Chapter 12 - Gases
-
Expand to fill a volume (expandability)
Compressible
Form homogeneous mixtures with other gases
All are due to large distances between the gas
molecules.
Pressure - force acting on an object per unit area.
F
P
A
- Atmospheric pressure is measured with a barometer.
- Standard atmospheric pressure is the pressure
required to support 760 mm of Hg in a column.
- Units:
- Pascal (Pa), N/m2 (SI unit)
- Millimeters of Mercury (mmHg)
- Torr (same as mmHg) (torr)
- Atmospheres (atm)
- Conversion Factors
- 1 atm = 760 mmHg
- 1 atm = 760 torr
- 1 atm = 1.01325  105 Pa
- 1 atm = 101.325 kPa
The Gas Laws
4 variables are required to describe a gas:
-
Amount in moles
Volume (usually Liters):
Pressures (usually atm):
Temperature (usually Kelvin):
n
V
P
T
Gas laws - equations that relate 2 of these variables
when the other 2 variables are held constant
1. Pressure-Volume Relationship: Boyle's Law
The volume of a fixed quantity of gas at constant
temperature is inversely proportional to its pressure.
1
P
(constant n and T )
V
P1V1  P2V2
PV  constant
2. Temperature-Volume Relationship- Charles’ Law
The volume of a fixed quantity of gas at constant pressure
increases as the temperature increases.
V  T (constant n and P )
V1 V2

T1 T2
V  constant  T
V
 constant
T
3. Moles-Volume relationship - Avogadro’s Law
The volume of gas at a given temperature and pressure is
directly proportional to the number of moles of gas.
V  n (constant P and T )
The Ideal Gas Equation (Law)
Combines the gas laws (Boyle, Charles, Avogadro) into
one equation.
PV = nRT
P = pressure (atm)
V = volume (L)
n = moles
T = temperature (K)
R = Ideal gas constant (constant of proportionality)
= 0.08206 L-atm/K-mol
Standard gas conditions
STP (standard temperature and pressure)
T= 0C, 273.15 K
P=1 atm
Standard Molar Volume
Volume of 1 mol of gas at STP = 22.4 L
Independent of what gas it is.
Gas Densities and Molar Mass
- Rearranging the ideal-gas equation with M as molar
mass yields
- Recall d = g/V and M = g/mol (n = mol)
PM
d
RT
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 + …
Partial pressure= pressure due to an individual gas
Proportional to its mole fraction
- Mole fraction of gasi
- i = moles of gasi/ total moles = n i /ntotal
Partial pressure of gasi = Pi = iPt
Kinetic-Molecular Theory
- Helps explain gas behavior
- General description of a gas:
– Large number of molecules in constant
random motion.
– Volume of individual molecules negligible
compared to volume of container.
– No attractive or repulsive forces between gas
molecules
– Energy can be transferred between molecules,
but total kinetic energy is constant at constant
temperature.
– Average kinetic energy of molecules is
proportional to temperature
– Picture as tiny billiard balls that move in
straight paths and can bounce off of each
other
Boyle's Law
• Pressure exerted by a gas is the result of
bombardment of the walls of the container by the
gas molecules.
• Pressure varies directly with the number of
molecules hitting the wall per unit time.
– If the volume is reduced the number of
impacts is increased; therefore, the pressure is
increased.
Charle's Law
• The force that a gas molecule strikes the side of a
container is directly proportional to the
temperature.
• As the temperature is increased the kinetic energy
(force) of the gas particles increases.
• For the pressure to be constant, the area the force
is applied to must be increased (the volume is
increased).
Dalton's Law
• There are large distances between the gas
molecules.
• The components of a mixture will bombard the
walls of the container with the same frequency in
the presence of a mixture as it would by itself.
Molecular Speeds
• As kinetic energy increases, the velocity of the gas
molecules increases.
• Root mean square speed, u, is the speed of a gas
molecule having average kinetic energy.
• Average kinetic energy, KE, is related to root
mean square speed:
KE = ½mu2
• Consider two gases at the same temperature: the
lighter gas has a higher u than the heavier gas.
• Mathematically:
u
3RT
M
• The lower the molar mass, M, the higher the u for
that gas at a constant temperature.
Effusion – The escape of gas through a small opening.
• Gas escaping from a balloon is a good example.
Graham’s Law of Effusion
r1
M2

r2
M1
Diffusion – The spreading of one substance through
another.
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.
• At sea level, mean free path is about 6  10-6 cm.
Real Gases: Deviations from Ideal Behavior
• Ideal gas 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.
The Van der Waals Equation
• Two terms are added to the ideal gas equation
• One to correct for volume of molecules
• One to correct for intermolecular attractions.
nRT
n2a
P
 2
V  nb V
• a and b are constants, determined by the
particular gas.