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Published bySheldon Wimbrow Modified about 1 year ago

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T HE I DEAL G AS L AW

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A COMBINATION OF LAWS : Boyle’s Law k = PV at constant T and n Charles’ Law V = bT at constant P and n Avogadro’s Law V = an at constant P and T These laws show how the volume of a gas is dependent on the temperature, pressure, and number of moles present The ideal gas law can be used to solve almost any gas problem.

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T HE I DEAL G AS L AW Defines the ideal behavior of a gas Pressures less than or equal to 1 atm Temperatures greater than or equal to 0 o C Units must be in L, atm, K, and mol. The Universal Gas Constant: R = 0.08206 L atm/K mol Ideal Gas Law Equation: PV = nRT

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S AMPLE P ROBLEM #1 A sample of hydrogen gas, H 2, has a volume of 8.56 L at a temperature of 0 o C and a pressure of 1.5 atm. Calculate the number of moles of H 2 present in this gas sample. Identify the Variables: P = 1.5 atmn = ??? V = 8.56 LT = 0 o C Convert units if needed: T = 0 o C = 0 + 273 = 273 K Set up the Equation: PV = nRT RT n = PV RT Solve: n = (1.5 atm)(8.56 L) (0.08206 L K atm mol )(273 K) n = 0.57 mol

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S AMPLE P ROBLEM #2 Suppose we have a 0.240-mol sample of ammonia gas at 25 o C with a volume of 3.5 L at a pressure of 1.68 atm. The gas is compressed to a volume of 1.35 L at 25 o C. Use the ideal gas law to calculate the final pressure Identify the Variables: P 1 = 1.68 atmP 2 = ? V 1 = 3.5 LV 2 = 1.35 L n 1 = 0.240 moln 2 = 0.240 mol T 1 = 25 o CT 2 = 25 o C *n and T are constant Convert units if needed: T = 25 o C = 25 + 273 = 298 K Set up the Equation: PV = nRT *Set it up so that the variables that change are on one side and the constants are on the other. P 1 V 1 = nRT and P 2 V 2 = nRT Because nRT is constant, we can write: P 1 V 1 = P 2 V 2 or P 2 = P 1 V 1 V 2 Solve: P 2 = (1.68 x 3.5) ÷ (1.35) P 2 = 4.4 atm

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I DEAL G AS P RACTICE P ROBLEMS Given the following sets of variables, calculate the unknown quantity using the Ideal Gas Law: 1. P = 782.4 mm Hg; V = ?; n = 0.10121 mol; T = 26.2 o C 2. P = ? mm Hg; V = 27.5 mL; n = 0.007812 mol; T = 16.6 o C 3. P = 1.045 atm; V = 45.2 mL; n = 0.002241 mol; T = ? o C 4. Calculate the mass (g) of argon gas required to fill a 20.4- L container to a pressure of 1.09 atm at 25 o C. 5. What volume does 2.25 g of nitrogen gas, N 2, occupy at 273 o C and 1.02 atm? 6. What mass of helium gas is needed to pressurize a 100.0- L tank to 255 atm at 25 o C? 7. What mass of oxygen gas would be needed to pressurize the same gas tank? 8. At what temperature will a 1.0-g sample of neon gas exert a pressure of 500 torr in a 5.0-L container?

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