Ideal Gas Law PV = nRT P= pressure (atm) V= volume (L) n= Mole Gas (mol) T= temperature (K) R= universal gas constant Ex: H2 has a volume of 8.56 L at 0oC and 1.5 atm. Calculate the moles of H2 present. R = 0.08206 L* atm mol * K Given V= 8.56 L T = 0oC + 273 = 273 K P = 1.5 atm n = ? R = 0.08206 atm L/mol K n = PV RT ____ n = (1.5 atm)(8.56 L) _______________________ (0.08206 atm L/mol K)(273 K) n = 0.57 mol

Learning Check Ideal Gas Law formula: Unit for P: Unit for V: Unit for n: Value & unit of R: Unit for T:

Dalton’s Law of Partial Pressures Partial Pressure – pressure that a gas would exert if it alone in the container. Ptotal = P1 + P2 + P3… Ex: A container holds three gases: oxygen, carbon dioxide, and helium. The partial pressures of the three gases are 2.00 atm, 3.00 atm, and 4.00 atm, respectively. What is the total pressure inside the container? Given P1= 2.00 atm P2= 3.00 atm P3= 4.00 atm Ptotal= ? Ptotal = P1 + P2 + P3 Ptotal = 2.00 atm + 3.00 atm + 4.00 atm Ptotal = 9.00 atm

A common method of collecting gas samples in the laboratory is to bubble the gas into a bottle filled with water and allow it to displace the water. When this technique is used, however, the gas collected in the bottle contains a small but significant amount of water vapor. As a result, the pressure of the gas that has displaced the liquid water is the sum of the pressure of the gas plus the vapor pressure of water at that temperature. The vapor pressures of water at various temperatures are given in Table. PTotal - Pvapor = PGas

Ex: A student collects oxygen gas by water displacement at a temperature of 16°C. The total volume is 188 mL at a pressure of 92.3 kPa. What is the pressure of oxygen collected? Given T = 16°C Pvapor = V = 188 mL (doesn’t matter) Ptotal = 92.3 kPa Pgas= ? PTotal - Pvapor = PGas 1.82 kPa 92.3 kPa – 1.82 kPa = PGas Pgas = 90.5 kPa

Ex: Hydrogen gas is collected by water displacement Ex: Hydrogen gas is collected by water displacement. Total volume collected is 0.461 L at a temperature of 17°C and a pressure of 0.989 atm. What is the pressure of dry hydrogen gas collected? How many moles of hydrogen are present? PTotal - Pvapor = PGas Given T = 17°C + 273 = 290. K Pvapor = V = 0.461 L Ptotal = 0.989 atm Pgas= ? ngas = 99.7 kPa – 1.94 kPa = PGas 1.94 kPa Pgas = 97.8 kPa x ________ kPa atm 101.3 1 = 0.965 atm atm kPa 1 101.3 x ________ = 99.7 kPa n = (0.965 atm)(0.461 L) _______________________ (0.08206 atm L/mol K)(290. K) n = PV RT ____ n = 0.0187 mol

Learning Check Dalton’s Law formula: In a sentence summarize how Dalton’s Law works. What does it mean to collect gas over water?

Gas Stoichiometry or use PV = nRT STP = Standard Temperature and Pressure Standard Temperature = 0oC Standard Pressure = 1 atm Molar Volume 1.00 molgas = 22.4 Lgas Ex 1: A sample of N2 has a volume of 1.75 L at STP. How many moles of N2 are present? 1 mol 1.75 L x ________ = 0.0781 mol 22.4 L or use PV = nRT

Ex 2: Calculate the volume of O2 produced at 1 Ex 2: Calculate the volume of O2 produced at 1.00 atm and 25 oC by the decomposition of 10.5g KClO3. 2KClO3  2KCl + 3O2 V = nRT P ____ Given V= ? T = 25oC + 273 = 298 K P = 1.00 atm R = 0.08206 atm L/mol K n = 10.5 g KClO3 V = (0.128 mol) (0.08206 atm L/mol K)(298 K) _______________________________ 1.00 atm 1 mol KClO3 3 mol O2 x ___________ x __________ = 0.128 mol 122.6 g KClO3 2 mol KClO3 V = 3.13 L

Ex 3: Calculate the volume of CO2 produced at STP from 152g of CaCO3. CaCO3  CaO + CO2 152 g CaCO3 1 mol CaCO3 1 mol CO2 22.4 L x ___________ x __________ x _______ = 100.1 g CaCO3 1 mol CaCO3 1 mol 34.0 L or use PV = nRT

Learning Check What does STP mean? STP Temperature = STP Pressure =   STP Temperature = STP Pressure = 1 mole of gas = ______ L of gas