THE BEHAVIOR OF GASES
A. Kinetic Theory Revisited
1. Basic assumptions -- gases (ch. 10!)
a. Made of atoms or molecules
b. Great distance between atoms
1. compressible
c. no attractive forces between atoms
1. Move freely, fill container
d. Move rapidly in straight lines until a collision
1. Collisions = perfectly elastic
B. Variables that describe a Gas
1. Pressure (P) -- units are kPa, atm, mmHG, torr or psi
2. Volume (V) -- units are Liter (L)
3. Temperature (T) -- units are Kelvin (K)
4. Number of moles (n)
A. Amount of Gas
1. If increase # of particles, then increase # of collisions, therefore increase pressure
a. Double # of particles, double pressure
b. DIRECT RELATIONSHIP
2. If decreases # of particles, then decrease # of collisions, therefore decrease pressure
a. Half # of particles, half pressure
3. Open container
a. Particles move from areas of high pressure to areas of low pressure
B. Volume
1. If decrease volume, then increase # of collisions, therefore increase pressure
a. Half volume, double pressure
b. INDIRECT RELATIONSHIP
2. If increase volume, then decrease # of collisions, therefore decrease pressure
a. Double volume, half pressure
C. Temperature
1. If increase temperature, then increase # of collisions, therefore increase pressure
a. Double temperature, double pressure
b. DIRECT RELATIONSHIP
2. If decrease temperature, then decrease # of collisions, therefore decrease pressure
a. Half temperature, half pressure
III. The Gas Laws
A. The Pressure-Volume Relationship: Boyle's Law
1. Def. -- For a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure
a. Any two sets of P & V at constant T is a constant
b. PV = k P1V1 = P2V2
c. INDIRECT RELATIONSHIP
B. The Temperature-Volume Relationship: Charles' Law
1. Def. -- The volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant
a. Any two sets of V & T at constant P is a constant
b. V/T = k V1/T1 = V2/T2
C. The Temperature-Pressure Relationship: Gay-Lussac's Law
1. Def. -- The pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant
a. Any two sets of P & T at constant V is a constant
a. P/T = k P1/T1 = P2/T2
D. Combined Gas Law
1. Combine the first three
(P1V1)/T1 = (P2V2)/T2
IV. Ideal Gases
A. Ideal Gas Law
1. Gases behave ideally if they conform to the gas laws
2. Insert n (# of moles) into combined formula
(P1V1)/(T1n1) = (P2V2)/(T2n2)
a. Each side is a constant
b. Remember that 1 mol = 22.4 L at STP
c. Plug in STP values and solve for constant
d. Ideal gas constant (R) = 1.831 (L kPa)/(K mol)
3. Usual form of ideal gas law:
PV = nRT
B. The ideal gas law and kinetic theory
1. Kinetic theory and all laws assume that all gases are ideal
a. Follows all laws at any T & P
b. Ideal gases do not exist
2. Real gases do come close to ideal in certain conditions
3. Real gases can liquefy and solidify at low T & high P (not ideal)
C. Departures from the ideal gas law
1. Take the ratio for ideal gas (PV)/(nRT)
a. Will always be constant for an ideal gas = 1
b. Real gases deviate from 1
2. Reasons
a. Attractive force between molecules (Low temperature, molecules move slower, greater attraction)
1. Lowers volume --> Lowers ratio (<1)
b. Volume of gas molecules (High pressure, less space, molecule volume becomes a factor)
1. Raises volume --> Raises ration (>1)
V. Gas Molecules: Mixtures & Movements
A. Avogadro's Hypothesis
1. Equal volumes of gases at the same pressure and temperature contain equal # of particles
a. Different gas molecules have different size
b. Reason for ... 1 mol of any gas at STP = 22.4 L
B. Dalton's Law
1. If mixture of gases, then each individual gas pressure can be added to get total pressure
a. Partial pressure -- contribution of each individual gas
2. Dalton's Law of Partial Pressure
a. Def. -- At constant volume & temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each gas
1. P(total) = P1 + P2 + P3 + ...
b. Frational contributions of each gas do not change as V, T, and P change
c. Fractional contribution of each gas is related to the mole ratio for each gas
C. Graham's Law
1. Diffusion -- the tendency of molecules to move from areas of high concentration to areas of low concentration
2. Effusion -- process by which a gas escapes through a tiny hole in its container
3. Graham's Law of Effusion
a. Def. -- The rate of effusion of a gas is inversely proportional to the square root of the gas's molar mass (same for diffusion)
b. If two molecules with different masses have the same KE (same T), then the lighter molecule must be moving faster since... KE = 1/2mv2
c. Smaller molecules move faster, effuse/diffuse faster
Rate(a)/Rate(b) = S.R.{molar mass(b)/molar mass(a)}
Outline based upon:
Matta, M. S., Staley, D. D., Waterman, E. L., & Wilbraham, A. C. (2000). Chemistry, Addison-Wesley (5th ed.). Menlo Park, CA: Prentice Hall. pp. 327-354.
