The Combined Gas Law Expresses the relationship between pressure, volume, and temperature of a fixed amount of gas. PV/T = k or P1V1/T1 = P2V2/T2 Charles’ Law Episode 903

Ex: A sample of gas has a volume of 201 L when its temperature is 293 K and its pressure is 224 mm Hg. What volume will the gas occupy at STP? Given: V1 = 201 L P1 = 224 mm Hg T1 = 293 K V2 = ? P2 = 760 mm Hg T2 = 273 K P1V1/T1 = P2V2/T2 (224 mmHg)(201L)/293 K = (760 mmHg)V2/273 K (224mmHg)(201L)(273 K) = V2 (760mmHg)(293 K) 55 L= V2 Episode 903

Diffusion The spontaneous spreading or mixing of a substance. Graham’s Law of Diffusion Under the same conditions of temperature and pressure, gases diffuse at a rate inversely proportional to the square root of their density (or molar mass). v1/v2 or d2/d1 or m2/m1 Episode 903

Ideal Gas Equation PV = nRT New variables n = amount of gas in moles R = Universal Gas Constant Proportionality constant value depends on units used for pressure and volume value of R when using kPa and liters R = 8.314 kPa•L/mol•K Value of R when using atm and liters R = 0.0821 atm•L/mol•K Episode 903

Ex: The average lung capacity for a female student is 3. 9 L Ex: The average lung capacity for a female student is 3.9 L. At normal body temperature, 37⁰C, and 110 kPa, how many moles of air could her lungs hold? Given: P = 110 kPa V = 3.9 L T = 37 ⁰C n = ? R = 8.314 kPa•L/mol•K (310 K) PV = nRT (110 kPa)(3.9 L) = n(8.314 kPa•L/mol•K)(310 K) 0.17 mol = n Episode 903

Avogadro’s Law Equal volumes of different gases under the same conditions have the same number of particles. Conversely, if samples of different gases at the same temperature and pressure contain the same number of particles, then the volumes of all the samples must be equal. At STP, one mole of any gas occupies a volume of 22.4 Liters. 22.4 Liters is the molar volume of a gas. Episode 903

Mole Ratio Molar Volume Ex: 3.2 moles of KNO3 are heated, producing O2 and KNO2. Calculate the volume of O2 in liters, that could be obtained at STP. 2KNO3  O2 + 2KNO2 ? Liters O2 = 3.2 moles KNO3 3.2 mol KNO3 1 mol O2 22.4 L O2 = 36 L O2 2 mol KNO3 1 mol O2 Mole Ratio Molar Volume Episode 903

Dalton’s Law of Partial Pressures The pressure of a gas mixture is the sum of the individual pressure of each gas alone. PT = P1 + P2 + P3 + … Episode 903

PT = PH2O + PO2 95.0 kPa = 3.17 kPa + PO2 91.8 kPa = PO2 Ex: Oxygen gas has been collected over water at a total pressure of 95.0 kPa and a temperature of 25⁰C. What is the pressure of the dry oxygen gas? PT = PH2O + PO2 95.0 kPa = 3.17 kPa + PO2 PT = 95.0 kPa 91.8 kPa = PO2 PH2O @ 25⁰C = 3.17 kPa (Look on water vapor chart) Episode 903