Chapter V Gases

Gases Properties of a Gas: It has no fixed shape and volume. The earth’s atmosphere is a mixture of gases that consists mainly of elemental nitrogen (N2) and oxygen (O2). The gases in the atmosphere also shield us from harmful radiation from the sun and keep the earth warm by reflecting heat radiation back toward the earth. Properties of a Gas: It has no fixed shape and volume. The distance between gas atoms/molecules is larger as compared to particle size. Uniformly fills any container. Mixes completely with any other gas.

PRESSURE SI units of pressure = Newton/meter (N/m2) = 1 Pascal (Pa) 1 standard atmosphere = 101,325 Pa 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr

Barometer Device used to measure atmospheric pressure. Mercury flows out of the tube until the pressure of the column of mercury standing on the surface of the mercury in the dish is equal to the pressure of the air on the rest of the surface of the mercury in the dish. A device to measure atmospheric pressure, the barometer, was invented in 1643 by an Italian scientist named Evangelista Torricelli (1608–1647), who had been a student of Galileo.

5. 1. Ideal Gas Equation

PV = nRT PV (1 atm)(22.414L) R = = nT (1 mol)(273.15 K) The conditions 0 0C and 1 atm are called standard temperature and pressure (STP). Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L. PV = nRT R = PV nT = (1 atm)(22.414L) (1 mol)(273.15 K) R = 0.082057 L • atm / (mol • K)

5. 2. Stoichiometry of gaseous reaction

PV = nRT nRT V = P 1.37 mol x 0.0821 x 273.15 K V = 1 atm V = 30.6 L What is the volume (in liters) occupied by 49.8 g of HCl at STP? T = 0 0C = 273.15 K P = 1 atm PV = nRT n = 49.8 g x 1 mol HCl 36.45 g HCl = 1.37 mol V = nRT P V = 1 atm 1.37 mol x 0.0821 x 273.15 K L•atm mol•K V = 30.6 L

PV = nRT n, V and R are constant nR V = P T = constant P1 T1 P2 T2 = Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0C is heated to 85 0C at constant volume. What is the final pressure of argon in the lightbulb (in atm)? PV = nRT n, V and R are constant nR V = P T = constant P1 = 1.20 atm T1 = 291 K P2 = ? T2 = 358 K P1 T1 P2 T2 = P2 = P1 x T2 T1 = 1.20 atm x 358 K 291 K = 1.48 atm

Example: A sample of hydrogen gas (H2) has a volume of 8 Example: A sample of hydrogen gas (H2) has a volume of 8.56 L at a temperature of 0C and a pressure of 1.5 atm. Calculate the moles of H2 molecules present in this gas sample.

5.3. Gas mixture: partial pressure and mol fractions The total pressure of the mixture P total can be represented as:

Dalton’s Law of Partial Pressures V and T are constant P1 P2 Ptotal = P1 + P2

5.4. Postulates of the Kinetic Molecular Theory The gas particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero). 2. The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. 3. The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other. 4. The average kinetic energy of the particles is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy.

(a) (b) (c) (a) A balloon filled with air at room temperature. (b) The balloon is dipped into liquid nitrogen at 77 K. (c) The balloon collapses as the molecules inside slow down due to the decreased temperature. Slower molecules produce a lower pressure.

Graham’s law of effusion Figure A. The effusion of a gas into an evacuated chamber. The rate of effusion (the rate at which the gas is transferred across the barrier through the pin hole) is inversely proportional to the square root of the molar mass of the gas molecules. The relative rates of effusion of two gases at the same temperature and pressure are given by the inverse ratio of the square roots of the molar masses of the gas particles: where M1 and M2 represent the molar masses of the gases. This equation is called Graham’s law of effusion.

Graham’s law of effusion Example: Calculate the ratio of the effusion rates of hydrogen gas (H2) and uranium hexafluoride (UF6). To calculate the molar masses: Molar mass of H2 2.016 g/mol, and molar mass of UF6 352.02 g/mol. Using Graham’s law, The effusion rate of the very light H2 molecules is about 13 times that of the massive UF6 molecules.

White ring of NH4Cl(s) forms where the NH3 and HCl meet. Conti. Two cotton plugs soaked in ammonia and hydrochloric acid are simultaneously placed at the ends of a long tube. A white ring of ammonium chloride (NH4Cl) forms where the NH3 and HCl molecules meet several minutes later: White ring of NH4Cl(s) forms where the NH3 and HCl meet.