Gas Laws

1
Gas Laws
BOYLE
CHARLES
AVOGADRO
GAY-LUSSAC
2
Consider This
What happens to the volume of a gas when you
increase the pressure? (e.g. Press a syringe
that is stoppered)
3
Consider This
What happens to the volume of a gas when you
increase the pressure? (e.g. Press a syringe
that is stoppered)
4
Consider This
What happens to the Volume of a Gas When you
Increase the Pressure? (e.g. Press a syringe
that is stoppered)
Why?
There is lots of space between gas particles.
Therefore, gases are compressible!
5
Lets investigate the relationship between
pressure and volume if the quantity of gas and
temperature are held constant.
6
100
50
Volume 50 L
7
100
50
200
25
Volume 25 L
8
100
50
200
25
400
12.5
Volume 12.5 L
9
What is the mathematical relationship between P
and V? P x V constant
100
50
5000 5000 5000 5000
200
25
400
12.5
800
6.25
Volume 6.25 L
10
Boyles Law
In the 17th Century Robert Boyle described this
property as, the spring of air.
Boyle showed that when temperature and amount of
gas were constant then P ? 1/V OR PV k
11
Boyles Law
For a fixed quantity of gas at a constant
temperature, the volume and pressure are
inversely proportional.
Boyle showed that when temperature and amount of
gas were constant then P ? 1/V OR PV k
12
Who Cares?
Scuba Divers!
At sea level air pressure 100 kPa At 10 m
deep in water pressure 200 kPa At 20 m deep
300 kPa At 30 m deep 400 kPa
SCUBA provides air at the same pressure
13
A Scuba Diver goes to a depth of 90 m and takes
a breath of 3 L volume from her tank.
Suddenly! A Dolphin lunges at the diver and
takes the SCUBA! The Diver holds her breath and
quickly returns to the surface.
What will the volume of air in the divers lungs
be at the surface (100 kPa)? What will happen to
the diver?
14
A Scuba Diver goes to a depth of 90 m and takes
a breath of 3 L volume from her tank.
Assuming that T is constant we can use Boyles
Law PV k
At 90 m k P1V1 At surface k
P2V2 Therefore! P1V1 P2V2
(1000 kPa)(3 L) 100 kPa(V2) V2 300 L Yikes
Exploding lungs
15
Consider This!
Two balloons are filled with equal volumes of air.
What happens to the Volume of each if one is
heated and the other is frozen?
16
HEATED BALLOON
50oC, V1.18 L
FROZEN BALLOON
17
HEATED BALLOON
60oC, V1.22 L
40oC, V1.14 L
FROZEN BALLOON
18
HEATED BALLOON
70oC, V1.25 L
30oC, V1.11 L
FROZEN BALLOON
19
HEATED BALLOON
80oC, V1.29 L
20oC, V1.07 L
FROZEN BALLOON
20
HEATED BALLOON
90oC, V1.32 L
10oC, V1.04 L
FROZEN BALLOON
21
HEATED BALLOON
100oC, V1.36 L
0oC, V1.00 L
FROZEN BALLOON
22
To study this relationship lets look at this
data in a table.
Graph this data using temperature as the
independent variable
23
(No Transcript)
24
If this line is extended backwards the volume of
0 L of gas is found to be
-273 oC
25
-273.15 oC is known as absolute zero. When using
gas laws, temperature must be expressed using a
temperature scale where 0 is -273.15oC. This is
called the Kelvin scale of absolute temperature.
0 K -273.15 oC When changing oC to K simply
add 273.15 What is 12.3oC in K? 12.3 273.15
285.45 285.5 K
26
Now lets look at this table with temperatures in
Kelvin (K).
Can you spot a mathematical relationship between
T and V.
27
V/T in Kelvin is a constant.
0.0037 0.0037 0.0037 0.0037 0.0037 0.0037 0.0037 0
.0037 0.0037 0.0037 0.0037
28
Charles Law
In the 17th Century Jacques Charles examined the
relationship between Temperature and Volume
Charles showed that when Pressure and amount of
gas were constant then V ? T OR V/T k
29
Charles Law
For a fixed quantity of gas at a constant
pressure, absolute temperature and volume are
directly proportional.
Charles showed that when Pressure and amount of
gas were constant then V ? T OR V/T k
30
Combined Gas Law
If

V1P1
V2P2
and

then

or
V1P1 T2 V2P2 T1


V2T1
V2T1
What does P2 ?
31
RECAP
Boyles Law At Constant T and n VP k
Charles Law At Constant P and n V/T k
Combined Gas Law For a fixed quantity of
gas VP/T k
32
If 12.5 L of a gas at a pressure of 125 kPa is
placed in an elastic container at 15oC what
volume would it occupy if the pressure is
increased to 145 kPa?
Given V1 12.5 L P1 125 kPa T1 15oC V2
? P2 145 kPa T2 15oC

Since T1 T2 cancel them to get
(12.5 L)(125 kPa) V2(145 kPa) V2 (12.5 L)(125
kPa)/145 kPa V2 10.8 L
33
Does this answer make sense?
34
Does this answer make sense?
35
Does this answer make sense?
36
Does this answer make sense?
Yes, as the pressure increases at constant
temperature the volume decreases.
V reduced to 10.8 L
37
If 15.6 L of a gas at a pressure of 165 kPa is
placed in an elastic container at 15oC what
volume would it occupy if the temperature is
increased to 98oC?
Given V1 15.6 L P1 165 kPa T1 15oC V2
? T2 98oC P2 165 kPa

Since P1 P2 cancel them to get
288 K
(15.6 L)/(288 K) V2/(371 K) V2 (15.6 L)(371
K) / 288K V2 20.1 L
371 K
38
If 5.3 L of a gas at a pressure of 75 kPa is
placed in an elastic container at 24oC what
volume would it occupy if the temperature is
increased to 62oC and pressure to 155 kPa?
Given V1 5.3 L P1 75 kPa T1 24oC V2 ? T2
62oC P2 155 kPa
V1P1T2 V2P2 T1

OR
(5.3 L)(75 kPa)(335 K)
297 K
V2
(155 kPa)(297K)
335 K
V2 2.9 L
39
Ideal Gas Law An Ideal Gas is a hypothetical gas
that obeys all the gas laws perfectly under all
conditions. PV nRT Where n is the number of
moles of gas, P is pressure in kPa, R 8.313
kPaL/molK and T is temperature in K. Find the
mass of helium gas which would be introduced into
a 0.95 L container to produce a pressure of 125
kPa at 25oC.
40
Find the volume occupied by 25 g of chlorine gas
at SATP. 4.2 g of propane gas is introduced into
a 325 mL container at 45oC. What is the pressure
of the container. Propane is C3H8. What is the
density of NH3 gas at STP if 1.0 mol of this gas
occupies 22.4 L. At what temperature does methane
gas have a density of 1.2 mg/L if its pressure is
65 kPa. Methane is CH4.
41
Dalton's Law of Partial Pressure
42
170 kPa
43
170 kPa
If another gas is injected into the same
container and it exerts a pressure of 70 kPa what
is the total pressure in the container?
44
170 kPa
If another gas is injected into the same
container and it exerts a pressure of 70 kPa what
is the total pressure in the container?
45
The total pressure of a gas mixture is the sum of
the partial pressures of each of the gases in the
mixture. Example If a container of air has a
pressure of 100 kPa and the of N2 in the
container is 78, of O2 is 21, what are the
partial pressures of each of these gases inside
this container. PN2 78 kPa, PO2 21 kPa
46
What would the total pressure be if the gas in
container 1 was injected into container 2.
1
5.0 L 300 K 125 kPa
6.0 L, 400 K, 155 kPa
2
47
The total pressure is the sum of the pressures of
gas 1 and gas 2.Since gas 1 changed volume and
temperature its pressure changed.
1
5.0 L 300 K 125 kPa
6.0 L, 400 K, 155 kPa
2
48
V15.0 L, V26.0 L, T1300 K, T2 400 K P1125
kPa, P2? V1P1T2V2P2T1
1
5.0 L x 125 kPa x 400 K
P2
139 kPa
6.0 L x 300 K
5.0 L 300 K 125 kPa
6.0 L, 400 K, 155 kPa
2
49
Total pressure is 155 kPa 139 kPa 294 kPa
2.9 x 102 kPa
1
5.0 L 300 K 125 kPa
6.0 L, 400 K, 155 kPa
139 kPa
2
50
Find the total pressure in container 1 if the gas
in container 2 is injected into container 1.
1
5.0 L 300 K 125 kPa
6.0 L, 400 K, 155 kPa
2
51
V16.0 L, V25.0 L, T1400 K, T2 300 K P1155
kPa, P2? V1P1T2V2P2T1
1
6.0 L x 155 kPa x 300 K
P2
139.5 kPa
5.0 L x 400 K
5.0 L 300 K 125 kPa
6.0 L, 400 K, 155 kPa
2
52
Total pressure is 125 kPa 139.5 kPa 264.5 kPa
2.6 x 102 kPa
1
5.0 L 300 K 125 kPa
6.0 L, 400 K, 155 kPa
2
139.5 kPa