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Chapter 12 Notes: Gas Laws
Introductory Vocabulary
Kinetic energy is the energy of motion of molecules.
Temperature is a measure of the average kinetic energy of the particles of a substance.
Gas state of matter made up of tiny particles (atoms or molecules). Each atom or molecule
is very far from other atoms or molecules. Virtually all of the volume of a gas is empty
space.
The kinetic theory of matter states that particles which make up all types of matter are
in constant motion.
Kelvin
K= °C + 373
STP (Standard Temperature and Pressure) means pressure is equal to 1 atm and
temperature is 273 K.
The kinetic theory of gases assumes the following :
1. Gases consist of large numbers of tiny particles that are far apart.
2. Gas particles are in constant, rapid motion.
3. There are no forces of attraction or repulsion between gas particles.
4. Gas particles do not lose energy when they collide with other gas particles (total
kinetic energy remains constant)
Three units used to measure atmospheric pressure are
pascals (Pa) · millimeter of mercury
(mm Hg)
atmospheres (atm)
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1 atm = 760 mm Hg
1 atm = 101.3 kPa
1 atm = 760 torr
1 atm = 29.92 inches Hg
1 kPa = 1000 Pa
Examples
Convert 825 mm Hg to atm
Convert 1.07 atm to kPa
Convert 125 kPa to torr
Convert 8.20 x 106 Pa to inches of Hg
The three factors which determine the physical behavior of gases are :
1. Pressure
2. Temperature
3. Volume
Gas Laws
Dalton's law of partial pressures
states that at constant temperature and volume, the total pressure exerted by a mixture
of gases is equal to the sum of the partial pressures. a partial pressure is the pressure
exerted by one of the gases in the mixture.
Ptotal = P1 + P2 + P3 ....
Examples:
Calculate the total pressure of a mixture of gases where the partial pressures are: 425
mm Hg of O2, 215 mm Hg of N2 and 240 mm Hg of CO2.
In a mixture of oxygen, nitrogen, and hydrogen, the oxygen exerts a pressure of 0.526
atm and nitrogen exerts a pressure of 220.0 mm Hg. If the total pressure exerted by the
mixture of gases is 760.0 mm Hg, what is the pressure exerted by hydrogen?
Boyle's law
states that for a given mass of gas at a constant temperature, the volume of a gas varies
inversely with pressure. That is if we increase pressure the volume decreases and vice
versa. If we increase the volume the pressure decreases and vice versa.
P1 x V1 = P2 x V2
Examples
A balloon is filled with helium gas at 1.0 atm of pressure and has a volume of 32.0L.
Assuming constant temperature, what will its volume be if it rises in the atmosphere to a
height where the pressure is 0.75 atm?
Calculate the final pressure of a gas (in kPa) when the volume of the container increases
from 250 mL to 1.0 L. The gas is initially at 3.75 atm. Assume constant temperature.
Charles' law
states that the volume of a fixed mass of gas is directly proportional to its temperature
(K) if the pressure is kept constant. That is if we increase temperature volume increases
and vice versa.
V1/T1= V2/T2.
Examples:
A balloon is inflated to a volume of 1.0 L in a room at 298 K. What is final temperature if
the volume decreases to 250 mL while the pressure remains constant?
A gas has a volume of 250.0 L at a temperature of 20.0°C. At constant pressure, what will
the volume of the gas be if the temperature changes to 30.0°C?
Gay-Lussac's law
states that the pressure of a gas is directly proportional to the Kelvin temperature if the
volume is kept constant.
P1/T1 =P2/T2
Examples:
A tank of nitrogen gas has a temperature of 273 K and a pressure of 3.30 atm. Assuming
constant volume, if the temperature rises to 293 K, what will the resulting pressure be?
A mass of air has a pressure of 0.25 atm at 101oC. What will the temperature be if the
pressure is increased to 750 mm Hg while the volume remains constant?
Boyles, Charles, and Gay-Lussacs Law each have one factor which is held constant and does
not appear in the equations (use this to help remember which equation to use). But what
if all the factors change? Then the combined gas law is used.
P1 x V1 /T1 = P2 x V2 /T2.
Examples:
A cylinder of compressed nitrogen has a volume of 20.0 L at 120.0 atm and 273K. If all the
gas of the cylinder is used to fill an inert atmosphere which has a volume of 1000.0 L and a
temperature of 225K, what will the pressure be?
Calculate the volume of a gas present at STP if the gas starts off with a volume of 225 mL
at 123 kPa and 25oC.
The ideal gas law
mathematical expression that relates the moles of a gas (indicated in the equation by the
variable "n") to T,V and P. It uses the ideal gas constant (R).
PV = nRT
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P = pressure, in atm
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V = volume, in L
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n = number of moles, in moles
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R = ideal gas constant
0.0821 L atm/K mol
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T = temperature, in K
The units must be the same as the R to put it into the ideal gas law equation. If not
then you must convert each unit first before putting it into the equation.
Example:
In an industrial reaction 12.4 mol of nitrogen are produced filling a 60.0 L reaction vessel
at 300.0 K. If nitrogen is the only gas producing the pressure what would the pressure be?
What is the volume, in mL, of 0.825 moles of a gas that is at 940 mm Hg and 25oC?
How many grams of N2O gas are present in a 750 mL container at 12oC and 115 kPa?
If a gaseous mixture is made of 2.41 g of Helium and 2.79 g of Ne in a 1.04 L container at
25°C, what will be the partial pressure of each gas and the total pressure in the container?