Chapter 12 Gas Laws

Introduction A. Gases are affected by: 1) volume 2) temperature 3) pressure 4) the number of molecules B. Changing any one of these affects the others

C. What would you expect to happen… 1) … to volume when a gas is heated? 2) … to pressure when a gas is heated? 3) … to pressure when volume gets smaller? 4) … to temperature when volume shrinks?

D. What factors are involved in each? a) inflating a tire with air b) heating an aerosol can c) warming up a closed bottle of soda d) cool liquid felt coming from a spray can

E. Gas behaviors assume that … 1) gases are tiny particles 2) there is a huge distance between molecules 3) gas particles do not attract each other 4) they travel in a straight line until they hit another molecule or the wall 5) no energy is lost after any collisions 6) the average kinetic energy is the same for any gas at the same temperature (but their speed isn’t the same)

II. The Gas Law Formulas A. The variables involved are: units Temperature (T) Kelvin [oC + 273] Volume (V) mL , L Pressure (P) mm Hg, torr, atm, kPa Moles (n) moles Conversions for pressure units: 1 mm Hg = 1 torr 760 torr = 1 atm 101.3 kPa = 1 atm

B. Combined gas law: C. If any variable is constant, don’t use it … if temperature is constant (Boyle’s Law) … if volume is constant (Gay-Lussac’s Law) … if pressure is constant (Charle’s Law)

D. Dalton’s Law of Partial Pressures: Ptotal = P1 + P2 + P3 + ... The sum of individual partial pressures of each gas equals the total pressure of the mixture E. The Ideal Gas Law: PV = nRT P = pressure (atm) V = volume (liters) n = moles R = 0.0821 (L-atm/K-mol) T = Kelvin

Collecting a Gas Sample Over Water (Application of Dalton’s Law) The pressure in the collection container is equal to the atmospheric pressure. The pressure of the gas collected plus the pressure of water vapor at the collection temperature is equal to the atmospheric pressure.

Oxygen collected over water.

Ptotal = 760 torr = PO2 + PH2O PO2 = PO2 = 760 - PH2O PO2 = 760 - 23.8 A sample of O2 was collected over water in a bottle at a temperature of 25oC when the atmospheric pressure was 760 torr. What is the pressure of the O2 alone? The vapor pressure of water at 25oC is 23.8 torr. (“The pressure of the gas alone” is sometimes phrased as “the pressure of the dry gas”) Ptotal = 760 torr = PO2 + PH2O PO2 = PO2 = 760 - PH2O PO2 = 760 - 23.8 = 736 torr

P1 = 729 torr P2 = 760 torr V1 = 300. mL V2 = ? T1 = 296 K T2 = 273 K A sample of nitrogen was collected over water and occupies 300. ml at 23oC and 750 torr. If the pressure is increased to 760 torr and the temperature is decreased to 0oC, what would be the new volume of the dry nitrogen? Vapor pressure of H20 @ 23oC is 21.0 torr. P1 = 729 torr P2 = 760 torr V1 = 300. mL V2 = ? T1 = 296 K T2 = 273 K

A sample of nitrogen was collected over water and occupies 300 A sample of nitrogen was collected over water and occupies 300. ml at 23oC and 750 torr. If the pressure is increased to 760 torr and the temperature is decreased to 0oC, what would be the new volume of the dry nitrogen? Vapor pressure of H20 @ 23oC is 21.0 torr. Step 2. Write and solve the equation for the unknown V2.

A sample of nitrogen was collected over water and occupies 300 A sample of nitrogen was collected over water and occupies 300. ml at 23oC and 750 torr. If the pressure is increased to 760 torr and the temperature is decreased to 0oC, what would be the new volume of the dry nitrogen? Vapor pressure of H20 @ 23oC is 21.0 torr.

III. The Ideal Gas Law A. “ideal” gases are defined as gases: 1) whose volume is insignificant 2) that have no attractions to other gas molecules B. PV = nRT involves moles of gas … and moles = g/M C. By rearranging this equation, you can find: 1) g = 2) M = 3) density =

IV. Gas Law Stoichiometry A. Avogadro’s Law - equal volumes of different gases at the same temperature and pressure have the same number of molecules B. If gases are at the same temperature and pressure, then the coefficients of a balanced equation represent VOLUME of gas (liters, milliliters) ex: How many liters of nitrogen gas are required to completely react with 1.00 liter of hydrogen gas to form ammonia if both gases are at the same temperature and pressure? ANS: 0.333 liters

C. STP = “standard temperature and pressure” 1) standard temperature = 273 K [0 oC] 2) standard pressure = 1 atm [760 torr] D. Molar Volume = the volume of any gas measured at STP occupies 22.4 L * At conditions other than STP, the PV=nRT equation would be needed to find volume.

E. Gas law stoichiometry problems 1) PV=nRT is used to calculate moles of gas 2) stoichiometry is used to calculate moles or grams of solids F. Which equation do you use first? 1) it depends … 2) if grams of solid are given, start with stoichiometry 3) if grams of solid are unknown, start with gas law

F. Examples: 1) What volume of oxygen gas can be formed at 0.970 atm and 20.0 C from the decomposition of 1.00 g of KClO3? 2 KClO3  2 KCl + 3 O2

F. Examples: 2) What mass of magnesium will produce 250. mL of hydrogen gas measured at 20 C and 755 torr? Mg + 2 HCl  MgCl2 + H2

F. Examples: 3) What mass of nitrogen gas measured at STP will produce 28.0 g of ammonia at STP? N2 + 3 H2  2 NH3

V. Graham’s Law of Effusion A. All gases have the same average kinetic energy at the same temperature B. The velocity of gas molecules is inversely proportional to their molecular weights C. Example: An unknown gas effuses at a rate of 31.50 ml/min when oxygen effuses at a rate of 30.50 ml/min under the same conditions. Which of these gases could be the unknown? CH4 CO NO CO2 NO2

D. Example: An unknown gas effuses at a rate 1. 21x the rate of CO2 D. Example: An unknown gas effuses at a rate 1.21x the rate of CO2. What is the molecular weight of the unknown gas? Ans: 44 g/mol Chapter 12 …. even numbered problems: 26-64 ….. 68, 70, 78, 88, 90, 92, 96