Ideal Gas Law
1. Avogadro’s Principle


How much volume will one mole of hydrogen,
oxygen, and helium occupy at STP?
Using the molar mass and gas density at STP :
2x1.00794 g
 H2 :
1mole


O2 :
2x16.0 g
1mole
He :
1x4.0 g
1mole
cm 3
0.0000899 g
cm 3
0.001429 g
cm 3
0.00017847 g
mL
cm 3
mL
cm 3
mL
cm 3
L
1000mL
L
1000mL
L
1000mL

22.4 L
mole H2

22.4 L
mole

O2
22.4 L
He
mole



It appears that :
 1 mole of a gas, at STP occupies 22.4 L
 STP – standard temperature and pressure
 STP - 0ºC, 101.3 kPa (1 atm, 760 mmHg)
 6.02 x 1023 gas particles, at STP, 22.4 L
Avogadro’s Principle – At equal temperature
and pressure, equal volumes of gases contain
equal number of molecules.
V
= constant
n
V = volume, n = moles




Moles ↑ Volume ↑
Direct Relationship
Moles ↓ Volume ↓
A relationship between the number of particles
and the volume
NOT a relationship between mass and volume!
H2
1 mole
2.016 g
22.4 L
0°C, 1 Atm
O2
1 mole
32.0 g
22.4 L
0°C, 1 Atm
He
1 mole
4.0 g
22.4 L
0°C, 1 Atm
Different
Masses
Same
Volume
Same
Temperature
Pressure
Different Same Number
Gases
of particles





Molar Volume – the
volume of 1 mole of a gas,
at a specified temperature
and pressure.
Molar volume at STP, is
22.4 liters.
1 mole H2, at STP,
occupies 22.4 L
1 mole O2, at STP,
occupies 22.4 L
1 mole CO2, at STP,
occupies 22.4 L
2. Ideal Gas Law

V
Avogadro’s Principle :
= constant
n
V
= volume
n = moles

Combined Gas Law :

Ideal Gas Law :
PV
 constant
T
PV
 constant
nT
or PV = nRT Where R = Ideal Gas Constant

PV = nRT
 P = pressure, kilopascals, kPa
 V = volume, Liters, L
 n = number of moles
 (convert grams to moles using Molar Mass)
 T = temperature, kelvin, K
kPa L
 R = Ideal Gas Constant, 8.314
mole K

Convert all units to the above, and you will only
have to memorize one ideal gas constant!




Calculate the ideal gas constant for STP, 1 mole
of gas, and 22.4 liters!
PV=nRT
(101.3 kPa)(22.4L) = (1mole)(R)(273K)
(101.3kPa) (22.4L)
=R
(1mole)(27 3K)
kPa L
 R = 8.314
mole K
3. Ideal and Real Gases

What volume does 3.5 moles of nitrogen gas
occupy at STP?

How many grams of hydrogen gas are in 9.0 L at
STP?

What volume will 125 g of carbon dioxide occupy
at STP?

What is the volume (in liters) of 2.00 g CS2 vapor
at 276 mm Hg and 70°C?

How many grams are in a sample of ammonia
gas at 786 mm Hg, 2.5 L, and 28°C?

What pressure, in kPa, is exerted by 1.75 g of
hydrogen gas in a 4.08 liter container at 35°C?

What is the volume of a gas that is 0.023 mole of
nitrogen gas at STP?

How many moles of air are in a 6.0 L tire at STP?

How many moles of oxygen are in a 5.5 L
canister at STP?

What mass of helium is in a 2.00 L balloon at
STP?

Calculate the number of moles of gas that occupy
a 3.45 L container at a pressure of 150 kPa and a
temperature of 45.6°C.

What is the pressure in mmHg that a 0.44 g
sample of carbon dioxide gas will exert at a
temperature of 46.2°C when it occupies a volume
of 5.00 L?

Calculate the mass of oxygen gas present in a
2.50 L sample kept at 1.66 atm pressure and a
temperature of 10.0°C.
5. Density of a Gas






Density = mass
volume
PV = nRT
P
n

RT V
n
moles

V volume
moles grams grams
x

Liters mole
Liters
P
x Molar Mass
so Density =
RT

What is the density of ammonia gas if the
pressure is 700.0 mmHg and the temperature is
63.0°C?

What is the density of sulfur dioxide at STP?

What is the density of carbon dioxide at 26.0°C
and 1.15 atm?
6. Molar Mass of Gases





Molar mass = grams
mole
Used to identify a gas.
PV=nRT
Solve for moles (n) from given pressure, volume,
and temperature.
Divide given grams by calculated moles (n).

What is the molar mass of a 1.25 g sample of gas
with a volume of 1.00 L, at 730.0 mmHg, and
27.0°C?

What is the molar mass of 0.427 g of a gas that
occupies 125 mL at STP?

What is the molar mass of a sample of gas that
has a density of 0.285 g/L at 101 kPa and 29°C?

What is the molar mass of a gas if 142 g of the
gas occupies a volume of 45.1 L at 28.4°C and
94.6 kPa?
7. Gas Stoichiometry







2 H2(g) + O2(g)  2 H2O(g)
2 molecules H2 + 1 molecule O2  2 molecules H2O
2 moles H2 + 1 mole O2  2 moles H2O
at STP
2(22.4 L) H2 + 1(22.4 L) O2  2 (22.4 L) H2O
2 volumes H2 + 1 volume O2  2 volumes H2O
At constant pressure and temperature, the
volumes of gaseous reactants and gaseous products
can be expressed as ratios of small whole numbers.


At constant pressure and temperature, the mole
ratio is equal to the volume ratio.
Calculating volumes of gases in chemical
reactions:
1. Write a balanced chemical equation.
2. If the temperature and pressure remains
constant during the chemical reaction, use
the volume ratio.
3. Remember at STP, 1 mole of any gas
occupies 22.4L.


If you are dealing with chemical reactions
where:
 Mixture of solids, liquids, and gases
 Change in temperature and/or pressure for
gases
You will have to use the Ideal Gas Law.
1.
2.
3.
4.
Write a balanced chemical equation.
Calculate moles of gas from PV=nRT
Use mole ratio.
Convert moles of product to volume using PV=nRT.

Reactant A(gas) + B  Product C + Product D(solid)
mass, grams
gas = P, V, T
MM D
PV=nRT
moles A
moles D
moles A
moles D

Reactant A(gas) + B  Product C(solid) + Product D(gas)
gas, P, V, T
gas = P, V, T
PV=nRT
PV=nRT
moles A
moles D
moles A
moles D

If I have 27.0 L of hydrogen gas that reacts with
an excess amount of nitrogen gas, how many
liters of ammonia will be produced at the same
temperature and pressure?

How many liters of carbon monoxide, at 27.0°C
and 25.0 kPa can be produced from burning
65.5 g of carbon?

What volume of oxygen can be collected at
100.0 kPa and 25°C when 30.6 g KClO3
decomposes?

What volume of bromine gas (at 0.00°C, 98.0 kPa)
is produced when 95.0 L of chlorine (at 50.0°C,
50.5 kPa) react with excess HBr?

Calculate the mass of hydrogen peroxide needed
to obtain 0.460 L of oxygen gas at STP.

Magnesium metal will “burn” in carbon dioxide to
produce elemental carbon and magnesium oxide.
What mass of magnesium will “burn” in a 255 mL
container of CO2 at 77.0°C and 65.0 kPa?