Review of Gases and the
Gas Laws
PV = nRT
Kinetic Molecular Theory
Postulates:
• A gas consists of a collection of small particles traveling in
straight-line motion and obeying Newton's Laws.
• The molecules in a gas occupy no volume (that is, they are
points).
• Collisions between molecules are perfectly elastic (that is,
no energy is gained or lost during the collision).
• There are no attractive or repulsive forces between the
molecules.
• The average kinetic energy of a molecule is 3kT/2. (T is the
absolute temperature and k is the Boltzmann constant.)
PV = nRT
•
•
•
•
•
•
Boyle’s Law (isothermal & fixed amount)
Charles’s Law (isobaric & fixed amount)
Avogadro’s Law (isothermal & isobaric)
Ideal Gas Law (isochoric & fixed amount)
Ideal Gas Law (isothermal & isochoric)
Ideal Gas Law (isobaric & isochoric)
Boyle’s Law
PV  nRT
or P1V1  P2V2
L  atm 

PV  (1mol) 0.0821
(273K )
K  mol 

P  V  22.4 L  atm
P  V  22.4 L  atm
• Pressure and volume are inversely
proportional.
• As pressure increases, volume decreases.
• If pressure increases by 2x, volume cuts
in half.
Charles’s Law
V nR
V1 V2

or

T
P
T1 T
L  atm 

(1 mole) 0.0821

V
K  mol 


T
1 atm
• Temperature and volume are directly proportional.
• As temperature increases, volume also increases.
• If temperature increases by 2x, volume also
doubles.
• Temperature must be measured in Kelvin.
Avogadro’s Law
V RT

n
P
L  atm 

 0.0821
(273K )
V 
K  mol 

n
(1atm)
V
L
 22.4
n
mol
• Moles of gas and volume are directly proportional.
• As the number of moles increases, the volume also
increases.
• If the number of moles increases by 2x, the
volume also doubles.
PV = nRT
P
V
T
n
R
=
=
=
=
=
pressure
volume
temperature (Kelvin)
number of moles
gas constant
Standard Temperature and Pressure (STP)
T = 0 oC or 273 K
P = 1 atm = 101.3 kPa = 760 mm Hg
1 mol = 22.4 L @ STP
Solve for constant (R)
PV
nT
Recall: 1 atm = 101.3 kPa
Substitute values:
(1 atm) (22.4 L)
(1 mole)(273 K)
= R
R = 0.0821 atm L / mol K
R = 0.0821 atm L
mol K
or
(101.3 kPa)
( 1 atm)
R = 8.31 kPa L / mol K
= 8.31 kPa L
mol K
Ideal Gas Law – P & n
P RT

n V
L  atm 

 0.0821
(273K )
P 
K  mol 

n
22.4 L
P
atm
1
n
mol
• Moles of gas and pressure are directly
proportional.
• As the moles of gas increase, the pressure
also increases.
• If the number of moles of gas increases by
2x, the pressure also doubles.
Ideal Gas Law – n vs T
nT 
PV
R
nT 
(1atm)( 22.4 L)
L  atm 

 0.0821

K  mol 

n  T  273K  mol
• Moles of gas and temperature are inversely
proportional.
• As the number of moles of gas increase,
the temperature decreases.
Units of Pressure
• 1 atm = 760 torr = 760 mmHg
• 1 atm = 101.325 kPa
• 1 bar = 105 Pa = 100 kPa
• 1 Pa =
1N
2
m
Dalton’s Law of Partial
Pressures
Pressure is additive.
Write each pressure as,
PT  Pa  Pb
nRT
P
V
nT RT na RT nb RT


V
V
V
Continue
Dalton’s Law of Partial
Pressures
nT RT na RT nb RT


V
V
V
Multiply through by V (the combined volume of
the gases) and divide by R T.
nT  na  nb
Moles are indeed
additive.
Mole Fraction & Partial
Pressure
na
Xa 
nT
and
nb
Xb 
nT
na nb na  nb
Xa  Xb 


nT nT
nT
Therefore,
Xa  Xb 1
or
nT
nT
Collecting Gas Over Water
Pgas  P  PH 2O
Gas Law Problem #1
2 HCOONa + H2SO4  2 CO + 2 H2O + Na2SO4
A 0.964 gram sample of a mixture of sodium formate and
sodium chloride is analyzed by adding sulfuric acid. The
equation for the reaction for sodium formate with sulfuric
acid is shown above. The carbon monoxide formed measures
242 milliliters when collected over water at 752 torr and
22.0°C. Calculate the percentage of sodium formate in the
original mixture.
Gas Law Problem #2
A 6.19 gram sample of PCl5 is placed in an evacuated 2.00
liter flask and is completely vaporized at 252°C.
(a)Calculate the pressure ion the flask if no chemical reaction
were to occur.
(b) Actually at 252°C the PCl5 is partially dissociated
according to the following equation:
PCl5(g)  PCl3(g) + Cl2(g)
The observed pressure is found to be 1.00 atmosphere. In
view of this observation, calculate the partial pressure of
PCl5 and PCl3 in the flask at 252°C.
Gas Problem #3
A mixture of H2(g), O2(g), and 2 millilitres of H2O(l) is present in a 0.500
litre rigid container at 25°C. The number of moles of H2 and the number
of moles of O2 are equal. The total pressure is 1,146 millimetres mercury.
(The equilibrium vapor pressure of pure water at 25°C is 24 millimetres
mercury.)
The mixture is sparked, and H2 and O2 react until one reactant is completely
consumed.
(a) Identify the reactant remaining and calculate the number of moles of the
reactant remaining.
(b) Calculate the total pressure in the container at the conclusion of the
reaction if the final temperature is 90°C. (The equilibrium vapor pressure
of water at 90°C is 526 millimetres mercury.)
(c) Calculate the number of moles of water present as vapor in the container
at 90°C.
Answer:
(a)
2 H2 + O 2  2 H2 O
mol H2 = mol O2 initially, but 2 mole H2 react for every 1 mol of O2,
therefore, O2 is left.
PT = PH2 + PO2 + PH2O
1146 mm Hg = PH2 + PO2 + 24 mm Hg
PH2 + PO2 = 1122 mm Hg
1122 mm Hg / 4 = PO2 left (1/2 of initial PO2 which is 1/2 total)
PO2 = 280.5 mm Hg
(b)
28 0 . 5 mmHg
29 8 K

PO
2
36 3 K
; P O  34 2 mmHg
2
PT = PO2 + PH2O = (342 + 526)mm Hg = 868 mm Hg
(c)
n 
PV
RT
52 6

( 7 6 0 atm )( 0 . 50 0 L )
0 . 08 21
L a t m
m ol K
( 363 K )
 0 . 011 6 m o l
What Makes a Gas Ideal?
The ideal gas law, PV = nRT, relates variables that describe a sample of
an ideal gas.
To be an ideal gas:
• Size of gas molecules is negligible relative to distances between
adjacent molecules. Most of volume occupied by a gas is empty space.
• Gas molecules are in constant random motion and each molecule
continues to travel in a straight line unless it collides with another
molecule or with wall of container.
• Gas molecules do not attract each other and all collisions are elastic.
• Average kinetic energy of molecules is proportional to absolute
temperature.
What makes a gas “Real”?
Real gases:
• follow ideal gas equation only at low pressures and high temperature
• Boyle’s Law doesn’t hold at high pressures (PV ≠ C)
• Charles’ Law doesn’t hold at low temperatures (V/T ≠ C).
• Deviations of real gases and from the Ideal Gas Equation, worsen as
temperature decreases and pressure increases.
These deviations are revealed in the compressibility factor (z) of the gas,
where:
z = PV/nRT
For ideal gases, z=1 under all conditions. For real gases, z ≠ 1.The farther
away from 1 that z gets, the more poorly the ideal gas equation is being
followed.
Comparison of Real vs. Ideal Gases
Ideal Gases
Real Gases