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The Ideal Gas Law

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**A combination of laws: Boyle’s Law Charles’ Law Avogadro’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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**Ideal Gas Law Equation:**

The Ideal Gas Law Defines the ideal behavior of a gas Pressures less than or equal to 1 atm Temperatures greater than or equal to 0 oC Units must be in L, atm, K, and mol. The Universal Gas Constant: R = L atm/K mol Ideal Gas Law Equation: PV = nRT

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Sample Problem #1 A sample of hydrogen gas, H2, has a volume of 8.56 L at a temperature of 0 oC and a pressure of 1.5 atm. Calculate the number of moles of H2 present in this gas sample. Identify the Variables: P = 1.5 atm n = ??? V = 8.56 L T = 0 oC Set up the Equation: PV = nRT PV = nRT RT RT n = PV RT Convert units if needed: T = 0 oC = = 273 K Solve: n = (1.5 atm)(8.56 L) ( LK atm mol)(273 K) n = 0.57 mol

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Sample Problem #2 Suppose we have a mol sample of ammonia gas at 25 oC 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 oC. Use the ideal gas law to calculate the final pressure 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. P1V1 = nRT and P2V2 = nRT Because nRT is constant, we can write: P1V1 = P2V2 or P2 = P1V1 V2 Identify the Variables: P1 = 1.68 atm P2 = ? V1 = 3.5 L V2 = 1.35 L n1 = mol n2 = mol T1 = 25 oC T2 = 25 oC *n and T are constant Convert units if needed: T = 25 oC = = 298 K Solve: P2 = (1.68 x 3.5) ÷ (1.35) P2 = 4.4 atm

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**Ideal Gas Practice Problems**

Given the following sets of variables, calculate the unknown quantity using the Ideal Gas Law: P = mm Hg; V = ?; n = mol; T = 26.2 oC P = ? mm Hg; V = 27.5 mL; n = mol; T = 16.6 oC P = atm; V = 45.2 mL; n = mol; T = ? oC Calculate the mass (g) of argon gas required to fill a L container to a pressure of 1.09 atm at 25 oC. What volume does 2.25 g of nitrogen gas, N2, occupy at 273 oC and 1.02 atm? What mass of helium gas is needed to pressurize a L tank to 255 atm at 25 oC? What mass of oxygen gas would be needed to pressurize the same gas tank? 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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