1 Chapter 12: Gases and Their Properties

2 Properties of Gases Gases form homogeneous mixtures Gases are compressible All gases have low densities  air g/mL  water1.00 g/mL  iron7.9 g/mL Gases expand to fill their containers uniformly A gas exerts a pressure

3 Kinetic Molecular Theory Gases consist of molecular particles moving in straight lines at any given instant. Molecules collide with each other and the container walls without any net loss of energy. Gas molecules behave independently -- attractive/repulsive forces between them are negligible. Gas molecules are widely spaced, the actual volume of molecules is negligible compared to the space they occupy. The average kinetic energy of the gas particles is proportional to the temperature.

4 Kinetic Graph

5 Pressure, Volume, and Temperature Relationships A. Pressure, volume, and temperature units B. Boyle's law C. Charles' law D. Gay-Lussac's law E. Avogadro's law

6 Pressure = -measured with barometer or manometer force unit area SI:1 pascal (Pa) = 1 N/m 2 common:1 atm = 760 mm Hg = 760 torr = 14.7 lb/in 2 (psi) = kPa = bar Volume: mL, L Temperature: K A. Pressure, Volume, and Temperature Relationships

7 Pressure Defined as force per unit area

8 Atmospheric pressure

9 Barometer

10 Manometers

11 Pressure Units kPa = 760 mmHg =760 torr =1 atm =30 in Hg =14.7 psi

12 Robert Boyle, 1662: for a sample of gas at constant T, V  1/P V = orPV = constant  P 1 V 1 = P 2 V 2 (at constant T) constant P B. Boyle’s law

13 Boyles Law

14 Jacques Charles, 1787: for a sample of gas at constant P, V  T (K) V = constant x T or = constant  VTVT V1T1V1T1 V2T2V2T2 =(at constant P) C. Charles’ law

15 Charles Law

16 Joseph Gay-Lussac, ~1800: for a sample of gas at constant V, P  T (K) P = constant x T or = constant  PTPT P1T1P1T1 P2T2P2T2 =(at constant V) D. Gay-Lussac’s law

17 E. Avogadro’s law Amadeus Avogadro, 1811: at constant T and P, V  n V = constant x n or = constant  VnVn V1n1V1n1 V2n2V2n2 =(at constant T & P)

18 Since PV = constant, P/T = constant, V/T = constant, and V/n = constant  = constant, R (universal gas constant) or PV = nRT PV nT The Ideal gas laws

19 STP: 0ºC (273 K) and 1.00 atm (760 torr) molar volume = average volume occupied by one mole of gas at STP = 22.4 L/mol R = = = L·atm/mol·K = 6.24 x 10 4 mL·torr/mol·K PV nT (1.00 atm)(22.4 L) (1.00 mol)(273 K) STP and molar volume

20 mw = since n =  mw = and since d =  mw = e.g., If one finds that a g sample of gas occupies a volume of 238 mL at 25ºC and 525 torr, what is the molecular weight of the gas? mnmn PV RT mRT PV mVmV dRT P Gas densities and molar mass

21 partial pressure, p = pressure exerted by each gas in a mixture of gases e.g., If 6.00 g of O 2 and 9.00 g of CH 4 are placed in a 15.0-L container at 0º, what is the partial pressure of each gas and the total pressure in the container. Dalton’s law of partial pressures 1. Dalton’s law

22 P T = p 1 + p 2 + p 3 …  p 1 = X 1 P T e.g., Air is 78 mol % N 2 and 22 mol % O 2. What is the partial pressure of each gas if the atmospheric pressure is 713 torr? Dalton’s law of partial pressures 2. mole fraction

23 vapor pressure = pressure exerted by evaporation of a liquid (or sublimation of a solid) vacuum liquid or solid equilibrium at some T p vap p vap increases with T e.g., H 2 O T p vap 0ºC4.6 torr 25ºC23.8 torr 100ºC760 torr (boils!) Dalton’s law of partial pressures 3. collecting gases over water

24 Mixture of gas and water vapor. P T = p gas + p vap (H 2 O) Dalton’s law of partial pressures 3. collecting gases over water

25 Mole Fraction