COMBINED GAS LAW
-combination of Boyle’s law and Charle’s law.
-the pressure and the volume of a gas is inversely proportional to each other, but are
both directly proportional to the temperature of that gas.
-number of moles are contant.
-General Formula: P1V1=P2V2
T2
T1
-The temperature must be in Kelvin (+273).
Sample Problem:
1. A 20.0 ml bubbles is released from a tank at a pressure of 4.0 atm and a
temperature of 10 ℃. What will be the volume of the bubble when it reaches the water
surface where the pressure is 1.0 atm and the temperature is 19℃?
Given:
Volume 1: 20.0 ml
Volume 2: ?
Pressure 1: 4.0 atm
Pressure 2: 1.0 atm
Temperature 1: 10℃ + 273 = 283 K
Temperature 2: 19℃ + 273 = 292 K
Formula:
P1V1 = P2V2
T1
T2
P1V1T2
P2T1
Derived Formula:
V2 =
Solution:
(4.0 atm) (20.0 ml) (292 K)
V2 =
(1.0 atm) (283 K)
V2 =
23, 360
283
V2 = 82.5 ml
Solve this! (1 whole sheet of paper)
1. A gas has a volume of 2.0 L at 100 kPa and 27 ℃. What will be the volume if the
pressure becomes 200 kPa and the temperature becomes 127 ℃?
2. A gas has a pressure of 150 kPa, volume of 3.0 L, and temperature of 300 K. What
is the final pressure if the volume decreases to 1.5 L and the temperature increases to
600 K?
3. A gas occupies 4.0 L at 101 kPa pressure and 300 K temperature. If the pressure
increases to 202 kPa and the volume becomes 2.0 L, what is the final temperature?
Avogadro’s Law
-The Avogadro’s Law states that at constant temperature and pressure, the volume of
a gas is directly proportional to its number of moles.
-General Formula:
V1
n1
=
V2
n2
Sample Problem:
1. A weather balloon filled with 2.0 mol helium has a volume of 40.0 L. To what
volume, in L, will the balloon expand if 4.0 mol of helium is added, to give a total of
6.0 mol of helium keeping the temperature and pressure the same?
Given:
V1 = 40.0 L
n1 = 2.0 mol
n2 = 6.0 mol
V2=?
Formula:
V1
n1
V2
=
n2
Derived Formula:
V1
n1
V2 =
V2
=
n2
V1n2
n1
V2 = 120 L
Solve this! (1 whole sheet of paper)
1. A gas occupies 10 L at 1 mole. What will be the volume if the amount of gas is
increased to 2 moles, keeping temperature and pressure constant?
2. A gas has a volume of 15 L with 3 moles. How many moles are present if the volume
(40. 0 L) (6.0 mol)
V2 =
becomes 25 L?
2.0constant
mol
3. A gas expands from 12 L to 30 L at
temperature and pressure. If the initial
amount of gas was 1.6 moles, how many moles are present after expansion?
Ideal Gas Law
-Combination of the different gas laws – Boyle’s law, Charles’ law, Gay-Lussac’s law
and Avogadro’s law.
-The equations representing these laws may be combined to arrive at one equation
that interrelates pressure (P), volume (V), temperature (T) and the amount of gas (n).
This combination gives the expression called Ideal gas law.
-The constant R is known as the universal gas constant with a value of 0.0821 Latm/mol-K.
-Pressure (P) : atm, kPa, or torr
-Volume (V) : liters (L) or cubic meters (m³)
-Temperature (T) : in Kelvin (K) (never °C) + 273
-Number of moles (n) : mol
-Gas constant (R)
-General Formula:
V = (R)
nT
P
Sample Problem:
1. 6.5 moles of carbon dioxide (CO2) gas are present in a container with a volume 31.5
L. What is the pressure of this gas in atm if the temperature is 65oC?
Given:
n = 6.5 moles
T = 65.0oC + 273 K = 338 K
V = 31.5 L
R = 0.0821 atm-L/mol-K
P=?
Formula:
V = (R)
nT
P
Derived Formula:
P=
RnT
V