Calculate the number of liters of oxygen that must
be used to produce 64.0 liters of carbon dioxide at STP.
C3H8 + O2  CO2 + H2O
♦ C3H8 + 5 O2  3 CO2 + 4 H2O (Volume to Volume Problem)
1. Converts of liters of H2 to moles
64 L / 22.4 L = 2.86 M
2. Mole Ratio
CO2 = 3 = 2.86M  x = 4.76 M
O2
5 xM
3. Convert moles to grams
4.76 Moles × 32 grams = 152.4 grams