3 basic gas laws
Definitions
Volume – refers to the space matter (gas) occupies. Measured in liters (L).
Pressure – the number of times particles collide with each other and the
walls of the container (force exerted on a given area). Measured in
atmospheres (atm).
1.000 atm = 760.0 millimeters Hg ( Barometers use Hg)
1.000 atm = 760.0 torr (Named after Torricelli for the invention of the
barometer)
1.000 atm = 101.3 kPa – kilopascals
Memorize Table 1. P. 542
*all have 4 sig dig
STP: standard temperature and pressure (0°C, 101.3 kPa or 1atm).
SATP: standard ambient temperature and pressure (25°C, 100 kPa).
Sample Problems
Convert 4.400 atm to mmHg.
1 atm =
4.40atm
760 mmHg
x
x = 3344 mmHg
Convert 212.4kPa to mmHg.
101.3 kPa =
212.4 kPa
760 mmHg
x
x = 1594 mmHg
Definitions
Temperature – average kinetic energy as temperate increases gas particles move faster,
as temperature decreases gas particles move slower.
Measured in Kelvin (K). K = 273 + C
Number of Moles – tells you how much of a certain
gas you have
1 mole = number of grams of the compound or
element (molar mass)
Kelvin Practice
What is the approximate temperature for absolute
zero in degrees Celsius and kelvin?
Absolute zero is – 273C or 0 K
Calculate the missing temperatures
273
= _______
K
373
100C = _______
K
– 173
100 K = _______
C
243
– 30C = _______
K
0C
27
300 K = _______
C
25C
298
= _______
K
403 K
130
= _______
C
0K
– 273
= _______
C
Boyle’s Law - Pressure and Volume (when
temperature remains constant)
V1P1 = V2P2
V1 = initial or old volume
V2 = final or new volume
P1 = initial or old pressure
P2 = final or new pressure
Inverse Relationship (As pressure increases, volume
decreases and as pressure decreases, volume
increases.)
Effect of Pressure on Volume
Boyle’s Law
1 atm
2 atm
5 atm
5
5
5
3
3
3
1
1
1
Which picture represents what the gas will
look like when the pressure is doubled?
(Assume constant n, T)
Boyle’s Law
P a 1/V
P x V = constant
P1 x V1 = P2 x V2
Constant temperature
Constant amount of gas
5.3
Kinetic
Molecular theory of gases and …
• Boyle’s Law
P a collision rate with wall
Collision rate Increases with decreased volume
P a 1/V
Increase P, decrease volume
An increase in pressure decreases the
volume of air in the lungs.
A sample of chlorine gas occupies a volume of 946 mL at a
pressure of 726 mmHg. What is the pressure of the gas (in
mmHg) if the volume is reduced at constant temperature
to 154 mL?
P1 x V1 = P2 x V2
P2 =
P1 = 726 mmHg
P2 = ?
V1 = 946 mL
V2 = 154 mL
P1 x V1
V2
=
726 mmHg x 946 mL
154 mL
= 4460 mmHg
Sample Problems
What is the new pressure when 80.0mL of gas at
500.mmHg is moved to a 100.mL container?
(ans: 400. mmHg)
A gas at 800.torr of pressure has a volume of 5.00L.
What volume does this gas occupy at 1.00X103torr
of pressure?
(ans: 4.00 L)
Charles’ Law -Volume and Temperature
(when pressure is constant)
V1/T1 = V2/T2
V1 = initial or old volume
V2 = final or new volume
T1 = initial or old temperature
T2 = final or new temperature
Direct Relationship (As temperature increases,
volume increases and as temperature decreases,
volume decreases.)
The volume of a gas increases with and
increase in temperature.
How Volume Varies With Temperature
If we place a
balloon in
liquid
nitrogen it
shrinks:
So, gases shrink if cooled.
Conversely, if we heat a gas it
expands (as in a hot air balloon).
Let’s take a closer look at
temperature before we try to
find the exact relationship of
V vs. T.
Which picture represents what the gas will
look like when the temperature is increased?
(Assume constant n, P)
Kinetic theory of gases and …
Charles’ Law
-Average kinetic energy a T
-Increase T, Gas Molecules hit walls with greater
Force, this Increases the Pressure
BUT since pressure must remain constant, and only
volume can change
-Volume Increase to reduce Pressure
-Increase Temperature, Increase Volume
A sample of carbon monoxide gas occupies 3.20 L at 125
0C. At what temperature will the gas occupy a volume of
1.54 L if the pressure remains constant?
V1/T1 = V2/T2
T2 =
V1 = 3.20 L
V2 = 1.54 L
T1 = 398.15 K
T2 = ?
V2 x T1
V1
=
1.54 L x 398.15 K
3.20 L
= 192 K
2. A sample of gas occupies 3.5 L at 300 K. What volume
will it occupy at 200 K?
V1 = 3.5 L, T1 = 300K, V2 = ?, T2 = 200K
Using Charles’ law: V1/T1 = V2/T2
3.5 L / 300 K = V2 / 200 K
V2 = (3.5 L/300 K) x (200 K) = 2.3 L
3. If a 1 L balloon is heated from 22°C to 100°C, what will its
new volume be?
V1 = 1 L, T1 = 22°C = 295 K
V2 = ?, T2 = 100 °C = 373 K
V1/T1 = V2/T2, 1 L / 295 K = V2 / 373 K
V2 = (1 L/295 K) x (373 K) = 1.26 L
Gay-Lussac’s Law - Pressure and
Temperature (when volume is constant)
P1/T1 = P2/T2
P1 = initial or old pressure
P2 = final or new pressure
T1 = initial or old temperature
T2 = final or new temperature
Direct Relationship - As the temperature of
the gas increases the pressure of the gas
Increases.
Sample Problems
The gas in an aerosol can is at 3atm of pressure at
298K. What would the gas pressure in the can be at
325K?
At 120.C the pressure of a sample of nitrogen gas is
769torr. What will the pressure be at 205C?
The Combined
Gas
Law
Combining the gas laws
• So far we have seen three gas laws:
Robert Boyle
P1V1
=
P2V2
Jacques Charles
V1
=
T1
V2
T2
These are all subsets of a more encompassing law: the
combined gas law
Joseph Louis Gay-Lussac
P1
P2
=
T1
T2
P1V1
P2V2
=
T1
T2
Sample Problems
A helium filled balloon has a volume of 50.0mL at
298K and 1.08atm. What volume will it have at
0.855atm and 203K?
Given 700.mL of oxygen at 7.00C and 7.90atm of
pressure, what volume does is occupy at 27.0C and
4.90atm of pressure?
Note: any unit for pressure will work, provided the same units are used throughout.
The only unit that MUST be used is K for temperature.
• CW/ HW
• Complete ISU booklet – 1st page
• Practice questions on 1st 3 laws on 2nd page