Ideal Gas Law
PV=nRT
Remember…
Boyle’s Law
Charles’ Law:
P1V1  P2V2
V1 V2

T1 T2
Combined Gas Law:
(Units MUST Match
Temp in Kelvin!!!)
P1V1 P2V2

T1
T2
A gas with a volume of 350 ml is collected
at 15o C and 120 kPa. If the temperature
changes to 30o C, what pressure would be
required to put this gas in a 300 ml
container?
120kPa  350ml P2  300ml

288K
303K
P2  147.3kPa
A balloon has a volume of 500 ml at a
temperature of 22oC and a pressure of 755
mmHg. If the balloon is cooled to 0o C and
a pressure of 145 mmHg, what is its new
volume?
755mmHg  500ml 145mmHg  V2

295K
273K

2409
.
3
ml
V2
Avogadro’s Principle
Under similar conditions (same Temperature
and Pressure) equal volumes of gases
contain equal numbers of particles.
10 L of H2 (g) and 10 L of O2 (g)
Both at Standard Temperature and
Pressure (STP) contain…
The same number of particles!
Molar Volume
The volume of 1 mole of gas particles at
STP is 22.4 L
Try this:
1 mole of gas occupies 22.4 L at STP
= __________ ml
(22400)
= ___________ moles of gas
(1 mole)
= ___________ particles
(6.02 x 1023)
44.8 L
L
22.4
mole
How many particles in 11.2 dm3 of gas at STP?
0.5 moles = 3.01 x 1023 particles
22,400 cm3 of NH3 gas at STP weighs?
= 22.4 L = 1 mole = 17 grams (add up MW)
44.8 L of NH3 at STP weighs?
= 2 moles = 34 grams
28.00 grams = 1 mole of nitrogen gas
_____
22.4 L at STP?
= _____
How many N2 molecules are
in 22.4 dm3 at STP?
= 1 mole = 6.02 x 1023
What volume will 1.2 x 1024 H2 molecules
occupy at STP?
= 2 moles = 44.8 L at STP
Ideal Gas Equation
Use when NOT at STP!!!
PV= nRT
P = Pressure (in kPa)
V = Volume (in Liters or dm3)
n = number of moles
T = Temperature (in Kelvin)
R = 8.31 L• kPa
mole • K
Select the R value carefully
R = 0.0821 L * atm/(K*mol)
R = 8.3145 J/mol·K
R = 8.31 L * kPa/(mol*K)
Development of R in
kPa  L
mole  K
PV 101.3kPa  22.4 L
kPa  L
R

 8.31
nT
1mole  273K
mole  K
1. What volume will 2 moles of NO2 occupy
at 300 Kelvin and 90 kPa?
PV  nRT
90kPa  V  2moles  8.31  300 K
2  8.31  300
V
 55.4 L
90
What will be the temp of 2 grams of
H2 if 5000 cm3 is at 5 atm?
PV  nRT
506.5kPa  5L  1mole  8.31 T
506.5  5
 T  304.8K
1 8.31
Finding Molecular Weight of a Gas
Remember: MW = grams / moles
Converting grams to moles
– Divide grams by the molecular weight
1) 5.0 L of a gas weighs 30.00 g at 20o C &
92 kPa. What is the mole weight of the gas?
grams 30.00 g
MW 

moles
? mol
PV=nRT
92kPa • 5.0 L= n • 8.31 • 293 K
n = 0.19 mol
30.00 g
MW 
 158 g/mol
0.19 mol
2)If the mole weight of a gas is 26 g/mol and
18.00 g of the gas is 30 L at 21o C, what is the
pressure of the gas?
PV= nRT
g
18.00 g
n

 0.69 mol
MW 26 g/mol
P x 30 L=0.69 mol x 8.31 x 294 K
P = 56.2kPa
Molar Mass Using Ideal Gas Law
Need:
Temperature
Pressure
Correct R value
density
Molar mass = dRT/P
D - density
R - gas law constant
T - temperature (K)
P - pressure
Practice Problem
A chemist has synthesized a greenish-yellow
gaseous compound of chlorine and oxygen and
finds that its density is 7.71 g/L at 36°C and 2.88
atm. Calculate the molar mass of the
compound.
Molar mass = dRT/P
(7.71g/L*0.0821 L*atm/(L*mol) * 309K)/ 2.88atm
69.7 g/mol
Real Gas
The ideal gas makes the assumption that all
gas particles are completely independent of
each other.
The reality is there are some intermolecular
forces that lead to the need to reduce of the
volume and increase in the pressure.
Correcting Pressure
P ideal = P real + an2/V2
an2/V2 is known as the correction term
A is a constant, n is the number of moles
and V is the volume
The real pressure is smaller then the ideal
pressure and it is a function of the ratio
between moles and volume.
Correcting Volume
V –nb
b is the constant
n is the number of moles
As the number of moles increase, the
expected real volume occupied by the atoms
becomes a factor so the volume of the ideal
is larger then the real volume.
Corrected Ideal Gas Law (real)
(P + an2/V2)(V-nb) = nRT
No you do not need to memorize the
formula.
What you need to know is that gas
molecules take up some of the space and
intermolecular forces result in some
atoms/molecules to stick together.
Real Gases Vs Ideal
Real Gas
The atoms/molecules
actually take up some of the
volume.
The real atoms/molecules
have intermolecular forces
that stick them together at
times.
Ideal Gas
The molecules/atoms take
up NO space.
The ideal gases have not
attraction to each other.