AP Chemistry : Ch. 5 Notes Mr. Niedenzu Providence High School

AP Chemistry : Ch. 5 Notes Mr. Niedenzu Providence High School

A. Gases

0. Characteristics :

a. expand spontaneously to fill its container (no definite volume)

b. gases are highly compressible

c. form homogeneous mixtures

d. individual molecules are relatively far apart and exert little influence on each other

1. Pressure

a. Devices used to measure gas pressure :

- barometer - device used to measure atmospheric pressure - mercury or aneroid

- manometer - used to measure the pressure of a contained gas - see Fig. 5.3

b. Units of gas pressure

- mm Hg - equal to the amount of air pressure needed to push a mercury column up 1 mm

- torr - named after Evangelista Torricelli - (inventor of barometer), equals 1 mm Hg

- standard atmosphere (atm) equals 760 mm Hg (or 760 torr)

- pascal (Pa) - SI unit of gas pressure (N/m2) = 101,325 Pa = 1 atm

- Pa are very small and not frequently used

2. The Gas Laws of Boyle, Charles, and Avogadro

a. Four factors which determine the state of a gas :

- Pressure

- Temperature

- Volume

- amount (usually measured in moles)

b. Boyle's law : Volume and pressure are inversely related at constant temperature

- PV = k, where k is a constant for a given sample of a gas at a specific temperature

- or, P1 x V1 = P2 x V2

- a gas that strictly obeys Boyle's law is an ideal gas

- Boyle's law only holds precisely at low pressures

c. Charles's law : The Kelvin temperature and volume vary directly with each other at constant pressure.

- linear relationship

- V = bT, where T is in Kelvins and b is a proportionality constant

- or, V1/T1 = V2/T2

- K = ºC + 273

- If Charles's law is extrapolated backwards to where V = 0, the value of absolute zero having a value of -273 K can be obtained

d. Avogadro's law : for a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas present.

- Or, equal volumes of gases at the same temperature and pressure have the same number of particles.

- V = an, where n = number of moles and a = proportionality constant

- this relationship is closely obeyed at low pressures

3. The Ideal Gas Law

a. PV = nRT , where : R = universal gas constant (.08206 L·atm/K·mol)

- it is important to remember that the gas laws describe ideal gases, not real gases

- real gas behavior approaches ideal gas behavior at high temperatures and low pressures

- for calculations you may assume ideal gas behavior unless told otherwise

Note : The other above gas laws can be derived from the ideal gas law. e.g. Boyle's law : If n,R and T are constant, then under condition set one : P1V1 = nRT, and under condition set two P2V2 = nRT, or P1V1 = P2V2.

4. Gas Stoichiometry

a. The molar volume of an ideal gas at STP is 22.42 L

b. STP - standard temperature and pressure (0 ºC and 1 atm)

c. Determination of the molar mass of a gas from an ideal gas law derivation : Molar mass = dRT/P, where d = density of a gas and R = universal gas constant.

5. Dalton's Law of Partial Pressures - For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone.

a. mathematically : Ptotal = P1 + P2 + P3 …. Where P1, P2 and P3 represent the partial pressure of each gas in the mixture.

b. The pressure of a gas is unaffected by the identity of a gas. Therefore :

- the volume of the individual gas particles is not important

- the forces between the particles is unimportant

c. The pressure of a gas is directly proportional to the moles of gas present, therefore the mole fraction of a gas is directly proportional to the partial pressure of a gas :

where a = one of the gases in a mixture of gases

d. When a gas is collected over water by water displacement the vapor pressure of the water needs to be subtracted from the total pressure of the container to obtain the pressure of the gas alone. (Ptotal = Pgas + PH2O)

6. The Kinetic Molecular Theory of Gases - a model based on observations used to explain and predict the behavior of ideal gases.

a. The Kinetic Molecular Theory of gases states that :

- The particles of a gas are so small compared to the distances between particles that the volume of the individual particles can be assumed to be zero.

- The particles of a gas are in constant motion. Gas pressure is created by the collisions of the gas particles with the walls of the container. Collisions of gas particles are elastic - no kinetic energy is lost.

- The particles exert no forces on each other.

- The average kinetic energy of a collection of gas particles is directly proportional to the Kelvin temperature of the gas.

b. The relationship between kinetic energy and temperature is given by the following equation :

c. The root mean square velocity of a gas can be calculated using the following equation :

- where : urms = root mean square

R = universal gas constant (8.3145 J/K·mol)

M = mass of one mole of the particles in Kg

d. Gas particles travel at varying speeds due to collisions with other particles.

e. Mean free path - the average distance traveled by a particle between collisions

7. Effusion and Diffusion

a. Effusion - the passage of a gas through a tiny hole into an evacuated chamber.

- the rate of effusion of a gas is inversely proportional to the square root of the mass of the particles of a gas (Graham's law)

- Graham's law of effusion :

b. Diffusion - the mixing of gases due to the random motion of the particles of the gas

- much more complex to mathematically describe due to the collisions between particles

8. Real Gases

a. No gas exactly follows ideal gas behavior. Real gases best approach ideal gas behavior under conditions of high temperature and low pressure.

b. van der Waal's equation - describes the behavior of a real gas by correcting for the actual volume of gas particles and the forces between gas particles :

where : Pobs = observed pressure

V = volume of container

a(n/V)2 = pressure correction

V-nb = volume correction

a and b are proportionality constants obtained from observing the real gas

9. Chemistry in the Atmosphere

a. Air pollution

- cars and trucks can produce NO when nitrogen burns in the piston chambers of the engine

- NO oxidizes into NO2 in the air

- photochemical smog - light induced chemical reactions which forms pollutants such as ozone and other chemicals formed by reactions with ozone

- process of ozone formation :

NO2(g) à NO(g) + O(g)

O(g) + O2(g) à O3(g)

NO(g) + ½O2(g) à NO2(g)

3/2O2(g) à O3(g)

- acid rain can also be formed when nonmetallic oxides formed by burning nitrogen in the air or sulfur in coal react with water in the air :

S (from coal) + O2(g) à SO2(g)

2 SO2(g) + O2(g) à SO3(g)

H2O(l) + SO3(g) à H2SO4(aq)