Kinetic Molecular Theory Particles in an ideal gas… have no volume. have elastic collisions. are in constant, random, straight-line motion. don’t attract or repel each other. have an avg. KE directly related to Kelvin temperature. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Real Gases Particles in a REAL gas… Gas behavior is most ideal… have their own volume attract each other Gas behavior is most ideal… at low pressures at high temperatures in nonpolar atoms/molecules Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Characteristics of Gases Gases expand to fill any container. random motion, no attraction Gases are fluids (like liquids). no attraction Gases have very low densities. no volume = lots of empty space Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Characteristics of Gases Gases can be compressed. no volume = lots of empty space Gases undergo diffusion & effusion. random motion Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Properties of Gases V = volume of the gas (liters, L) Gas properties can be modeled using math. Model depends on: V = volume of the gas (liters, L) T = temperature (Kelvin, K) P = pressure (atmospheres, atm) n = amount (moles, mol)

Pressure - Temperature - Volume Relationship P T V P T V P T V Pressure versus volume – At constant temperature, the kinetic energy of the molecules of a gas and the root mean square speed remain unchanged. – If a given gas sample is allowed to occupy a larger volume, the speed of the molecules doesn’t change, but the density of the gas decreases and the average distance between the molecules increases: they collide with one another and with the walls of the container less often, leading to a decrease in pressure. – Increasing the pressure forces the molecules closer together and increases the density, until the collective impact of the collisions of the molecules with the walls of the container balances the applied pressure. Volume versus temperature – Raising the temperature of a gas increases the average kinetic energy and the root mean square speed (and the average speed) of the gas molecules. – As the temperature increases, the molecules collide with the walls of the container more frequently and with greater force, thereby increasing the pressure unless the volume increases to reduce the pressure – An increase in temperature must be offset by an increase in volume for the net impact (pressure) of the gas molecules on the container walls to remain unchanged. Pressure of gas mixtures – If gaseous molecules do not interact, then the presence of one gas in a gas mixture will have no effect on the pressure exerted by another, and Dalton’s law of partial pressures holds. Boyle’s P 1 V a ___ Charles V T a Gay-Lussac’s P T a

5. 1. Ideal Gas Equation

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

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