CHAPTER 11
PROPERTIES OF GASES
 Gases have an indefinite shape: a gas takes the shape of its container
and fills it uniformly. If the shape of the container changes, so does
the shape of the gas.
 Gases can expand: a gas continuously expands and distributes itself
throughout a sealed container. This means that the volume of gas
increases when we enlarge the volume of container.
 Gases can compress: the volume of gas in a sealed container
decreases when we reduce the volume. If we reduce the volume
sufficiently, the gas will eventually liquefy.
 Gases have low densities: the density of air is about 0.001g/mL
(g/L). The density of water, on the other hand, is 1.0g/mL, thus air is
about 1000 times less dense than water.
 Gases mix completely with other gases in the same container: air is
a common example of gaseous mixture. During photosynthesis, plants
release oxygen gas which mixes with other gases in the atmosphere.
ATMOSPHERIC PRESSURE
Gas pressure is the result of conversely moving molecules striking the
inside surface of their container. The pressure that a gas exerts depends
on how often and how hard these molecules strike the walls of the
container.
 If the molecules collide more often, the gas pressure increases.
 If the molecules collide with more energy, the pressure increases.
As temperature increase, the molecules move faster and collide more
frequently and with more energy.
Atmospheric pressure is the result of air molecules in the
environment. The pressure of the atmosphere is about 15 pounds on every
square inch of surface. Atmospheric pressure operates in all directions. A
barometer is used to measure atmospheric pressure. Standard atmospheric
pressure is 1 (atm), which at sea level, Torricelli showed that the height
which of mercury measures 29.9 inches.
The table below is an expression for the same standard pressure; we
can relate one unit to the other:
Unit
Standard Pressure
Atmosphere
1 atm
Inches of mercury
29.9 in Hg
Centimeters of mercury
76 cm Hg
Millimeters of mercury
Torr
Pounds per square inch
Kilopascal
760 mmHg
760 torr
14.7 psi
101 KPa
Converting 2550 torr to atm,
2550 torr x 1 atm
= 3.36 atm
760 torr
Example: Given that the guage pressure of an automobile tire is 34.0 psi,
express the pressure in each of the following units: atm, cmHg, torr, and
KPa.
34.0psi x 1 atm
= 2.31 atm
14.7 psi
34.0 psi x 76 cmHg
= 175.8 cmHg
14.7 psi
34.0 psi x 760 torr
= 1757.8 torr
14.7 psi
34.0 psi x 101 KPa
= 233.6 KPa
14.7 psi
VARIABLES AFFECTING GAS PRESSURE
I.
Increase or decrease the volume of the container.
When we increase the volume, gas molecules are further apart and collide
less frequently, and thus pressure decrease. When decrease the volume
however, gas molecules are closer together and collide more frequently,
and pressure increases, the pressure is INVERSELY related to volume.
(Increase in volume brings about decrease in pressure and vice versa)
II.
Increase or decrease the temperature of the gas.
When we increase the temperature, gas molecules move faster and collide
with greater frequency and energy. When we decrease temperature
however, the gas molecules move slower and collide less frequently. The
pressure is said to be DIRECTLY related to temperature. (Increase in
temperature brings about increase in pressure and vice versa)
III. Increase or decrease the number of molecules in the container.
Avogadro’s theory states that equal volumes of gases, at the same
temperature and pressure, contain equal number of molecules. When we
increase the number of molecules, there are more collisions and pressure
increases. When we decrease number of gas molecules, there are fewer
collisions and pressure decrease. The pressure is said to be DIRECTLY
related to the number of moles of gas or the number of gas molecules.
(Increase in the number of molecules increases the pressure and vice
versa)
BOYLE’S LAW
Boyles law states that the volume of a gas is INVERSELY
proportional to the pressure when the temperature remains constant.
Inversely proportional means two variables have reciprocal relationship,
as one increases, the other decreases. Boyle’s demonstrated this law
using the J-tube experiment with varying pressure to illustrate this law.
Vα 1 (temperature constant)
P
V = volume, P = pressure, α = proportional sign, 1/ = inverse
V=Kx1
(cross multiplying)
P
PV = K
P1V1 = K = P1V2
P1V1 = P2V2
Example: In an experiment 5.00L of propane gas is compressed and the
pressure increases from 1.00atm to 1.5atm, calculate the final volume.
Using, P1V1 = P2V2
P2
P2
V2 = P2V2
P2
V2 = 1.00atm x 5.00L
1.5atm
CHARLES’ LAW
Charles states that the volume of a gas is DIRECTLY proportional to
the Kelvin temperature if pressure remains constant. As the Kelvin
temperature increases, the volume also increases.
V α T (pressure is constant)
V = KT
V=K
T
V1 = K = V2
T1
T2
Example: In an experiment, a sample of argon gas at 225K is heated and the
volume increases from 3.50L to 12.5L, calculate the final temperature.
Using, V1 = V2
T1
T2
T2V1 = T1V2
V1
V1
(cross multiplying)
T2 = T1V2
V1
T2 = 12.5L x 225K = 803.6K = 804K
3.50L
GAY- LUSSAC’S LAW
Gay- Lussac’s law states that the pressure of a gas is DIRECTLY
proportional to the Kelvin temperature if the volume remains constant. As
the pressure increases, there is increase in temperature.
PαT
(volume is constant)
P=KT
T T
P=K
T
P1 = k = P2
T1
T2
Example: A copper container has a volume of 555 mL and is filled with air
at 25oC. The container is immersed in dry ice, and the pressure of the gas
drops from 761 torr to 495 torr. What is the final temperature of the air in the
copper container? T1 = 25 oC + 273 = 298 K
Using, P1 = P2 (cross multiplying)
T1
T2
T2 P1 = T1 P2
P1
P1
T2 = T1 P2
P1
T2 = 495 x 298
761
= 193.8K = 194K (-79 oC)
COMBINED GAS LAW
These three laws- Boyles, Charles’ and Gay-Lussac’s laws can be
combined, considering the fact that we could limit our treatment of gases to
two variables. Experiments showed that all these three variables
(temperature, volume and pressure) usually change simultaneously. The
resulting expression is known as combined gas law.
V1 P1 = V2 P2
T1
T2
Example: Consider the table below,
Condition
Pressure
Initial
1.00 atm
Final
P2
Volume
10.0L
20.0L
Temperature
300K
600K
Using, V1 P1 = V2 P2
T1
T2
P2 = V1 P1 T2
V2T1
= 1.00 atm x 10.0L x 600K
20.0L x 300K
= 1.00 atm
The standard temperature and pressure (STP) for a gas are 0oC and 1
atm. We also express standard pressure in other units such as 760mmHg,
760 torr or 760mmHg.
Example 2: A nitrogen gas sample occupies 50.5mL at -80 oC and 1250 torr.
What is the volume at STP?
Condition
Initial
Final
Pressure
1250 torr
760 torr
Volume
50.5mL
V2
Temperature
-80+273= 193K
273K
Using, V1 P1 = V2 P2
T1
T2
V2 = V1 P1 T2
P2T1
= 1250 torr x 50.5 mL x 273K
193K x 760 torr
= 117 mL
THE VAPOR PRESSURE CONCEPT
Vaporization occurs when molecules have enough energy to
escape from liquid phase to gaseous phase. This process occurs when the
container is opened, but when the container is closed, the molecules are
trapped above the liquid. As the molecules vaporize into gaseous phase, they
also turn from gas to liquid phase (condensation) at constant temperature. A
kind of pressure is introduced due to this effect, the pressure is known as
vapor pressure. The barometer is used to measure vapor pressure.
DALTON’S LAW (PARTIAL PRESSURE)
Dalton’s law of partial pressures states that the total pressure of
a gaseous mixture is equal to the sum of the individual pressures of each gas.
P1 + P2 + P3 …………= Ptotal
The pressure exerted by each gas in the mixture is called partial
pressure. We can collect a gas over water to determine the volume by
displacement. A wet gas collected over water contains water vapor.
Pgas + Pwater vapor = Patmosphere
Pgas = Patmosphere - Pwater vapor
IDEAL GAS BEHAVIOR
KINETIC THEORY OF GASES
An ideal gas, is a gas that always behaves in a consistent and
predictable manner. Experimentally, a real gas such as oxygen, hydrogen
does not behave ideally under all conditions. According to kinetic theory of
gases, an ideal gas has the following characteristics:
 Gases are made up of very tiny molecules, for example, molecules
occupy a negligible volume.
 Gas molecules demonstrate rapid motion, move in straight lines,
and travel in random directions.
 Gas molecules have no attraction for one another, example, they
do not stick together after collision.
 Gas molecules undergo elastic collisions, for example, they do not
lose kinetic energy after collision.
 The average kinetic energy of gas molecules is proportional to the
Kelvin temperature that is K.E α T .At the same temperature; all
molecules have the same kinetic energy.
When you have two different elements in a compound, at the
same temperature, they will have same K.E but the one that is lighter moves
faster than heavier one.
ABSOLUTE ZERO
The temperature at which the pressure and volume of a gas
theoretically reaches Zero is referred to as ABSOLUTE ZERO. This is the
coldest possible temperature and it corresponds to -2730C or 0K.
An ideal gas at absolute zero has no kinetic energy and therefore
no molecular motion.
IDEAL GAS LAW
P α nT
V
P = RnT
(cross multiplying)
V
PV = nRT
P = Pressure; n = number of moles; V = Volume; T = Temperature; R = gas
constant ( 0.0821 atm.L/mol)
This is called ideal gas law.
Example: If a sealed container holds 1.10 mol of nitrogen gas at 250C and
3.75 atm, what is the volume in Liter?
Using,
P = RnT
V
V = nRT
P
V = 1.10 x 0.0821 x 298
3.75
= 7.18L