The Behavior of Gases
Variables that Describe a Gas
 Compressibility: a measure of how much the volume of matter decreases under pressure.
 Pressure: a physical force pushing on or against an object; abbreviated P, measured in
atmospheres (atm), torr, mmHg, Pascals (Pa), or kilopascals (kPa).
o Standard pressure (STP) is 1 atm = 760 torr = 760 mmHg = 101,300 Pa = 101.3 kPa
 Volume: the amount of space an object occupies; abbreviated V, measured in liters, milliliters,
cubic meters, or cubic centimeters.
 Temperature: a measurement of the average kinetic energy in an object; abbreviated T,
measured in Celsius or Kelvin (use Kelvin for math problems).
o Standard temperature (STP) = 0°C = 273 K
 Mole: a measurement of the number of particles in an object; abbreviated n, measured in moles.
One mole is equal to 6.02 x 1023 particles (atoms, molecules, or formula units).
The Gas Laws
 Boyle’s Law for Pressure-Volume Changes
o For a given mass of gas at constant temperature, the
volume of the gas varies inversely with pressure.
P1V1 = P2V2
or
P1 = V2
P2
V1
o You do not need to convert pressure or volume to specific
units for these problems because they use ratios.
o Example: A gas is collected in a 242 mL container. The pressure
of the gas in the container is measured and determined to be 87.6
kPa. What is the volume of this gas at 101.3 kPa? Assume the
temperature is constant.

Charles’ Law for Temperature-Volume Changes
o The volume of a fixed mass of gas is directly proportional to
its Kelvin temperature if the pressure is kept constant.
V1 = V2
T1 T2
or
V1 = T1
V2 T2
o Temperature must be in Kelvin. K = °C + 273
o Example: A sample of gas at 15°C and 1 atm has a volume of 2.58
L. What volume will this gas occupy at 38°C and 1 atm? Assume
the pressure is constant.

Gay-Lussac’s Law for Temperature-Pressure Changes
o The pressure of a gas is directly proportional to the Kelvin
temperature if the volume is kept constant.
P1 = P2
T1 T2
or
P1 = T1
P2 T2
o Temperature must be in Kelvin. K = °C + 273
o Example: A 2.0 L flask contains helium gas at a pressure of
685 torr and a temperature of 0°C. If the temperature is
raised to 150.°C, what is the new pressure in the flask?

The Combined Gas Law
o This law combines pressure, volume, and temperature.
Temperature must be in Kelvin. K = °C + 273
o By canceling out any constant terms, we can derive Boyle’s,
Charles’, and gay-Lussac’s law from the combined gas law.
o Easy way to remember: “Peas and Vegetables on the Table”
o Example: If a helium-filled balloon has a volume of 3.40 L at 25.0°C and 120.0 kPa, what
is its volume at STP?

Real vs. Ideal Gases
o Ideal gases follow the gas laws at all conditions of temperature and pressure. They do
not exist in reality (for example, real gases can be liquefied and sometimes solidified;
ideal gases cannot).
o Real gases “deviate” from ideal gas behavior. Real gases
behave most ideally at high temperature and low pressure.
o The ideal gas law allows us to relate the pressure, volume,
number of moles, and temperature of a gas to each other. This
law uses the ideal gas constant, R. For the ideal gas law,
 Pressure must be in atm
 Volume must be in L
 n must be moles (it always is)
 R = 0.08206 L*atm/mol*K
 T must be in Kelvin
o Example: A 5.0 L flask contains 0.60 g O2 at a temperature of 22°C. What is the
pressure (in atm) inside the flask?
o How many grams of krypton are present in a 600. mL container at 1010°C in which the
pressure of krypton is 10.0 atm?
How many atoms is this?

Gas Molecules: Mixtures and Movements
o Avogadro’s Hypothesis
 Equal volumes of gases at the same
temperature and pressure contain
equal numbers of particles.
 At STP, 1 mole of particles of any
gas = 22.4 L.
o Dalton’s Law of Partial Pressure
 At constant volume and
temperature, the total pressure
exerted by a mixture of gases is
equal to the sum of the partial
pressures.
Ptotal = P1 + P2 + P3…

Example: Determine the total pressure of a gas mixture that contains nitrogen
and oxygen if the partial pressure of the nitrogen is 725 mmHg and the partial
pressure of the oxygen is 426 mmHg.
o Gases are often collected by water displacement.
 The total of the gas pressure plus the water vapor pressure is equal to the
atmospheric pressure.
Patmospheric = Pgas + PH2O


When we work a problem like this we must always look up and subtract the water
vapor pressure to get the gas pressure.
Example: A sample of N2 gas is collected by the downward displacement of water
from an inverted bottle. What is the partial pressure of the N2 gas at 20.0°C, if the
atmospheric pressure is 752 mmHg? The water vapor pressure is 17.5 mmHg at
20.0°C.