Gases
Chapter 10
Characteristics of Gases
- Expand to fill a volume (expandability)
- Compressible
- Readily forms homogeneous mixtures with other
gases
- Have extremely low densities.
- These behaviors are due to large distances between
the gas molecules.
Pressure
• Pressure is the
amount of force
applied to an area.
F
P=
A
• Atmospheric
pressure is the
weight of air per
unit of area.
Units of Pressure
• Pascals
– 1 Pa = 1 N/m2
• Bar
– 1 bar = 105 Pa = 100 kPa
• mm Hg or torr
– These units are literally the difference in the
heights measured in mm (h) of two connected
columns of mercury.
• Atmosphere
– 1.00 atm = 760 torr
Pressure
- Conversion Factors
- 1 atm = 760 mmHg
- 1 atm = 760 torr
- 1 atm = 1.01325  105 Pa
- 1 atm = 101.325 kPa.
Manometer
Used to measure the
difference in pressure
between atmospheric
pressure and that of a
gas in a vessel.
Manometer at <, =, > P of 1 atm
Example
• On a certain day the barometer in a
laboratory indicates that the
atmospheric pressure is 764.7 torr. A
sample of gas is placed in a vessel
attached to an open-end mercury
manometer. A meter stick is used to
measure the height of the mercury
above the bottom of the manometer.
Level of the mercury in the open end
arm of the manometer has a
measured height of 136.4 mm, and
that in the arm that is in contact with
the gas has a height of 103.8 mm.
– What is the pressure of the gas?
– What is the pressure of the gas in kPa
The Gas Laws
- There are four variables required to describe
a gas:
-
Amount of substance
Volume of substance
Pressures of substance
Temperature of substance
- The gas laws will hold two of the variables
constant and see how the other two vary.
Boyle’s Law
The volume of a fixed quantity of gas at
constant temperature is inversely proportional
to the pressure.
As P and V are
inversely proportional
A plot of V versus P
results in a curve.
Since PV = k
V = k (1/P)
This means a plot of
V versus 1/P will be
a straight line.
A sample of chlorine gas occupies a volume of 946 mL
at a pressure of 726 mmHg. What is the pressure of
the gas (in mmHg) if the volume is reduced at constant
temperature to 154 mL?
Charles’s Law
• The volume of a fixed
amount of gas at
constant pressure is
directly proportional to its
absolute temperature.
• i.e.,
V =k
T
A plot of V versus T will be a straight line.
A sample of carbon monoxide gas occupies 3.20 L at
125 0C. At what temperature will the gas occupy a
volume of 1.54 L if the pressure remains constant?
Avogadro’s Law
• The volume of a gas at constant temperature
and pressure is directly proportional to the
number of moles of the gas.
• Mathematically, this means
V = kn
Ammonia burns in oxygen to form nitric oxide (NO)
and water vapor. How many volumes of NO are
obtained from one volume of ammonia at the same
temperature and pressure?
Ideal-Gas Equation
• So far we’ve seen that
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
• Combining these, we get
nT
V
P
The Ideal Gas Equation
- Combine the gas laws (Boyle, Charles,
Avogadro) yields a new law or equation.
Ideal gas equation:
PV = nRT
R = gas constant = 0.08206 L.atm/mol-K
P = pressure (atm) V = volume (L)
n = moles
T = temperature (K)
The conditions 0 0C and 1 atm are called standard
temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal
gas occupies 22.414 L.
R = 0.082057 L • atm / (mol • K)
What is the volume (in liters) occupied by 49.8 g of HCl
at STP?
Argon is an inert gas used in lightbulbs to retard the
vaporization of the filament. A certain lightbulb
containing argon at 1.20 atm and 18 0C is heated to
85 0C at constant volume. What is the final pressure of
argon in the lightbulb (in atm)?
Densities of Gases
If we divide both sides of the ideal-gas
equation by V and by RT, we get
n
P
=
V
RT
Densities of Gases
• We know that
– moles  molecular mass = mass
n=m
• So multiplying both sides by the
molecular mass ( ) gives
m P
=
V RT
Densities of Gases
• Mass  volume = density
• So,
m P
d=
=
V RT
• Note: One only needs to know the
molecular mass, the pressure, and the
temperature to calculate the density of
a gas.
Molecular Mass
We can manipulate the density equation
to enable us to find the molecular mass
of a gas:
P
d=
RT
Becomes
dRT
= P
Gas Stoichiometry
What is the volume of CO2 produced at 370 C and 1.00
atm when 5.60 g of glucose are used up in the reaction:
C6H12O6 (s) + 6O2 (g)
6CO2 (g) + 6H2O (l)
Gas Mixtures and Partial Pressures
Dalton’s Law
Dalton’s Law - In a gas mixture the total
pressure is given by the sum of partial
pressures of each component:
Pt = P1 + P2 + P3 + …
- The pressure due to an individual gas is called
a partial pressure.
Consider a case in which two gases, A and B, are in a
container of volume V.
nART
PA =
V
nA is the number of moles of A
nBRT
PB =
V
nB is the number of moles of B
PT = PA + PB
PA = XA PT
nB
XB =
nA + nB
nA
XA =
nA + nB
PB = XB PT
Pi = Xi PT
where i is the mole fraction (ni/nt).
A sample of natural gas contains 8.24 moles of CH4,
0.421 moles of C2H6, and 0.116 moles of C3H8. If the
total pressure of the gases is 1.37 atm, what is the
partial pressure of propane (C3H8)?
Partial Pressures
• When one collects a gas over water, there is
water vapor mixed in with the gas.
• To find only the pressure of the desired gas,
one must subtract the vapor pressure of
water from the total pressure.
Kinetic-Molecular Theory
This is a model that
aids in our
understanding of what
happens to gas
particles as
environmental
conditions change.
Kinetic-Molecular Theory
- Theory developed to explain gas behavior
- To describe the behavior of a gas, we must
first describe what a gas is:
– Gases consist of a large number of molecules in
constant random motion.
– Volume of individual molecules negligible
compared to volume of container.
Kinetic-Molecular Theory
– Intermolecular forces (forces between gas
molecules) negligible.
– Energy can be transferred between molecules,
but total kinetic energy is constant at constant
temperature.
– Average kinetic energy of molecules is
proportional to temperature.
Kinetic-Molecular Theory
ε = ½ mu2
Application to the Gas laws
•
•
Effect of Volume increase at constant temperature
•
More space
•
Fewer collisions
•
u is unchanged
Effect of a temperature increase at constant volume
•
Less Space
•
More collisions
•
Increase in u
Molecular Effusion and Diffusion
• Consider two gases at the same temperature:
the lighter gas has a higher u than the heavier
gas.
• Mathematically:
u
3 RT
M
• The lower the molar mass, M, the higher the
u for that gas at a constant temperature.
Molecular Effusion and Diffusion
Effusion
The escape of
gas molecules
through a tiny
hole into an
evacuated
space.
Diffusion
The spread of
one substance
throughout a
space or
throughout a
second
substance.
NH4Cl
NH3
17 g/mol
HCl
36 g/mol
Molecular Effusion and Diffusion
Graham’s Law of Effusion
Graham’s Law of Effusion – The rate of
effusion of a gas is inversely proportional to
the square root of its molecular mass.
r1
M2

r2
M1
• Gas escaping from a balloon is a good
example.
Molecular Effusion and Diffusion
Diffusion and Mean Free Path
• Diffusion of a gas is the spread of the gas
through space.
• Diffusion is faster for light gas molecules.
• Diffusion is slowed by gas molecules colliding
with each other.
• Average distance of a gas molecule between
collisions is called mean free path.
Real Gases
In the real world, the
behavior of gases
only conforms to the
ideal-gas equation at
relatively high
temperature and low
pressure.
Real Gases: Deviations from Ideal
Behavior
• From the ideal gas equation, we have
PV = nRT
• This equation breaks-down at
– High pressure
• At high pressure, the attractive and repulsive forces
between gas molecules becomes significant.
– Small volume
• At small volumes, the volume due to the gas
molecules is a source of error.
Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular
model break down at high pressure and/or low
temperature.
Corrections for Nonideal
Behavior
• The ideal-gas equation can be adjusted to
take these deviations from ideal behavior
into account.
• The corrected ideal-gas equation is
known as the van der Waals equation.
Real Gases: Deviations from Ideal
Behavior
The Van der Waals Equation
• Two terms are added to the ideal gas equation to correct
for volume of molecules and one to correct for
intermolecular attractions.
2
n a
nRT
P

V  nb V 2
• a and b are constants, determined by the particular gas.
The van der Waals Equation
n2a
(P + 2 ) (V − nb) = nRT
V
Example
• Consider a sample of 1.00 mol of carbon
dioxide gas confined to a volume of
3.000L at 0.0 C. Calculate the pressure of
the gas using the van der waals equation