PROPERTIES OF GASES
A. all gases obey the same set of physical laws (gas laws)
1. Four properties that relate to gas laws
a. pressure (P)
b. volume (V)
c. temperature (T)
d. number of moles (n)
II. Pressure. Its Measurement and Units
A. Atmospheric Pressure and the Barometer
1. Pressure = force per unit area
2. Atmospheric pressure -- the amount of pushing force the atmosphere applies due to gravitational pull
3. Barometer -- instrument used to measure atmospheric pressure
B. Units of Pressure
1. Standard atmosphere (atm) -- average pressure at sea level
a. Pascal (Pa) -- SI unit [1 atm = 101325 Pa = 101.3 kPa]
b. torr --- Laboratory unit [1 atm = 760 torr]
c. millimeter of mercury (mm Hg) -- used with barometers [1 atm = 760 mm Hg]
C. Manometer -- instrument used to measure pressure in a closed system
1. Open-end manometer -- U-tube partly filled with a liquid
a. If P(gas) = P(atm), then same value
b. If P(gas) > P(atm), then P(gas) = P(atm) + P(Hg)
c. If P(gas) < P(atm), then P(gas) = P(atm) - P(Hg)
2. Closed-end manometer -- U-tube completely filled with a liquid
a. The difference in two Hg levels corresponds directly to the atmosheric pressure
D. Liquids Other Than Mercury in Manometers and Barometers
1. Mercury is ideal due to it's high density
2. Others could included water, however, the length of the tube would have to be13.6 times larger than that for mercury
III. Pressure-Volume-Temperature Relationships for a Fixed Amount of Gas
A. Boyle's Law
1. the volume of a given amount of gas held at constant temperature varies inversely with the applied pressure
a. PV = C (P1V1 = P2V2)
B. The Concept of an Ideal Gas
1. Ideal gas -- obeys all the gas laws exactly over all temperatures and pressure
2. When a gas is under high pressure and/or low temperature, it does not act ideal
a. It's on the verge of becoming a liquid
C. Charles' Law
1. The volume of a fixed amount of gas is directly proportional to its Kelvin temperature when the gas pressure is held constant
a. V = CT (V1/T1 = V2/T2)
2. Absolute Zero -- temperature at 0 volume = -273.15 oC (0 K)
D. Gay-Lussac's Law
1. The pressure of a fixed amount of gas held at constant volume is directly proportional to the Kelvin temperature
a. P = CT (P1/T1 = P2/T2)
E. The Combined Gas Law
1. The ratio PV/T is a constant for a fixed amount of gas
a. P1V1/T1 = P2V2/T2
b. Previous three laws are derived from the combined gas law
IV. Ideal Gas Law
A. Relationship of gas volumes in Gas Phase Reactions
1.Coefficients of equations can also represent volumes
B. Avogadro's Principle
1. When measured at the same temperature and pressure, equal volumes of gases contain equal numbers of moles
a. The volume of a gas is directly proportional to its number of moles
C. Standard Molar Volume
1. The volume occupied by one mole af any gas, its molar volume, must be identical for all gases under the same pressure and tempertaure
2. Standard Temperautre-P{ressure (STP)
a. 1 atm and 273.15 K
3. The volume of one mole of a gas is 22.4 L (molar volume)
D. Formation of the Ideal Gas Law
1. PV/T constant is proportional to the number of moles
a. PV/T = n x another constant
1. Universal Gas Constant (R)
b. PV = nRT (Ideal Gas Law)
c. Can define the state of a given gas simply by specifying any three of the four variables
d. R = 0.0821 atm L/mol K (8.31 kPa L/mol K)
E. Determining the Molecular Mass of a Gas
1. Use ideal gas law to determine moles
2. Calculate ratio of grams per mole
V. Stoichiometry of Reactions Between Gases
A. Use relationship between volumes of gases
1. assume that the pressure and temperature are constant
a. See Examples page 440-441
VI. Dalton's Law of Partial Pressures
A. The total pressure of a mixture of nonreacting gases is the sum of their individual partial pressures
1. P(total) = P1 + P2 + P3 + ...
B. Collecting Gase Over Water
1. Vapor pressure -- pressure exert by a liquid's vapor in the space above that liquid
a. Vapor pressure depends on the temperature
2. Whe gas is collected over water, the Vapor pressure at that temperature must be subtracted to determine pressure of the dry gas
a. P(gas) = P(total) - P(water)
b. When the water level inside the container equals the water level outside, a barometer can be used to determine total pressure
C. Mole Fractions and Mole Percents
1. Mole fraction -- ratio of # of moles of one component over the total moles of all components
a. The sum of all mole fractions for a mixture must equal 1
2. Mole percent (mol%) -- multiply mole fraction by 100
D. Mole Fractions of Gases from Partial Pressures
1. The number of moles of a gas in a mixture of gases is directly proportional to the partial pressure of the gas
a. n(a) = P(a)V/RT --> n(a) = P(a)C --> sub into mole fraction formula
b. X(a) = P(a)/P(total)
1. the mole fraction of a gas mixture is simply the ratio of its partial pressure to the total presuure
E. Partial Pressures from Mole Fractions
1. Use above formula, rearranged, to determine partial pressures
VII. Graham's Law Effusion
A. Definitions
1. Diffusion -- the complete spreading out and intermingling of the molecules of one gas into and among those of another gas
2. Effusion -- the movement of gas molecules through an extremely tiny opening into a vacuum
B. Graham's Law -- the rates of efusion of gases are inversely proportional to the equare roots of their densities when compared at identical pressures and temperatures
1. Density is directly proportional to Molecular Mass
2. Effusion rate(A)/effusion rate (B) = square root of [MM(b)/MM(a)]
VIII. Kinetic theory and the Gas Laws
A. Postulates of the Kinetic Theory of Gases
1. A gas consists of an extremely large number of very tiny particles that are in constant, random motion
2. The gas particles themselves occupy a net volume so small in relation to the volume of their container that their contribution to the total volume can be ignored
3. The particles often collide in perfectly eleastic collisions with themselves and with the walls of the container, they move in straight lines between collisions neither attracting nor repelling each other
B. Kinetic Theory and Gas Temperature Revisted
1. temperature of a gas is proportional to the average molecular KE of the particles
C. Kinetic Theory and Boyle's Law
1. Reduce the volume by one half, then double the number of molecules per unit volume
2. Result -- double the number of collisions per second, double the pressure
D. Kinetic Theory and Gay-Lussac's Law
1. Increase temperature, then increase average velocity of the molecules
2. Higher velocities, strick the wall of the container more frequently, higher pressure
E. Kinetic Theory and Charles' Law
1. If increase temperature, then must increase volume to keep pressure constant
F. Kinetic Theory and Dalton's Law of Partial Pressures
1. Only if the particles of each gas do act independently can the partial pressures of the gases add up in a simple way to give the total pressure
G. Kinetid Theory and the Graham's Law of Effusion
1. two gases at same temperature have same average KE
a. substitute 1/2mv2 in for KE
b. rearrange ratio with velocities squared = mass
c. square root both sides
d. mass is proportional to Molar mass, sub in to formula
e. effusion rate proportional to average speed of molecules
2. effusion rates are proportional to inverse square root of the molar masses
H. Kinetic Theory and Absolute Zero
1. Gas temperature is proportional to the average molecular kinetic energy
2. if average molecular KE becomes zero, then temperature must become zero
3. Mass cannot be zero, so velocity must be zero
IX. Real Gases: Deviations from the Ideal Gas Law
A. Two reasons for deviation
1. ideal gas assumes that gas molecules individually have no volume, NOT TRUE
a. volume of molecules is very tiny fraction of total volume at ordinary pressures
b. volume taken up by molecuels would increase with increase number of molecules (increaed pressure)
c. As pressure increases, the volume occupied by the molecules increases
1. V in formulas is to large
2. Makes PV/T ratio greater in value
3. the particles do attract each other some in a real gas
a. particles "stick" together and collide with the wall of the container less frequently
b. Less pressure than expected
1. Makes PV/T ratio less in value at lower pressures
B. van der Waals Equation
1. [P + (n2a/V2)](V - nb) = nRT
a. a and b are called the van der Waals constants
b. a involves a correction for pressure (size of a relates to attractions between molecules)
1. larger values of a = stronger attractive forces between molecules
c. b involves a correction for volume (size of b relates to size of particles)
1. Larger values of b = larger molecular sizes
Outline based upon:
Brady, J. E., Holum, J. R., Russell, J. W. (2000). Chemistry: The Study of Matter and Its Changes. (3rd ed.). New York: John Wiley & Sons, Inc. pp. 423-456.
