Unit 3: Gases
Introduction to Gases
Recall: The Particle Theory
Solid
Liquid
Gas
Properties of Gases
- most gases are odourless, colourless
Do gases take up space?
Demo: Balloon in a pop bottle
Q: How much will the volunteer be able to inflate the balloon?
Q: After I puncture the bottle how much will the volunteer be able to inflate the balloon?
Q: How do you explain this?
- gases have variable volumes (the volume of a gas is simply the volume of its container)
- gases are easily compressed
Applications of gases
Q: Where do we use gases in everyday life?
- breathing - we use O2 and exhale CO2
- O2 tanks in medicine, scuba diving
- safety
- air bags
- fire extinguishers
- fuels
- natural gas to heat homes
- butane lighters (liquid under pressure, gas at room temp)
- foods
- soda pop
- cake/ bread
- whipcream in can
- structural - tires
Since gases have high kinetic energy the observed properties of gases can be explained using the
kinetic theory of gases.
Kinetic Molecular Theory of Gases
Assumptions
- volume of individual gas molecules negligible compared to container
means individual gas molecules are extremely far apart :. container mostly empty space
- no attractive/repulsive forces between molecules
this is why they can expand to fill their containers
- molecules move rapidly in straight lines
- collisions perfectly elastic (no energy lost)
- average kinetic energy of molecules directly related to temperature
when the temperature goes up will the molecules move faster or slower?
This theory describes a hypothetical gas called an ideal gas. Real gases behave like ideal gases at
high temperatures, low pressures.
Pressure
Pressure = Force / Surface Area
P=F/A
Q- who would exert more pressure, an elephant or a woman in high heels?
Ex.
Elephant 1000 kg
25 cm * 25 cm = 625 cm2
P = 1000 kg / 625 cm2
= 1.6 kg/cm2
Woman 55 kg
1 cm * 1 cm = 1 cm2
P = 55 kg / 1 cm2
= 55 kg/cm2
How does a gas exert a pressure?
- moving gas particles strike walls of container
- collective collisions from gas molecules exert a constant pressure on container
ex is blowing up volleyball, tires of car
Atmospheric Pressure
- air molecules are being pulled down by gravity, exert a pressure on all objects on Earth
Units of Pressure
Originally based on a barometer which measured as the height of a column of Hg
- mm Hg
- torr
- atmosphere (atm)
Q: what do we measure the pressure of tires in?
- pounds per square inch (psi)
- kilopascals (kPa) * S.I. unit
Standard atmospheric pressure at OºC = 760 mm Hg
= 760 torr
= 1 atm
= 101.3 kPa
= 14.7 psi
All these different units can be used so we must be able to convert between them using the above
relationships
Converting between units
Ex. Change 675 mm Hg to kPa
Set up a ratio
known ratio 101.3 kPa / 760 mm Hg = pressure / 675 mm Hg
Solve for unknown
pressure = 101.3 kPa (675 mm Hg)
760 mm Hg
= 90.0 kPa
Lab: Boyle’s and Charles’ Laws: Pressure, Temperature and Volume
1) Demonstration: pop can crushing
 fill can with a little bit of water, set on hot plate
 once water boils :what do you observe?
 Using tongs quickly invert can into beaker of cold water
 explain
Boyle’s Law
Pressure, Temperature and Volume of a Gas
Q: what happens to the pressure
as the volume decreases?
V
Demo: take a half filled balloon
and squeeze it discuss what is
occurring to the gas molecules
(they have less room, more
collisions, pressure increases)
1/P
“At a constant temperature, the volume of a given amount of gas is inversely
proportional to its pressure”
- doubling the volume decreases the pressure by two
pressure * volume = a constant
:. P1V1 = m
And P2V2 = m
Boyle’s Law: P1V1 = P2V2
so remember that as volume goes down, pressure goes up
Charles’ Law
V
-273 C
0K
T (C)
T (K)
Demo: balloon in hot water and one in cold water  the one in the hot water should
expand
According to our graph decreasing the temperature would decrease the kinetic motion
of the gas molecules causing them to take up less volume. Hypothetically at -273 ℃
the molecules would take up no volume :. This is the lowest possible temperature
(absolute zero)
The Kelvin scale was developed to take into account absolute zero (-273℃)
Q: if temperature doubles, what happens to the volume?
Q: what has been kept constant?
“At a constant pressure, the volume of a fixed mass of a gas is directly proportional to
its temperature (in kelvins).
Charles’ Law: V1/ T1 = V2/T2
Since we must work in kelvin for this formula to work how do we convert from ℃ to K?
(look at 0 K = -273 ℃)
K= ℃ + 273
Gay-Lussac’s Law
Demo: aerosol can
Q: why does it say that this container may explode if heated?
Like most containers, this can holding gases has a fixed volume- it cannot expand or
shrink
Q: what happens to the pressure of a gas if the temperature increases but the volume
can not increase?
“At constant volume, the pressure of a fixed mass of gas is directly proportional to its
temperature (in Kelvin)”
Gay-Lussac’s Law: P1/ T1 = P2/ T2
Examples using laws:
1) A sample of a gas has a volume of 10.0 L at 100.0 kPa. If the pressure is increased
to 120.0 kPa at constant temperature, what is the new volume of the gas?
P1 = 100.0 kPa
V1 = 10.0 L
P2 = 120.0 kPa
V2 = ?
2) A sample of gas with a volume of 2.66 L at 23C is heated at constant pressure to 27
℃. What volume will it occupy?
V1 = 2.66L
T1 = 23C
= 296 K
V2= ?
T2 = 27 ℃ cannot work in ℃, change to kelvin
= 300K
3) A gas in a metal cylinder has a pressure of 130 kPa at 28℃. What will its pressure
be in atm, if heated to 358℃?
Combined Gas Law
Recall:
What is Boyle’s Law? P1V1 = P2V2
Charles’ Law? V1/T1 = V2/T2
Gay-Lussac’s Law? P1/T1 = P2/T2
In all of these there are only 2 variables changing, 1 variable is held constant
What are we missing? What happens when all three variables change?
Combined Gas Law
Lets see what would happen if we changed all 3 variables
We will go in two steps
Initial Condition
Intermediate
Final Condition
V1
V*
V2
P1
P2
P2
T1
T1
T2
1 Boyle’s Law
1 Charles’ Law
(T constant)
(P constant)
In the first step we will keep temperature constant (Boyle’s Law)
In the second step will keep pressure constant (Charles’ Law)
Go from P1 to P2, and V1 to V*
then
V* to V2, and T1 to T2
1 P1V1 = P2V*
V*/ T1 = V2/ T2
V* = P1V1 / P2
V* = V2T1 / T2
Since both equal V* what equation can we set up?
P1V1 / P2 = V2T1 / T2
This is the combined gas law, but in this form it is not easy to memorize. How can we
rearrange it to make it easier?
Combined Gas Law
P1V1 / T1 = P2V2 / T2
When 3 factors change we use this law, if only 2
factors change we use one of the other laws we’ve
learned
Cover up T1, T2  Boyle’s Law
P1, P2  Charles’s Law
V1, V2  Gay-Lussac’s Law
This is why it’s the combined gas law
Ex. A 325 ml aerosol can contains a gas at 12 ºC. If the gas is allowed to escape to a
volume of 1.48 L at 101 kPa and 21 ºC, what was its original pressure?
V1 = 325 ml
= 0.325 L
P1 = ?
T1 = 12ºC
= 285 K
V2 = 1.48 L
P2 = 101 kPa
T2 = 21ºC
= 294 K
To compare results obtained in experiments across the world, scientists have defined a
standard temperature of 273 K and pressure of 101.3 kPa (STP).
Memorize STP conditions
Ex. A gas occupies 18.0 L at 88.7 kPa and 127 ºC. What would its volume be at STP?
V1 = 18.0 L
P1 = 88.7 kPa
T1 = 127 ºC
= 400 K
V2 = ?
P2 = 101.3 kPa
T2 = 273 K
It’s not nice to carry out experiments at STP (too cold!) so we have another set of
standard conditions for working in the lab. We must also memorize SATP
Standard Ambient Temperature and Pressure (SATP) is 25ºC (298 K) and
100 kPa.
Memorize SATP conditions
Ex. A gas occupies 6.40 L at SATP. What is its temperature in ºC when it occupies
5.75 at 125kPa?
V1 = 6.40 L
P1 = 100 kPa
T1 = 298 K
V2 = 5.75 L
P2 = 125 kPa
T2 = ?
Mixtures of Gases
Gases and the Mole
So far we have changed pressure, volume and temperature in our calculations. We have always
assumed a constant mass of gas. We need to consider what happens when the amount of gas
changes.
To do this we need some experimental data: react Mg with HCl
Reaction: Mg(s) + 2 HCl (aq) 
What are the products? What type of reaction is this?
Our objective is to determine the relationship between the volume of H 2 gas collected and the amount
of H2 gas in moles.
Data chart:
length of magnesium
Temperature of water
Atmospheric pressure
Volume of gas
= 4.4 cm
= 22ºC
= 100.4 kPa
=
1805 – Gay-Lussac’s experimental Data (constant temperature and pressure)
remember that back then they didn’t know about protons/electrons :. No chemical
formulas were yet known
1. hydrogen gas +
oxygen gas 
water vapour
20 L
10L
20 L
What is the ratio of the volumes?
Volume Ratio 2:1:2
2. nitrogen gas
5L
+
hydrogen gas
15L

ammonia gas
10L
Volume Ratio 1:3:2
Gay-Lussac’s Law of Combining Gas Volumes
Gases react in simple whole number ratios when all gases are measured at the same
temperature and pressure.
This new law caused a major debate between Gay-Lussac and Dalton because these
experimental results did not match Dalton’s theory
Avogadro came up with an explanation to explain why Gay-Lussac’s experimental data
was valid
Consider two identical cans
One holding Oxygen gas
One holding Nitrogen gas
- both at the same temperature and pressure
Q: What do you think would be true about the number of molecules in each container?
Avogadro’s Hypothesis
Equal volumes of gas at the same temperature and pressure contain the same number
of molecules.
Q: If the number of molecules increases at constant temperature and pressure, will the
volume increase or decrease? Increase
Q: Does this mean that volume is directly or inversely proportional to the number of
molecules?
:. ___________________________________
remember that it is easier to count moles than molecules
The question is “what is the volume of one mole of gas?”
However volume is dependent on temperature and pressure so we must state the
temperature and pressure we are working with
We will now use the experimental results to calculate the volume of one mole of gas at
STP
Experiment
1. mass Mg = ? set up ratio where what we know is on LHS, wanted is on RHS
0.85 g
100 cm
= mass Mg
4.4 cm
mass Mg =
2. # mol Mg = ?
# mol Mg =
3. # mol H2 = # mol Mg this is a given for now, at a later point in the course we
will learn why this is the case when we study stoichiometry
-3
# mol H2 = 1.5 * 10 mol
4. PH2 = Patm – PH2O Remove water vapour from the pressure inside the gas tube
=
5. P1V1 = P2V2
T1
T2
6. convert to volume for one mole
Accepted Value
The volume of one mole of gas at STP is 22.4 L.
Memorize this or you can solve for it once you learn the ideal gas law.
Ideal Gas Law
quick review:
-What is Boyle’s Law?
Is pressure directly or indirectly proportional to volume?
-What is Charles’ Law? directly proportional?
-What is Avogadro’s Hypothesis? Volume directly proportional to # moles
Mathematically proportionality is symbolized by α
Recall
Avogadro Hypothesis V α n (n is # mol)
Boyle’s Law Vα1/P
Charles’ Law V α T
To combine proportionalities we multiply them
Since V α n × 1/P × T
V α nT / P
PV α nT
- to go from proportionality to equation we multiply by a constant
Ideal Gas Law (where R is a constant)
R is the Universal gas constant which applies to all gases
Use this formula to solve problems when nothing changes
PV = nRT
For one mole of gas at STP:
P = 101.3 kPa
V = 22.4 L
n = 1.00 mol
T = 273 K
PV = nRT
(101.3 kPa) (22.4 L) = (1.00 mol) R (273 K)
R = (101.3 kPa) (22.4 L)
1.00 mol (273 K) Notice that when you plug this into your calculator you have to
either put brackets around the entire denominator or punch in ÷ , ÷
R = 8.31 kPa·L
mol·K
To use the ideal gas law we must work in units
of moles (not mass), kPa, L
Ex. 1 Determine the volume of 2.50 g of CO2 at 25ºC and 2.00 atm.
Since nothing is changing we know that we should use the ideal gas law.
We have been given pressure in atm, what do we need to do first?
P = 2.00 atm
Ex.2. 375 ml of oxygen is collected over water at 19ºC and 100.2 kPa. What mass of
oxygen has been collected?
Can’t calculate mass using our ideal gas law but what can we calculate that we can
convert into mass?
PH2O at 19ºC =
PV = nRT
PO2
= Patm – PH2O(g)
=
watch for diatomic elements
If there is a mixture of gases, the value of n corresponds to the total number of moles
of gas.