Gases
Chemistry
Gas Laws Master Reference Sheet
Formula:
1.
Clue:
Graham's Law
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2.
Dalton's Law
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3.
Boyle's Law
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4.
Charles' Law
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5.
Gay Lussac's Law
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6.
Combined Gas Law
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7.
Ideal Gas Law
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Variables in Gas Law Equations
n = # moles
V = in L or cm3
T = in K
(K = 273 + oC)
P = in 1 atm
= 101.3 kPa (kilopascals)
= 760. mm Hg (millimeters of mercury)
= 760. Torr
R = 0.0821 Latm
mol.K
= 62.4 Lmm Hg = 62.4 LTorr
mol.K
mol.K
= 8.31 LkPa
mol.K
= "a constant"
-1-
Gases
Chemistry
Kinetic (Molecular) Theory (for gases)
“Particles of matter are always in motion and this motion has consequences.”
1. Gases consist of large numbers of tiny particles, which have mass.
The distance between particles is great.
 Gas particles are neither attracted to nor repelled by each other.
2. a) Gas particles are in constant, rapid, straight-line, random motion.
They possess kinetic energy
b) Gas particles have elastic collisions (with each other and container walls)
(no net loss of KE)
e.g. elastic : pool balls (do not lose KE)
inelastic: car crash (lose lots of KE)
3. The average KE of the gas particles is directly proportional to the Kelvin temperature of
the gas.
(Reminder: KE = ½ mv2)
Properties of Gases







very low density (V(g) x 1000 V(l or s))
compressible and expandable: they have an indefinite volume
fluid
diffuse through each other (small)
have mass
exert pressure
1 mol at STP = 22.4 L
(STP = 0oC or 273 K; 1 atm)
Graham's Law
The speed or rate of gas diffusion is related to the molar mass of the gas.
e.g. At the same T, He diffuses faster than K.
KE = 1/2 mv2
m = molar mass in g/mol
v = velocity of particles in m/s
1/2 mava2 = 1/2 mbvb2
va =
vb
mm
b
a
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Gases
Chemistry
Gas Pressure
Pressure = Force
Area
Units: Force measured in Newtons (N)
Pressure measured in:
Pascals (1 N/m2) – 1 kPa = 103 Pa
torr
mm Hg
atmospheres
Standard Pressure (sea level)
= 101.325 kPa
= 760. mm Hg
= 760. torr
= 1 atm
= 14.7 psi
Instruments for Measuring Gas Pressure
(diagrams on p. 389 in textbook)
Barometer – instrument used to measure atmospheric pressure, using a column of Hg
 invented by Evangelista Torricelli in 1643
 atmospheric pressure presses down on a bowl of mercury, which causes a column of
mercury equal to that pressure to rise into the vacuum column.
Manometer – measures P of an enclosed gas relative to atmospheric P (open end)
Gas pressure
= atmospheric pressure  pressure of liquid in U-tube
Ask: Is the gas pressure higher or lower than atmospheric pressure?
If higher, add the pressure of the liquid to atmospheric P.
If lower, subtract the pressure of the liquid from atmospheric P.
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Gases
Chemistry
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Gases
Chemistry
Dalton’s Law of Partial Pressures
Ptotal = Pa + Pb + …..
Practice Problem:
A 1 L sample contains 78% N2, 21% O2 and 1.0% Ar.
The sample is at a pressure of 1 atm.
a) What is the partial pressure of each gas in mm Hg?
b) What is the partial volume of each gas in mL?
Collecting Gas by Water Displacement
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Gases
Chemistry
The gas bubbles through the water in the jar and collects at the top due to its lower density.
The gas has water vapor mixed with it.
Ptotal = Pgas + PH2O
Calculate the pressure of the dry gas:
Pgas = Ptotal – PH2O
Ptotal is what is measured (= atmospheric pressure),
PH2O can be found in standard tables of vapor pressure of water at different temperatures
Vapor Pressure of H2O at Various Temperatures
oC
kPa
kPa
0
0.61
26
3.36
5
0.87
27
3.56
10
1.23
28
3.77
15
1.71
29
4.00
16
1.81
30
4.24
17
1.93
40
7.37
18
2.07
50
12.33
19
2.20
60
19.92
20
2.33
70
31.15
21
2.49
80
47.33
22
2.64
90
70.01
23
2.81
100
101.3
24
2.99
105
120.8
25
3.17
110
143.2
o
Note: At 100 C, the normal boiling point, vapor pressure = atmospheric pressure = 101.3 kPa
oC
e.g. Hydrogen gas is collected over water at a total pressure of 95.0 kPa and temperature of
25oC. What is the partial pressure of hydrogen gas? (A: 91.8 kPa)
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Gases
Chemistry
Mole Fraction
mole fraction of gas A =
moles gas A
= PgasA
total # moles of gas Ptotal
Since partial pressures of gases reflect the quantity of a particular gas, comparing partial
pressure with total pressure will give you mole fraction.
1.
The partial pressure of oxygen was observed to be 156 torr in air with a total
atmospheric pressure of 743 torr. Calculate the mole fraction of O2 present.
PO2 = 156 torr = 0.210
Ptotal 743 torr
2.
The partial pressure of nitrogen was observed to be
590 mm Hg in air with a total atmospheric pressure of
760. mm Hg. Calculate the mole fraction of N2
present.
PN2 = 590 mm Hg = 0.78
Ptotal 760. mm Hg
Note: Mole fraction has NO units.
Dalton’s Law of Partial Pressures and Mole Fraction Practice Problems
1.
Determine the partial pressure of oxygen (O2) collected over water if the temperature
is 20.0oC and the total (atmospheric) gas pressure is 98.0 kPa. (A: (95.7 kPa)
2.
The barometer at an indoor pool reads 105.00 kPa. If the temperature in the room is
30.0oC, what is the partial pressure of the “dry” air? (A: 100.76 kPa)
3.
What is the mole fraction of hydrogen (H2) in a gas mixture that has a PH2 of 5.26
kPa? The other gases in the mixture are oxygen (O2), with a PO2 of 35.2 kPa and
carbon dioxide with a PCO2 of 16.1 kPa. (A: 0.0929)
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Gases
Chemistry
Describing Gases
To describe a gas, you need:
 Volume
 Pressure
 Temperature (K)
 # particles (moles)
 “Gas Laws”
Constant Temperature
What happens to pressure when volume decreases?
Constant Pressure
What happens to volume when temperature increases?
Constant Volume
What happens to pressure when temperature increases?
Constant Volume and Temperature
What happens to pressure when the # of particles is increased?
Constant Temperature and Pressure
What happens to volume when the # of particles is increased?
The Combined Gas Law
What happens to a gas when various conditions are changed?
P1V1 = P2V2
T1
T2
The Combined Gas Law includes Boyle’s,
Charles’s, and Gay-Lussac’s Laws...
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Gases
Chemistry
Boyle’s Law (constant T)
P1V1 = P2V2
T1
T2

P1V1 = P2V2
Demonstrates an inverse relationship between pressure and volume:
Charles’s Law (constant P)
P1V1 = P2V2
T1
T2

V 1 = V2
T1 T2
Demonstrates a direct relationship between volume and temperature:
Gay-Lussac’s Law (constant V)
P1V1 = P2V2
T1
T2

P 1 = P2
T1 T2
Demonstrates a direct relationship between pressure and temperature:
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Gases
Chemistry
Boyle's Law
The pressure on 2.50 L of anaesthetic gas is changed from 760. mm Hg to 304 mm Hg.
What will be the new volume if the temperature remains constant? (A: 6.25 L)
Charles's Law
If a sample of gas occupies 6.8 L at 327oC, what will be its volume at 27oC if the pressure
does not change? (A: 3.4 L)
Gay-Lussac's Law
A gas has a pressure of 50.0 mm Hg at 540 K. What will be the temperature, in oC, if the
pressure is 70.0 mm Hg and the volume does not change? (A: 483oC)
Combined Gas Law
1.
If a gas has a pressure of 2.35 atm at 25oC, and fills a container of 543 mL, what is the
new pressure if the container is increased to 750. mL at 50.1oC? (A: 1.84 atm)
2.
A sample of methane that initially occupies 250. mL at 500. Pa and 500. K is
expanded to a volume of 700. mL. To what temperature will the gas need to be
heated to lower the pressure of the gas to 200. Pa? (A: 560. K)
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Gases
Chemistry
Ideal Gases

Based on kinetic molecular theory

Follows gas laws at all T and P
Real Gases
Because particles of real gases occupy
space:
 Follow gas laws at most T and P

Assumes particles:
- have no volume
 impossible
- have no attraction to each
other
 if true, would be
impossible to liquefy
gases
(e.g. CO2 is liquid at
5.1 atm, < 56.6oC

At high P, individual volumes count

At low T, attractions count

The more polar the molecule, the more
attraction counts
Ideal Gas Law: PV = nRT
To describe a gas completely you need to identify:
V – volume
P – pressure
T – temperature in K
n - # of moles
n = mass
= m = g = moles
molar mass
M g
mol
The Ideal Gas Law:
1. Can be used to derive the combined gas law
2. Is usually used to determine a missing piece of information about a gas
(requires the ideal gas constant R)
PV = nRT
P, V
P, T
V, T
V, n
inversely related
directly related
directly related
directly related
BOYLE
GAY-LUSSAC
CHARLES
AVOGADRO
R = universal gas constant
Solve for R at STP: T = 0oC + 273 = 273 K; P = 1 atm;
1 mole has a volume of 22.4 L at STP
R = PV = (1 atm)(22.4 L) = 0.0821 Latm
nT
(1 mol)(273 K)
molK
depends on pressure units used
See Master Reference Sheet on
p. 1 of this handout
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Gases
Chemistry
Example Problem – Ideal Gas Law
Calculate the pressure, in atmospheres, of 1.65 g of helium gas at 16.0oC and
occupying a volume of 3.25 L.
P=?
PV = nRT
V = 3.25 L
n = 1.65 g (1 mol He) = 0.412 mol He
4.00 g He
R = 0.0821 Latm
molK
o
T = 16.0 C + 273 = 289 K
P = nRT = (0.412 mol)(0.0821 Latm)(289 K)
V
3.25 L
molK
= 3.01 atm
Ideal Gas Law Practice
1.
A sample of carbon dioxide with a mass of 0.250 g was placed in
a 350. mL container at 127oC. What is the pressure, in kPa,
exerted by the gas? (A: 54 kPa)
2.
A 500. g block of dry ice (solid CO2) vaporizes to a gas at room
temperature. Calculate the volume of gas produced at 25oC and
975 kPa. (A: 29.0 L CO2)
3.
At what temperature will 7.0 mol of helium gas exert a pressure
of 1.2 atm in a 25.0 kL tank? (A: 5.2 x 104 K)
4.
What mass of chlorine (Cl2) is contained in a 10.0 L tank at 27oC
and 3.50 atm? Hint: begin by solving for n. (A: 101 g)
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Gases
Chemistry
Density of Gases

Measured in g/L
(compared with density of liquids and solids: g/mL)

1 mole of any gas = 22.4 L at STP
(0oC or 273 K and 1 atmosphere)
 Practice: Derive density from the ideal gas law (RQ 14.3):
PV = nRT
n = m/M
Sample problems:
1.
What is the molar mass of a gas that has a density of 1.28 g/L at STP?
(A: 28.7 g/mol)
2.
A 0.519 g gas sample is found to have a volume of 200. mL at STP.
What is the molar mass of this gas? (A: 58.1 g/mol)
3.
A chemical reaction produced 98.0 mL of sulfur dioxide gas (SO2) at STP.
What was the mass (in grams) of the gas produced? (A: 0.280 g SO2)
4.
A 1.25 g sample of the gaseous product of a chemical reaction was found to have a
volume of 350. mL at 20.0oC and 750. mm Hg. What is the molar mass of this gas?
(A: 86.8 g/mol)
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Gases
Chemistry
Stoichiometry and Gases at STP
Calcium carbonate reacts with phosphoric acid to produce calcium phosphate, carbon
dioxide, and water.
3 CaCO3(s) + 2 H3PO4(aq)  Ca3(PO4)2(aq) + 3 CO2(g) + 3 H2O(l)
1. How many grams of phosphoric acid, H3PO4, react with excess calcium carbonate,
CaCO3, to produce 3.74 g of Ca3(PO4)2?
(A: 2.36 g H3PO4)
2. Assuming STP, how many liters of carbon dioxide are produced when 5.74 g of H 3PO4
reacts with an excess of CaCO3?
(A: 1.97 L)
Stoichiometry and Gases under non-STP conditions
(use binder paper to answer)
Two steps:
Either stoichiometry first (known = solid or liquid), followed by the Ideal Gas Law to find the
volume of a gaseous product,
or use the Ideal Gas Law to find the #moles of a gaseous reactant, followed by stoichiometry
to find the amount of a solid or liquid product.
Practice:
If water is added to magnesium nitride, ammonia gas is produced when the mixture is
heated.
Mg3N2(s) + 3H2O(l)  3 MgO(s) + 2 NH3(g)
1.
If 10.3 g of magnesium nitride is treated with water, what volume of ammonia gas
would be collected at 24oC and 752 mm Hg? (A: 5.03 L)
2.
When you produce 16.2 L of ammonia gas at 100.oC and 802 mm Hg, how many
grams of magnesium oxide are also produced? (A: 33.7 g MgO)
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