Gases Chapter 9
What parameters do we use to describe gases?
pressure: force/unit area 1 atm = 101 kPa;
volume: liters (L)
Temperature: K
What is meant by % volume? In principle, the actual molecular
volume of a gas is so small in comparison to the volume it will
occupy that we treat gases at mathematical points.
How do we measure pressure?
above 1 atmosphere
below 1 atmosphere
A column of air 1 m2 has a mass
of 10,300 kg, producing a
pressure of 101 kPa due to
gravity (14.7 pounds/in2)
1 atm = 76 cm Hg; 101 kPa
Boyle’s Law is concerned with the relationship of pressure and
volume using a fixed amount of gas ( a fixed number of
mols of gas)
P*V = constant at constant temperature
Avogadro’s Law is concerned with the relationship between the
number of molecules or mols (n) and the volume of a gas under
conditions of constant pressure and temperature
V  n at constant pressure and temperature
Charles’ Law is concerned with the relationship of temperature
and volume when dealing with a constant amount of gas (mols)
V  T when T is expressed in K. The K temperature scale is
derived from the behavior of gases
if V  T then V = kT where k is a constant at constant pressure
Ideal gas law: PV = nRT where R is a constant
R = 0.0821 L.atm/K.mol
Note that at constant n and T, PV = constant
Boyle’s Law
Note that at constant P and T V/n = constant
Avogadro’s Law
Note that at constant P and n, V/T = constant
Charles’s Law
Standard conditions of pressure and temperature
T = 0 °C (273 K)
Pressure: 1 atm
What volume does a mol of any ideal gas occupy at STP?
PV = nRT
V = 1mol(0.0821 L*atm/K*mol)(273 K)/(1 atm)
V = 22.4 L
This means that equal volumes of gases under identical
conditions of temperature and pressure contain equal number
of molecules
What is the difference between an ideal gas and a real gas?
The ideal gas equation was generated from the kinetic theory of gases
making the following assumptions
1. The molecules could be treated as points (ie molecular volume = 0)
2. There are no attractive interactions between molecules.
3. Gas particles move around at random
4. Collision of gas molecules with the wall are totally elastic
5. The kinetic energy of the gas particle is  to temperature (K)
In general, the ideal gas law works best at low pressures and high
temperatures
Real Gases: van der Waal’s equation
(P + an2/V2)(V-nb) = n RT
an2/V2 corrects for intermolecular attractions
nb corrects for the real volume of molecules
Dalton’s Law of partial pressures:
Total atmospheric pressure = 1 atm;
How much of the pressure is contributed by N2?
Pressure is a consequence of molecules colliding with each
other and the walls of the container
*062
For air if
If PTV = nTRT
and nT = (no2 + n N2 + ...)
at constant T, PTV = (no2 + n N2 + ...)RT
Since the actual volume of the molecules is small in comparison
to the volume occupied by the gas, all molecule occupy the same
volume V. The contribution to the total pressure is dependent on
the number of collision of each gas with the wall and this is
dependent on the number of molecule of each gas. Hence:
P = (PN2 + PO2 + ...)
PO2V = nO2RT ; PN2V = nN2RT ...
Temperature: a measure of the average kinetic energy of
molecules
Distribution of molecular speeds as a function of temperature
What are some of the consequences associated with the fact that
molecules at the same temperature have different speeds?
Diffusion: mixing of gases
Effusion: escape
through a small opening
The size of the pinhole needs to be small
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Two molecules of different mass at the same
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Two molecules of different mass at the same
temperature effusing through an opening
From the kinetic theory of gases
speed of a molecule u = (3RT/M)1/2
For two gases at the same temperature
1/2maua2 = 1/2mbub2 ua = average speed of molecule a
ub = average speed of molecule b
ma /mb = ub2 /ua2
The rate at which molecule a hits the pinhole  u if the comparisons
are made at the same concentration and temperature.
ub /ua = (ma /mb )1/2
Solving some problems involving gases
1. A sample of gas at 25 °C and 2 atm pressure in a 5 L vessel was
found to have a mass of 18 g. What is its molecular weight?
PV = n RT
2 atm*5 L = n*0.0821 (Latm/K mol)*298 K
n = 10/(0.0821*298) mol; 0.4087
n = wt/ mw;
mw = 44 g/mol
0.4087 = 18g/mw
Suppose the gas at the right
exerted a pressure of 15 cm as
shown.
Would the pressure of the gas
be greater or less than 1 atm?
15.2 cm How many atm of pressure is
the gas exerting?
1 atm = 76 cm
76 - 15.2 = 60.8
Suppose we have a sample of equal amounts of H2 and D2 in a
vessel and a small opening is introduced. What will be the initial
rates of effusion?
uH2/uD2 = mD2/mH2 = (4/2)0.5 = 1.42
Will the relative rate change with time?
What is the density of natural gas (CH4) at STP?
PV = nRT
density is g/mL or g/L
We know the molar volume of any gas is 22.4 L at STP
How many g of methane in a mole?
16g/22.4 L = 0.714 g/l or 7.14*10-4 g/mL or
PV =(wt/mw)*RT;
mw*P/RT = (wt/V)
The surface temperature of Venus is about 1050 K and the pressure
is about 75 Earth atmospheres. Assuming these conditions
represent a “Venusian STP, what is the standard molar volume of a
gas on Venus?
PV = nRT
75 atmV =1mol*0.0821(Latm/K mol)*1050 K; V = 1.15 L
Natural gas is a mixture of a number of substances including
methane (mol fraction, 0.94); ethane (mol fraction, 0.04); propane
(mol fraction, 0.015). If the total pressure of the gases is 1.5 atm,
calculate the actual pressure contributed by each of the gases
described.
mol fraction = mol A/(mol A + mol B + ....)
PT = 1.5 = P CH4+ PC2H6 + ...
Px V = nxRT
CH4 = 0.94*1.5
C2H6 = 0.04*1.5
C3H8 = 0.015*1.5
nCH4/nC2H6 = PCH4/PC2H6 = 0.94/.04