Gases and their Laws
Pressure (P)
Force/Area = N/cm3
Force/Small Area = Greater Pressure
Force/Large Area = Less Pressure
1 atm of atmospheric pressure at sea level
= 10.1 N/cm3
Measuring PressureAir pressure is measured using a
barometer
Two of the most common barometers
are the mercury barometer and the
aneroid barometer
Units of PressureUnit Symbol Conversions
Pascal Pa 1 Pa = 1 N/m2
Millimeter of Mercury mm Hg 760 mm Hg = 1 atm
Torr torr 1 torr = 1 mm Hg
Atmosphere atm *See below
Pounds per square inch psi 14.700 psi = 1 atm
Normal atmospheric pressure:
1 atm = 760 mm Hg (torr) = 101.3 kPa
Dalton’s Law of Partial Pressure
The total pressure of a mixture of
nonreacting gases is equal to
the sum of the partial pressures
of the individual gases
Ptotal = P1 + P2 + P3 + and so on…
Dalton’s Law of Partial Pressure
Dalton found that the total pressure of mixed
gases is equal to the sum of their individual
pressures (provided the gases do not react).
Ptotal = Poxygen + Pnitrogen
+
1 L oxygen
50 kPa
1 L nitrogen
100 kPa
1 L mixed gas
150 kPa
=
Note: all of these volumes are the same
Practice Problems with
Dalton’s Law1. Calculate the partial pressure in millimeters of
mercury exerted by the four main gases in the
air at 760 mm Hg. The gases abundance by
volume is as follows 78.08% N2, 20.95% O2,
0.934% Ar, and 0.035% CO2
2. A student has stored 100.0 mL of neon gas
over water on a day when the temperature is
27.0°C. If the barometer in the room reads
743.3 mm Hg, what is the pressure of the neon
gas in its container? (Water vapor pressure =
26.7 mm Hg)
Boyle’s Law: Pressure-Volume
If pressure increases volume decreases
If pressure decreases volume increases
Inverse relationship between pressure
and volume (PV = k)
P1V1 = P2V2
(At constant temperature)
Practice Problems with
Boyle’s Law1. The piston of an internal combustion engine
compresses 450.0 mL of gas. The final
pressure is 15 times greater than the initial
pressure. What is the final volume of the
gas, assuming constant temperature?
2. A helium-filled balloon contains 125 mL of
gas at a pressure of 0.974 atm. What
volume will the gas occupy at standard
pressure?
The study of gases in early 1800's in France concerned hot air balloons popularity and wanting to improve the performance of the balloons
Jacques Charles and Joseph-Louis Gay-Lussac (French scientists) were interested in the temperature-volume-pressure relationship for a gas in a hot air balloon
Charles and Gay-Lussac
Charles's Law: Volume-
TemperatureIf temperature increases volume increases
If temperature decreases volume decreases
Direct relationship between temperature and
volume (V/T = k) *Temperature must be in KELVIN
V1/T1 = V2/T2
(at constant pressure)
Practice Problems with
Charles’s Law1. Assume constant pressure: A balloon filled
with oxygen gas occupies a volume of 5.5 L
at 25°C. What volume will the gas occupy
at 100.0°C?
2. A sample of nitrogen gas is contained in a
piston with a freely moving cylinder. At
0.0°C, the volume of the gas is 375 mL. To
what temperature must the gas be heated
to occupy a volume of 500.0 mL?
Gay-Lussac's Law: Pressure-
TemperatureIf temperature increases pressure increases
If temperature decreases pressure decreases
Direct relationship between temperature and
volume (P/T = k) *Temperature must be in KELVIN
P1/T1 = P2/T2(at constant volume)
Practice Problems with
Gay-Lussac’s Law1. Assume a gas was at a constant volume: A
gas cylinder at room temperature (20°C) is
thrown into an incinerator where the
temperature reaches 500.0°C. If the gas
inside the container was initially at a
pressure of 1.0 atm, what pressure did it
reach inside the incinerator without
exploding?
The Combined Gas LawPressure-Volume-Temperature
Relationship of a gas at a
FIXED amount (PV/T = k)Temperature must be in Kelvin
P1V1/T1 = P2V2/T2
Practice Problems with
Combined Gas Law1. The volume of a gas at 27.0°C and
0.200 atm is 80.0 mL. What volume will
the same gas sample occupy at
standard conditions?
2. A gas occupying 75 mL at standard
conditions is heated to 17°C while the
pressure is reduced to 0.97 atm. What
is the new volume occupied by the gas?
Avogadro’s Law Equal volumes of gases at the same
temperatures and pressure contain
equal number of molecules
V = kn
n is moles of gas
Coefficients in reactions involving
gases = the relative # of molecules,
moles, and volumes
Practice Problems with
Avogadro’s LawOzone, O3, can be formed from diatomic
oxygen in the following reaction:
3O2(g) 2O3(g)
1. How many molecules of ozone are
formed from the reaction of 24 oxygen
molecules?
2. How many liters of ozone are formed
from 12 L of oxygen?
Volume at STPStandard Molar Volume: The volume
occupied by 1 mole of a gas at
standard temperature and pressure
1 mol = 22.4 L (at STP)
You are planning an experiment that requires 0.0580 mol
of NO. What volume would you need at STP?
Answer: 1.2992 L
Ideal Gas LawRelationship between: pressure-
volume-temperature-# of moles
PV = nRTn = # of moles
R = Universal Gas Law Constant
8.3145 J/mol K
Other values of R on Table 2 pg 384
Practice Problems with
Ideal Gas LawA 2.07 L cylinder contains 2.88 mol
of helium gas at 22°C. What is the
pressure in atmospheres of the
gas in the cylinder?
Graham’s Law of EffusionThe rates of effusion of gases at the
same temperature and pressure are
inversely proportional to the square
roots of their molar masses
½ MAvA2 = ½ MBvB
2
rate of effusion of A = √MB
rate of effusion of B √MA
MA = molar mass of gas A
vA = velocity of gas A
Practice Problems with
Graham’s Law
At 25°C, the average velocity of
oxygen molecules is 420 m/s.
What is the average velocity
of helium atoms at the same
temperature?