Chapter 6 – Gases
A gas is defined empirically as a substance that:





fills and assumes the shape of its container.
diffuses rapidly.
mixes readily with other gases.
increase in volume when heated.
decreases in volume when pressure is applied.
pressure – is defined as the force exerted per unit area.
P=F
a
N
m2
 The standard unit of pressure is the Pascal (Pa).
1 Pa = 1 N
m2
... 1 kilopascal (kPa) = 1000 Pa
 An increase in force causes an increase in pressure.
 An increase in area causes a decrease in pressure.
The amount of pressure that a gas exerts on the walls of its container depends
on:
a) the number of particles /unit volume.
b) the average kinetic energy of its particles.
Boyle’s Law (Robert Boyle – 1627 -1691, English)
Boyle’s Law – Assuming a constant temperature, the volume of a of gas
varies inversely with the pressure.
P
2P
V
V
2
4P
V
4
 Scientists agree that to compare volumes of gases, they need to be
measured at the same temperature and pressure.
 The two standard set of conditions are STP and SATP.
PV = k
P = pressure V = volume
k = constant
 This relationship can be written in a more convenient form if we compare
two sets of pressures and volumes.
We see that:
...
P1V1 = k and P2V2 = k
P1V1 = P2V2 or
V2 = V1 x P1
P2
 To correct the volume of a gas for a new set of conditions, multiply the old
volume by the pressure ratio.
Kelvin Temperature Scale
 When we measure temperature, we are really measuring the average kinetic
energy of the particles.
 the greater the temperature, the more energy the particles have, and the
faster they move.
 Lord Kelvin suggested that there is a temperature at which particle motion
ceases.
 He called this temperature absolute zero. (0 K = -273 oC)
 To convert from Co to K, we use the following:
K = Co + 273
Charles’ Law (Jacques Charles, 1746-1823, French)
 He discovered that for each degree that the temperature of a gas increased,
the volume increased by 1/273 of its volume at 0.0oC.
 The volume decreased with the same ratio for a decrease in temperature.
 Therefore, theoretically at – 273oC (absolute zero) a gas has no volume.
 Absolute zero is thought to be the lowest attainable temperature.
Charles’ Law – If the pressure remains constant, the volume of a gas varies
directly with the Kelvin temperature.
V
T
V = kT
2V
2T
V = volume T = Kelvin Temp.
k = constant
 To compare two sets of volume and temperature, we can see that:
...
V1 = k
T1
and
V2 = k
T2
V1 = V2
T1
T2
or
V 2 = V1
x
T2
T1
 To correct the volume for a new set of conditions, multiply the original
volume by the temperature ratio.
The Combined Gas Law
 When we combine Charles’ law and Boyle’s law we obtain the combined
gas law.
 It states: the product of the pressure and the volume of a gas is proportional
to its absolute temperature.
PV = kT
 When comparing gases at two sets of conditions, it is convenient to use the
following:
P1V1 = P2V2
T1
T2
or
V 2 = V1
x
P1
P2
x
T2
T1
Law of Combining Volumes
 In 1808 Joseph Gay-Lussac (French) and Alexander von Humboldt
(German) discovered the relative volumes of gases involved in chemical
reactions.
 They came up with the Law of Combining Volumes.
 It states: At the same temperature and pressure, volumes of gaseous
reactants and products are always in simple whole number ratios. (same as
coefficients)
ie. 2 C4H10 (g) + 13 O2(g)
2 mol
2 vol.
4L
13 mol
13 vol.
26 L
8 CO2(g) + 10 H2O(g)
8 mol
8 vol.
16 L
10 mol
10 vol.
20 L
Avogadro’s Hypothesis
 In 1811, Amadeo Avogadro (Italian) came up with a theory that explained
the relationship between volume ratios and coefficient ratios.
Statement:
If you have two gases at the same temperature and pressure, than :
 the average kinetic energy of the two gases is the same. (same temp.)
 ... if there is any difference in the pressure exerted by the two gases, it
would be due to the number of particles.
 however, since we have already stated that the pressures are equal, they
must contain equal #’s of particles.
Avogadro’s Hypothesis – equal volumes of gases at the same temperature
and pressure contain equal numbers of particles.
Molar Volume of a Gas
 From Avogadro’s hypothesis, if V1 = V2, than n1 = n2.
 Conversely, if n1 = n2, than V1 = V2. (assuming temp. and pressure are
constant.)
 ... 1 mol of any gas at STP or SATP will have the same volume.
 This is called the molar volume of a gas.
ie. 1 mol O2 = 32.0 g and 1000 cm3 = 1.43 g (experimental)
32.0 g
1 mol
1000 cm3
1.43 g
1L
1000 cm3
= 22.4 L/mol
... molar volume at STP = 22.4 L/mol
molar volume at SATP = 24.8 L/mol
Ideal Gas Equation
 Gas Laws are only exact for ideal gases.
ideal gas – an imaginary gas is made up of particles having mass, no volume,
and no attractive forces acting between them.(point masses)
 Real gases follow the laws very closely unless the gases are at low
temperatures and high pressures.
 There is a single relationship that combines all 4 variables. (P,V,T,n)
We see:
from Boyle’s law
from Charles’ law
from Avogadro’s hypothesis
Vα 1
P
Vα T
V α n
Combining these: V α 1 x T x n
P
 To change this proportion to an equality we must introduce a constant:
V = n R T
R – universal gas constant
P
or
PV = nRT
Ideal gas Equation
 If we fill in the standard values for P, V, n and T, we can find the value of
R.
R = PV
nT
R = (101.3 kPa) (22.4 L)
( 1.00 mol) (273 K)
R = 8.31 kPa . L
mol . K
 As long as 3 of the 4 variables are known, the ideal gas equation can be
used.
Molecular Mass and Density
The ideal gas equation can be used to solve a variety of problems.
i) molecular mass
since n = m
M
... P V = m R T or M = m R T
PV
ii) gas density
since D = m
V
... D = M P
RT
Gas Stoichiometry
 Since we now know the relationship between moles of a gas and the
volume, we can use this information in solving stoichiometry problems
with gases, because gases are usually measured in terms of volume and not
mass.
 Problems are solved in an almost identical fashion to mass-mass problems.
1) Mass-Volume
i. write a balanced reaction
ii. convert mass to mols
iii. do a mol ratio
iv. convert mols to a volume
2) Volume-Mass
i. write a balanced equation
ii. convert volume to mols
iii. do a mol ratio
iv. convert mols to mass
3) Volume-Volume
 Since all gases occupy the same volume at the same temp. and pressure ...
the ratio of combining gas volumes is the same as the ratio of combining
mols.
 ... you only need to do a volume ratio.
Limiting Reactants
 In a reaction, there is usually a reactant that is used up before all others and
... limits the amount of product produced.
 It is called a limiting reactant.
 Any reactant no used up is said to be in excess.
Steps:
i. write a balanced equation
ii. convert given volumes or masses to mols
iii. determine the # of mols of product that each reactant will produce
iv. choose the limiting reactant and complete the final step based on the
limiting reactant
Non-standard Conditions
 Gases are not always at STP or SATP.
 ... before converting volume to mols, the volume must be at STP or SATP.