# The Combined Gas Law Expresses the relationship between

The Combined Gas Law • Expresses the relationship between pressure, volume, and temperature of a fixed amount of gas. • PV/T = k or P 1 V 1/T 1 = P 2 V 2/T 2 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: – V 1 = 201 L P 1 V 1/T 1 = P 2 V 2/T 2 – P 1 = 224 mm Hg – – T 1 = 293 K (224 mm. Hg)(201 L)/293 K = (760 mm. Hg)V 2/273 K V 2 = ? P 2 = 760 mm Hg (224 mm. Hg)(201 L)(273 K) 2 T 2 = 273 K (760 mm. Hg)(293 K) = V 55 L= V 2 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). • v 1/v 2 or d 2/d 1 or m 2/m 1 Episode 903

Ideal Gas Equation • PV = n. RT • 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 k. Pa and liters R = 8. 314 k. Pa • 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. At normal body temperature, 37⁰C, and 110 k. Pa, how many moles of air could her lungs hold? Given: P = 110 k. Pa V = 3. 9 L T = 37 ⁰C (310 K) n=? R = 8. 314 k. Pa • L/mol • K PV = n. RT (110 k. Pa)(3. 9 L) = n(8. 314 k. Pa • 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

Ex: 3. 2 moles of KNO 3 are heated, producing O 2 and KNO 2. Calculate the volume of O 2 in liters, that could be obtained at STP. 2 KNO 3 O 2 + 2 KNO 2 ? Liters O 2 = 3. 2 moles KNO 3 3. 2 mol KNO 3 1 mol O 2 22. 4 L O 2 2 mol KNO 3 1 mol O 2 = 36 L O 2 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 = P 1 + P 2 + P 3 + … Episode 903

Ex: Oxygen gas has been collected over water at a total pressure of 95. 0 k. Pa and a temperature of 25⁰C. What is the pressure of the dry oxygen gas? P T = P H 2 O + P O 2 95. 0 k. Pa = 3. 17 k. Pa + PO 2 PT = 95. 0 k. Pa PH 2 O @ 25⁰C = 3. 17 k. Pa 91. 8 k. Pa = PO 2 (Look on water vapor chart) Episode 903

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