The physical behavior of most gases is nearly independent of chemical composition. The physical behavior of a gas is predominantly determined by VOLUME, AMOUNT (moles), TEMPERATURE, and PRESSURE. These four physical properties are related and dependent upon one another.
VOLUME
A gas expands uniformly to fill any container in which it is placed.
This means that the volume of a gas is the volume of its container. Volumes
of gases can be expressed in liters or cubic decimeters.
1 L = 1 dm3 = 1 x 103 cm3 = 1 x 10-3 m3
AMOUNT
Most commonly, the amount of matter in a gaseous sample is expressed
in terms of the number of moles (n). In some cases, the mass is given instead.
These two quantities are related through the molar mass, MW.
n = mass/MW
TEMPERATURE
The temperature of a gas is ordinarily measured using a thermometer
marked in degrees Celsius. However, in any calculation involving the
physical behavior of gases, temperatures must be expressed using the Kelvin
scale (K). The formula for converting between oC and K is:
K = oC + 273.15
PRESSURE
Pressure is defined as force per unit area. The SI unit for pressure
is the pascal (Pa) the pressure exerted by a force of one newton on an
area of one square meter (kg/ms2). Atmospheric pressure is about
105 Pa or 100 kilopascals (kPa).
Some common units for pressure are:
atmospheres (atm), defined by the relation: 1 atm = 1.01325 x 105 Pa.
millimeters of mercury (mmHg), the pressure exerted by a column of mercury one millimeter high. A column of mercury 760 mm high exerts a pressure of one atmosphere. The unit mmHg is often called the Torr.
1 standard atmosphere = 1 atm = 760 mmHg = 760 Torr
Units of Pressure
1 atm = 760 mmHg = 29.921 in Hg
= 760 Torr
= 14.696 lb/in2
= 14.696 psi
= 101,325 N/m2
= 101,325 Pa = 1.01325
x 105 Pa
= 101.325 kPa
= 1.01325 bar
= 1013.25 mb
STANDARD TEMPERATURE and PRESSURE (STP)
The conditions of 0oC (273.15 K), and 1 atm (760 Torr, 760
mmHg) are referred to as standard temperature and pressure (STP).
PROBLEM 1
Convert 0.9870 atm to: a) Pa
b) mmHg
BOYLE'S LAW Pressure and Volume are INDIRECTLY proportional.
PV = k' {at constant temperature}
P1V1 = P2V2
PROBLEM 2
A sample of chlorine gas occupies a volume of 946 mL at a pressure
of 726 mmHg. Calculate the pressure of the gas if the volume is reduced
to 154 mL. Assume that the temperature remains constant.
PROBLEM 3
An inflated balloon has a volume of 0.55 L at sea level (1.0 atm) and
is allowed to rise to a height of 6.5 km, where the pressure is about 0.40
atm. Assuming that the temperature remains constant, what is the final
volume of the balloon?
CHARLES' LAW Volume and Temperature are DIRECTLY proportional.
V/T = k" {at constant pressure}
V1/T1 = V2/T2
PROBLEM 4
Argon is an inert gas used in light bulbs. In one experiment, 452 mL
of the gas is heated from 22oC to 187oC at constant
pressure. What is its final volume?
PROBLEM 5
A sample of carbon monoxide, a poisonous gas, occupies 3.20 L at 125oC.
Calculate the temperature in Celsius at which the gas will occupy 1.54
L if the pressure remains constant.
COMBINED GAS LAW
PROBLEM 6
A sample of gas at 780 Torr and 4oC has a volume of 0.35
L. If the volume and temperature are changed to 0.31 L and 50oC,
calculate the pressure.
PROBLEM 7
A small bubble rises from the bottom of a lake, where the temperature
and the pressure are 8oC and 6.4 atm, to the water's surface,
where the temperature is 25oC and pressure is 1.0 atm. Calculate
the final volume (in mL) of the bubble if its initial volume was 2.1 mL.
AVOGADRO'S LAW equal volumes of any two gases at the same temperature and pressure contain the same number of molecules.
1 mol gas = 22.4 L (at STP)
THE IDEAL GAS LAW
PV = nRT
R is the universal gas constant which
has a value of:
0.0821 L.atm/mol.K
if the pressure is in atm.
62.4 L.Torr/mol.K
if the pressure in Torr or mmHg
PROBLEM 8
Sulfur hexafluoride (SF6) is a colorless, odorless, very
unreactive gas. Calculate the pressure (in atm) exerted by 1.82 moles of
gas in a steel vessel of volume 5.43 L at 69.5oC.
PROBLEM 9
Calculate the volume of 6.46 grams of helium at 27.0oC at
a pressure of 2.37 atm?
PROBLEM 10
A 2.00 L flask at 25oC and 730 Torr contains CH4
gas. How many moles of gas are in the flask?
PROBLEM 11
A 2.00 gram sample of solid CO2 (dry ice) is allowed to
sublime in a balloon. If the final pressure in the balloon is 0.565 atm
and the volume is 2.00 L, what is the temperature in oC?
GAS DENSITY
d = P(MW)/RT
PROBLEM 12
Calculate the density of N2, O2, CO2,
and CH4 at STP?
PROBLEM 13
A 205 mL sample of a gas at 100 oC and 755 Torr is found
to have a mass of 1.22 grams. What is the molecular weight of the gas?
GASES IN REACTION STOICHIOMETRY
Law of Combining Gases When gases measured at the same temperature and pressure are allowed to react, the volumes of gaseous reactants and products are in small whole-number ratios.
PROBLEM 14
How many liters of hydrogen chloride can be prepared at STP from the
reaction of 6 liters of chlorine gas with excess hydrogen?
PROBLEM 15
If 100.0 grams of H2O(l) are decomposed to H2(g)
and O2(g), what is the total volume of the gases at STP?
PROBLEM 16
How many liters of hydrogen gas can form at STP when 8.92 g of Fe react
completely with excess HCl?
2 Fe(s) + 6 HCl(aq) ----> 2 FeCl3(aq) + 3 H2(g)
DALTON'S LAW OF PARTIAL PRESSURES
PTotal = PA + PB + PC + ...
PROBLEM 17
If 100.0 mL of O2 are collected over water at 22.0oC
and atmospheric pressure of 754 Torr, what is the pressure of the "DRY"
O2? The vapor pressure of H2O at 22.0oC
is 19.8 Torr.
PROBLEM 18
If 200 mL of N2 at 25oC and a pressure of 250
Torr are mixed with 350 mL of O2 at 25oC and a pressure
of 300 Torr, so that the resulting volume is 300 mL, what would be the
final pressure of the mixture?
MOLE FRACTION
CA = nA / nTotal = PA / PTotal
PROBLEM 19
Calculate the mole fraction of each gas in a mixture of 0.210 mol carbon
dioxide, 0.750 mol oxygen, and 0.450 mol of nitrogen. (Ccarbon
dioxide = 0.210/1.41 = 0.149; Coxygen
= 0.750/1.41 = 0.532; Cnitrogen
= 0.450/1.41 = 0.319)
PROBLEM 20
A mixture of gases is composed of 0.563 mol of hydrogen and 0.841 mol
of chlorine in a 789 mL container at 84.2oC. What is the partial
pressure of each gas in the container and what is the total pressure of
the mixture?
PROBLEM 21
A gaseous mixture contains 2.00 moles of O2 and 0.500 moles
of H2 and has a total pressure of 3.00 atm. What is the partial
pressure of O2?
GRAHAM'S LAW OF EFFUSION
r1/r2 = (MW2/MW1)1/2
PROBLEM 22
Order the following gases in increasing rate of effusion.
Xe, UF6, Cl2, C2H6
PROBLEM 23
A balloon is filled with H2(g) and O2(g). If
the O2(g) effuses out of the balloon at a rate of 65 ml/hr,
calculate the rate of the H2(g) effusion.
PROBLEM 24
Four identical flasks at STP contain 1 mole each of the following gases:
He, Cl2, CH4, NH3
Which gas has the:
a) highest density?
b) highest average velocity?
c) fewest atoms? (He)