Gas Laws
• Boyle’s Law
• Charles’s law
• Gay-Lussac’s Law
• Avogadro’s Law
• Dalton’s Law
• Henry’s Law
1
Properties of Gases
•
•
•
•
•
Expand to completely fill their container
Take the shape of their container
Low density
Compressible
Mixtures of gases are always
homogeneous
• Fluid
Lets talk units for Gas Laws
P, V, n, T
• We need four variables:
• Volume (V) in Liters
• Pressure (P) ~ next slide
• Temperature (T) in Kelvin (T(K) = T(oC) + 273)
• Moles (n) in moles
3
Gas Pressure
• Pressure = total force applied to a certain area
• Larger force = larger pressure
• Smaller area = larger pressure
• Gas pressure caused by gas molecules colliding
with container or surface
• More forceful or more frequent collisions mean
higher gas pressure
Units of Gas Pressure
• Atmosphere (atm)
•
•
•
•
Height of a column of mercury (mm
Torr
Pascal (Pa)
Pounds per square inch (psi, lbs/in2)
Hg, in Hg)
• 1.000 atm = 760.0 mm Hg = 29.92 in Hg =
760.0 torr = 101,325 Pa = 101.3 kPa =
14.69 psi
Air Pressure
• Constantly present when air present
• Decreases with altitude
• Less air = less pressure
• Varies with weather conditions
Measuring Air Pressure
Barometer
Weight of
mercury
• The mercury in the tube pushes
down with its weight.
• The bottom of the tube is open
to the atmosphere.
• The air pushes on the open
surface of the mercury.
• On an average day, the
pressure of the air equals the
pressure exerted by a column of
mercury 760 mm high.
• Above 760 mm, there is a
vacuum in the tube.
Units conversions
1.000 atm = 760.0 mm Hg = 29.92 in Hg = 760.0 torr = 101,325 Pa = 101.3 kPa = 14.69 psi
T(K) = T(oC) + 273
1. 745 mm Hg to pascals?
2. 5.43 atm to mm Hg?
3. 35oC to Kelvin?
8
P, V, T, n (n = moles): Avogadro’s Law
• Imagine blowing up a balloon
• When P & T are held constant, The relationship
between n and V is directly proportional
• Volume directly proportional to the number of gas molecules
As moles , Volume 
V1
= constant, so
n1
V1 V2
=
n1 n 2
9
Avogadro’s Law (cont.)
• Count number of gas molecules by moles
• Equal volumes of gases contain equal numbers
of molecules.
• One mole occupies 22.4 L at standard conditions
• It doesn’t matter what the gas is!
Practice Problem 4
• If 2.55 mol of helium gas occupies a volume of 59.5 L at a particular
temperature and pressure, what volume does 7.83 mol of helium
occupy under the same conditions?
V1 V2

n1 n 2
Answer: 183 L
P, V, T, n (n = moles): Boyle’s Law
•When n & T are held constant, the relationship
between P and V is inversely proportional.
As Pressure , Volume 
•P x V = constant, so
P1 x V1 = P2 x V2
12
Practice Problem 8
A sample of helium gas has a pressure of 3.54 atm in a
container with a volume of 23.1 L. This sample is transferred
to a new container and the pressure is measured to be 1.87 atm.
What is the volume of the new container? Assume constant
temperature.
Answer: V2 = 43.7 L
Ideal Gas Law
PV = nRT
• Using the gas laws together, we can write a general
equation.
• Use the Ideal Gas Law when you have gas at one set of
conditions
• R is called the gas constant.
• R = 0.08206 atm*L/mol*K
ATTENTION TO UNITS!)
(PAY
Practice Problem 12
• A 5.00 mol sample of oxygen gas has a pressure of 1.25 atm at 22°C.
What volume does this gas occupy?
Answer: 96.8 L
PV = nRT
When are gases close to ideal?
• Low pressure- lots of empty space; molecules can
be treated as having no volume.
• High temperature- molecules have enough speed
that attractions are negligible.
Read Ch. 13
Do self-check problems
Also do end-of-chapter problems:
7, 11, 18, 20, 32, 34, 42, 50, 52, 56
Practice Problem 13
• A sample of neon gas has a volume of 3.45 L at 25°C and a pressure
of 565 torr. Calculate the number of moles of neon present in this
gas sample?
Answer: 0.105 mol
PV = nRT
Practice Problem 14
• A 0.250 mol sample of argon gas has a volume of 9.00 L at a
pressure of 875 mm Hg. What is the temperature (in °C) of the gas?
Answer: 232 °C
PV = nRT
Kinetic-Molecular Theory of Gases
•
•
•
•
20
KMT - the theory of moving molecules
Gases consist of large numbers of continuously moving particles.
The volume caused by the molecules is negligible.
The particles are in constant random motion, colliding with the
walls of the container. These collisions with the walls cause the
pressure exerted by the gas.
• Interactive (attractive or repulsive) forces are negligible.
• Energy is transferred during collisions but the average total stays
constant. (Collisions are perfectly elastic.)
• The average kinetic energy of the gas particles is directly
proportional to the Kelvin temperature of the gas.
P, V, T, n (n = moles): Charles’ Law
• Observe: on on top of the flask
• When n & P are held constant, The relationship
between V and T is
Directly proportional or Inversely proportional?
Directly proportional!
As Temperature , Volume 
V1
= constant, so
T1
V1 V2
=
T1 T2
21
Practice Problem 6
A sample of oxygen gas has a volume of 4.55 L at 25°C.
Calculate the volume of the oxygen gas when the temperature
is raised to 45°C. Assume constant pressure
• V1
T1
=
V2
T2
Answer: V2 = 4.86 L
P, V, T, n (n = moles): Gay-Lussac’s Law
• Observe: Absolute Zero devise and Soda can
• When n & V are held constant, The relationship
between P and T is
Directly proportional or Inversely proportional?
Directly proportional!
As Temperature , Pressure 
P1
= constant, so
T1
P1 P2
=
T1 T2
23