Chapter 13
Gases and the Gas Laws
Mythbuster – water heater
Intro to gas laws
Gas Laws in Action: workers steam cleaned this tanker car
and then sealed up the container, they came back the
following morning to this disaster. (video)
Kinetic Theory
Assumptions for an Ideal Gas





Gas particles are in constant, random motion
Gas particles themselves have virtually no
volume
Gas particles do not attract nor repel each other
No kinetic energy is lost when particles collide
If gases are at the same temp. they have the
same KE

NOTE:

Real gases (actual gases) do NOT obey all the
assumptions made by the kinetic theory (only
ideal gases behave this way- we will get
exceptions later)
Factors (variables) that Affect Gases
1.
2.
3.
4.
Number of gas particles present
Temperature
Pressure
Volume of the sample
In a tied off balloon the pressure from the outside = pressure
from the inside (in this chapter we will look at how changing
the factors, changes these values)
=
STP
Standard temperature and standard pressure
 Standard temperature = 0° C (273 K)
 Standard pressure = 101.3 kPa (1 atm or
760 mm Hg)

Boyles Law
States that the volume of a gas is inversely
proportional to its pressure if the
temperature remains constant
 As pressure goes up, volume goes down and
vice versa if temperature is constant
 PV = k

P
V
P1=
1 atm V1= 800 ml
P2=
2 atm V2= 400 ml
P3=
3 atm V3= 267 ml
P1V1 = 800
P2V2 = 800
Boyles Law
So: P1V1 = P2V2
PxV
800
800
800

If .600 L (V1)of a gas at 100.0 kPa (P1)
changes to 62.4 kPa.(P2) What is the new
volume if temperature remains constant?
P1V1 = P2V2
(100.0 kPa) (.600L) = (62.4 kPa) (V2)
.96153 L = V2
.962 L = V2
Note: you do not need to convert units as long as they match
on both sides of the equation
A 185 ml sample has a pressure of 4.2 atm.
What is it’s pressure when the volume is
250 ml if temperature remains constant?
P1V1 = P2V2
(4.2 atm)(185 ml) = P2 (250 ml)
3.1 atm = P2
Charles Law
Jacque Charles investigated the property of
changing temperature on the volume of a
gas (saw w/ each ° C change the volume
changed by 1/273rd)
 Charles Law – volume of a fixed mass of
gas is directly proportional to its kelvin
temperature if the pressure is constant
 Ex. Helium balloon deflates when walking
outside on a cold day


Charles Law:
V1 =
V2
T1
T2
***
or
V1T2 = V2T1
“T” must be in Kelvin ( K = C +273)

A balloon inflated in an air conditioned
room at 28° C (T1) has a volume of 4.0 L
(V1). If it is heated to a temperature of 58
°C ( T2), what is the new volume (V2) of the
balloon if pressure remains constant?
V1 =
V2
T1
T2
T1 = 28 + 273 = 301K
T2 = 58 + 273 = 331 K

V1T2 = V2
T1
(4.0 L ) (331 K) = V2
(301 K)
4.4 L = V2

Adjust the volume of 609 ml of a gas at
83°C to standard temperature.
Gay-Lussac’s Law
States that the pressure of a gas is directly
proportional to the Kelvin temperature if
volume is kept constant
 Ex. Spray paint can (rigid container) in a
bonfire

P1 =
P2
T1
T2
or
P1T2 = P2T1
“T” must be in Kelvin
The pressure of a gas in a tank is 3.20 atm
(P1) at 22.0 °C (T1). If the temperature is
raised to 60.0 °C (T2), what is the new
pressure (P2) if volume is held constant?
 T1 = 22.0 + 273 = 295 K
 T2 = 60.0 + 273 = 333 K

P1 =
P2
T1
T2
P1T2 = P2
T1
(3.20 atm) (333K) = P2
295 K
3.61 atm = P2
The Combined Gas Law
Many times it is hard to keep a variable
constant (and only deal with changing 2
variables at a time), so we have to use all
the laws together
 Combined Gas Law: all the variables of
pressure, temperature and volume change
(only thing that is constant is the number of
particles)

P1V1 = P2V2
T1
T2
or
P1V1T2 = P2V2T1
Find the volume of a gas at STP if it measures 806 ml at 26.0° C
and 103.0 kPa
P1V1 = P2V2
T1
P1 = 103.0 kPa
V1 = 806 ml
T1 = 26.0 + 273 = 299 K
P2 = 101.3 kPa (standard pressure)
V2 = ?
T = 273 K (standard temperature)
T2
(103.0 kPa) (806 ml) = (101.3 kPa) (V2)
299 K
273 K
(103.0 kPa) (806ml) (273 K)
(299 K) (101.3 kPa)
748 ml = V2
= V2
Gases and the MOLE
Avogadro’s Principle: at equal temperatures
and equal pressures, equal volumes of gases
contain the same number of molecules
 Molar Volume: volume occupied by 1 mole
of any gas under STP (0 °C, 101.3 kPa) is
22.4 L (conversion factor= 22.4 L/1 mole)

O2
He
1 mole O2 at STP
1 mole He at STP
6.02 x 10 23 molecules of O2
6.02 x 10 23 atoms He
32.0 g
4.00 g
22.4 L
22.4 L

What is the volume of 8.6 g of Cl2 at STP?
1.
2.
Convert g  moles (molar mass)
Convert moles  volume (22.4 L/ mole
1) 8.6 g Cl2 1 mole Cl2
71.0 g Cl2
.12 moles
2) .12 moles
22.4 L
1 mole
2.7 L
Ideal Gas
Combines Avogadro’s principle, Boyles,
Charles and Gay-Lussac’s Law into a
statement w/ P, V, T and # moles
 Changing one variable will affect the other
3 variables
 Ideal Gas Equation:

PV = nRT
PV = nRT
n = # of mole
 R = Ideal Gas Constant ( experimentally
determined constant based on Avogadro’s #
and STP  dependent on unit used for
pressure)


Pressure in:
atm use: R= .0821 L· atm/ mole ·K
 kPa
use : R = 8.314 L ·kPa/ mole· K
 mm Hg use: R = 62.4 L· mm Hg/ mole ·K

Calculate the number of moles of gas
contained in a 3.0 L vessel at 30Ō K and a
pressure of 1.50 atm.
 PV = nRT
 PV = n
R= .0821
RT
(1.50 atm) (3.0 L) = n
n = .18 moles
(.0821 · 30ŌK)

Applying the Ideal Gas Law

Calculate molar mass:
n (# of moles) = mass of gas = m
Molar mass M
So:
PV = nRT
PV = mRT
M
M = mRT
PV
or

Calculate density:
D= m/V
M = mRT
PV
(substitute D for m/v in this equation
M = DRT
Or D = MP
P

RT
Deviations from Ideal Behavior
Ideal Gases: have no attractive forces and
do not take up space (volume)
 Real Gases:

Occupy definite volume (take up space)- but
volume is small
 Under normal conditions real gases behave like
ideal gases (follow all gas laws)

Under high pressures: particles are forced
close together and can’t compress any
further, also attractive forces take over
 So: real gases will liquefy instead of
disappearing like Boyle predicted
 Same is true under really low temperatures

Gas Laws Test
Formulas, R values and periodic table will
be given to you
 > 40 questions
 12 multiple choice
 13 fill in the blank (need to know who did
what law/PTV card/variables)
 7 calculations (1 for each formula, 1 using
22.4 L= 1 mole, 1 PV= nRt)

Know:
Who did each law
 What each law stands for
 Scenerios with each law
 Absolute zero
 STP
 Molar Volume /avogadros principle
 Variables on a gas
 Real gas vs ideal gas


When a sample of gas was placed in a
sealed container with a volume of 3.35 L
and heated to 105 C, the gas vaporized and
the resulting pressure inside the container
was 170.0 kPa. How many moles of the gas
were present?

If you have 3.50 L of water vapor at STP,
how many grams of water do you have?

Convert 3.5 L of gas at a temp of 25C and
pressure of 96.6 kPa to STP.