GASES

Properties of a Gas Uniformly fills any container (no fixed shape) Large distance between molecules (no fixed volume) Mixes completely with any other gas Exerts pressure on its surroundings WHY?

Simple barometer invented by Evangelista Torricelli The pressure exerted by the surrounding air is equal to the pressure exerted by a column of Hg 760 mm in height. Simple barometer invented by Evangelista Torricelli

What is “pressure”? force/unit area English unit = pounds per square inch SI unit = Newton/meter2 = 1 Pascal (Pa) 1 standard atmosphere = 101,325 Pa 1 standard atmosphere = 1 atm = 760 mm Hg = 760 Torr What’s a Newton?

Which diagram, a or b, shows a low pressure day? Simple Manometer

Volume of a gas decreases as pressure increases Boyle’s Law P vs V Volume of a gas decreases as pressure increases at constant temperature

P vs V V vs 1/P BOYLE’S LAW DATA Why do we care about making the graph a straight line?

k = a proportionality constant Boyle’s Law (Pressure)( Volume) = k P V = k P1V1 = P2V2 V  1/P k = a proportionality constant as long as T is held constant and no additional gas is added or removed

Boyle’s Law Calculations In an automobile engine, the initial cylinder volume is 0.725 L. After the piston moves up, the volume is 0.075 L. The initial pressure is 1.00 atm, what is the final pressure? P1 = 1.00 atm P2 = ? V1 = 0.725 L V2 = 0.075 L V1P1 = V2P2 P2 = V1P1/V2 P2 = (0.725 L)(1.00 atm)/(0.075 L) P2 = 9.7 atm Is this answer reasonable?

Volume of a gas increases as heat is added Charles’s Law T vs V Volume of a gas increases as heat is added when pressure is held constant.

k = a proportionality constant Charles’s Law (Volume) = k (Temperature) V = k T V1 = V2 T1 T2 V  T T must be in Kelvin k = a proportionality constant as long as P is held constant and no additional gas is added or removed WHY?

Charles’s Law Calculations Consider a gas with a a volume of 0.675 L at 35 oC and 1 atm pressure. What is the temperature (in oC) of the gas when its volume is 0.535 L at 1 atm pressure? V1 = 0.675 L V2 = 0.535 L T1 = 35 oC = 308 K T2 = ? V1/V2 = T1/T2 T2 = (308 K)(0.535 L)/(0.675 L) T2 = 244 K - 273 T2 = - 29 oC

At constant temperature and pressure, increasing Avogardro’s Law n vs V At constant temperature and pressure, increasing the moles of a gas increases its volume.

k = proportionality constant Avogadro’s Law For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas. V = k n V  n k = proportionality constant

AVOGADRO’S LAW 3 O2(g)  2 O3(g) V1 = 12.2 L V2 = ? n1 = 0.50 mol A 12.2 L sample containing 0.50 mol of oxygen gas, O2, at a pressure of 1.00 atm and a temperature of 25 oC is converted to ozone, O3, at the same temperature and pressure, what will be the volume of the ozone? 3 O2(g)  2 O3(g) V1 = 12.2 L V2 = ? n1 = 0.50 mol n2 = 0.33 mol V1/V2 = n1/n2 V2 = (12.2 L)(0.33 mol)/(0.50 mol) V2 = 8.1 L What would happen if the volume was fixed?

Pressure exerted by a gas increases as temperature Gay-Lussac’s Law P vs T Pressure exerted by a gas increases as temperature increases provided volume remains constant.

k = a proportionality constant Gay-Lussac’s Law The pressure of a gas is directly proportional to temperature, if the volume is held constant. P = k T P  T k = a proportionality constant as long as V is held constant and no additional gas is added or removed

Ideal Gas Law P V = n R T R = proportionality constant = 0.0821 L atm  mol P = pressure in atm V = volume in liters n = moles T = temperature in Kelvins

Ideal Gas Law Calculations A 1.5 mol sample of radon gas has a volume of 21.0 L at 33 oC. What is the pressure exerted by the gas? P = ? V = 21.0 L n = 1.5 mol T = 33 oC + 273 T = 306 K R = 0.0821 L atm/mol·K PV = nRT P = nRT/V P = (1.5)(0.0821)(306) (21.0) P = 1.8 atm

Ideal Gas Law Calculations A sample of hydrogen gas, H2, has a volume of 8.56 L at a 0 oC and 1.5 atm. Calculate the number of moles of hydrogen present in this sample. P = 1.5 atm V = 8.56 L R = 0.0821 Latm/molK n = ? T = O oC + 273 T = 273K PV = nRT n = pV/RT n = (1.5)(8.56) (0.0821)(273) n = 0.57 mol

Standard Temperature and Pressure “STP” P = 1 atmosphere = 101.3 kPa = 760 torr = 760 mm Hg T = C or 273 K The molar volume of an ideal gas is approximately 22.4 liters at STP

as long as n is held constant, no additional gas is added or removed COMBINED GAS LAW as long as n is held constant, no additional gas is added or removed

IDEAL GAS 1. Molecules are infinitely small--zero molecular volume. 2. Zero attractive forces exist among the molecules. 3. Collisions between molecules are perfectly elastic (no energy loss). What real gases would behave most like an ideal gas?

REAL GAS 1.The volume of the molecule is small compared to the distance between molecules. 2. Very small attractive forces exist between molecules. What properties of a gas molecule would cause it to deviate most from an ideal gas?

Real Gases Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).

Real Gas Equation   corrected pressure corrected volume Pideal Videal Luckily, this equation will never be used.