Gases Lecture 3 PDF

GASES Topics 1. Properties of Gases 2. The Gas Laws 3. Kinetic Molecular Theory of Gases 4. Non-ideal Gases  GASES Properties of Gases 1- Expansion 2- Indefinite shape 3- Compressibility 4- Mi...

GASES Topics 1. Properties of Gases 2. The Gas Laws 3. Kinetic Molecular Theory of Gases 4. Non-ideal Gases  GASES Properties of Gases 1- Expansion 2- Indefinite shape 3- Compressibility 4- Mixing 5- Low density A- Expansion: Gases expand indefinitely to fill the space available to them.  GASES B- Indefinite shape: Gases fill all parts of a container evenly and so have no definite shape of their own. C- Compressibility: Gases are the most compressible of the states of matter. D- Mixing: Two or more gases will mix evenly and completely to the same container. E- Low density: Gases have much lower densities than liquids and solids.  GASES The Gas Laws 1- The ideal gas law PV = nRT Where (P) is Pressure, (V) is volume, (n) is number of moles, (T) is Absolut temperature, and (R) is the ideal gas constant, R = 0.0821 L.atm/K.mol, also be written as (0.0821 L atm K-1 mol-1) 2- Boyle's law It states that when the temperature is held constant, the volume of a given amount of gas is inversely proportional to the applied pressure. PV= k1 On rearranging, the equation becomes V= K1/ P  GASES For changes in pressure from P1 to P2, we can apply Boyle's law. Since the product PV is a constant, the value of PV at the initial pressure P1 will equal PV at the final pressure P2. P1V1 = P2V2 (n and T are constant)  GASES 3- Charles's law It states that at constant pressure the volume of a gas is directly proportional to its absolute temperature. V = k2T (Charles's law). Since V/T is equal to a constant, then V1/T1 at an initial temperature T1 and volume V1 will equal the quotient V2/T2 at a final temperature T2 and volume V2. V1/T1= V2/T2 (n and P are constant)  GASES 4- Avogadro's law It states that at the same temperature and pressure, equal volumes of different gases contain the same number of molecules (or moles); This is another way of saying that the volume of a gas is directly proportional to the number of moles present. Thus V = nk3 (Avogadro's law) The molar volume of an ideal gas is 22.4 L at STP. V = nRT / P = (1mol)(0.0821L.atm /k.mol)(273k) / 1atm = 22.4 L STD = Standard Temperature and Pressure 0°C = 273 K 1 atm = 14.7 psi = 760.0 mmHg = 760.0 torr  GASES for changes in pressure, volume, and temperature of a fixed number of moles of gas, the following relationship can be used P1V1/T1 = P2V2/T2 5- Gas Density The density of a gaseous compound is d = m / V, where m is the mass of the gas in grams. Recall the number of moles n of gas is n = m / μ (where μ is the molar mass). Substituting and rearranging for n in the ideal gas equation (PV = nRT) gives the density of a gas that follows the ideal gas law is d = Pμ / RT  GASES Note that 1- The density is directly proportional to its molar mass 2- The density increases as gas pressure increases 3- The density decreases as the temperature increases 6- Dalton's Law of Partial Pressures Each component gas of a mixture of gases uniformly fills the containing vessel. Each component exerts the same pressure as it would occupied that volume alone. Thus, the total pressure of a mixture is the sum of the individual pressures, called the partial pressures, of each component: Pt= PA + PB + PC + ……  GASES Also, the total number of moles n, is the sum of the number of moles of each component: nt= nA + nB + nC + …… P1 P2 Ptotal = P1 + P2  GASES According to Dalton's law, the partial pressure of a gas is proportional to its mole fraction in the mixture. PA = XAPt XA is the mole fraction of component A Whenever gases are collected by displacement of water, the total gas pressure is the sum of the partial pressure of the collected gas and the partial pressure of water vapor. Pt = Pgass + PH2O Consequently, the partial pressure of the collected gas is: Pgass = Pt – PH2O where the partial pressure of water depends on the temperature and corresponds to the vapor pressure of water.  GASES EXAMPLE 1 What volume will be occupied by 0.833 mole of fluorine (F2) at 645 mmHg and 15.0 oC?  GASES EXAMPLE 2 A gaseous compound has a density of 1.69 g/L at 25oC and 714 torr. What is its molar mass?  GASES EXAMPLE 3 Oxygen gas is collected over water at 30 oC, and the total pressure is 645 mmHg: a. What is the partial pressure of oxygen? The vapor pressure of water at 30 oC is 3l.8 mmHg. b. What are the mole fractions of oxygen and water vapor? a.  GASES b.