Gases The Ideal Gas Law General Organic and

Ideal Gas Law § The relationship between the four properties (P, V, n, and

Universal Gas Constant, R The universal gas constant, R, § can be calculated using

Learning Check Another value for the universal gas constant is obtained using mm. Hg

Solution What is the value of the universal gas constant, R, when the pressure

Summary of Units for Ideal Gas Constants General, Organic, and Biological Chemistry Copyright ©

Guide to Using the Ideal Gas Law General, Organic, and Biological Chemistry Copyright ©

Learning Check Dinitrogen oxide (N 2 O), laughing gas, is used by dentists as

Solution If a 20. 0 L tank of laughing gas contains 2. 86 moles

Solution STEP 2 Rearrange the ideal gas law for P. PV = n. RT

Learning Check A cylinder contains 5. 0 L of O 2 at 20. 0

Solution STEP 1 Organize the gas data and adjust units for R. P =

Solution (continued) STEP 2 Rearrange the ideal gas law for n (moles). n =

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Ideal Gas Law § The relationship between the four properties (P, V, n, and T) of gases can be written equal to a constant R. PV = R n. T § Rearranging this expression gives the expression called the ideal gas law. PV = n. RT General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. 2

Universal Gas Constant, R The universal gas constant, R, § can be calculated using the molar volume at STP § when calculated at STP, uses a temperature of 273 K, a pressure of 1. 00 atm, a quantity of 1. 00 mole of a gas, and a molar volume of 22. 4 L. P V R = PV = (1. 00 atm)(22. 4 L) n. T (1. 00 mole)(273 K) n T = 0. 0821 L atm mole K General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. 3

Learning Check Another value for the universal gas constant is obtained using mm. Hg for the STP pressure. What is the value of R when a pressure of 760 mm. Hg is placed in the expression? General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. 4

Solution What is the value of the universal gas constant, R, when the pressure of 760 mm. Hg is placed in the expression? R = PV = (760 mm. Hg)(22. 4 L) n. T (1 mole)(273 K) = 62. 4 L mm. Hg mole K General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. 5

Learning Check Dinitrogen oxide (N 2 O), laughing gas, is used by dentists as an anesthetic. If a 20. 0 L tank of laughing gas contains 2. 86 moles of N 2 O at 23 °C, what is the pressure (mm. Hg) in the tank? General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. 8

Solution If a 20. 0 L tank of laughing gas contains 2. 86 moles of N 2 O at 23 °C, what is the pressure (mm. Hg) in the tank? STEP 1 Organize data and adjust units to match the units of R. V = 20. 0 L T = 23 °C + 273 = 296 K n = 2. 86 moles R = 62. 4 L mm. Hg mole K P = ? mm. Hg General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. 9

Solution STEP 2 Rearrange the ideal gas law for P. PV = n. RT P = n. RT V STEP 3 Substitute gas data and solve for unknown. P = (2. 86 moles)(62. 4 L mm Hg)(296 K) (20. 0 L)(mole K) = 2. 64 x 103 mm. Hg General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. 10

Learning Check A cylinder contains 5. 0 L of O 2 at 20. 0 °C and 0. 85 atm. How many grams of oxygen are in the cylinder? General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. 11

Solution STEP 1 Organize the gas data and adjust units for R. P = 0. 85 atm V = 5. 0 L T = 293 K, n = ? g of O 2 R = 0. 0821 L atm mole K General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. 12

Solution (continued) STEP 2 Rearrange the ideal gas law for n (moles). n = PV RT STEP 3 Substitute gas data and solve for moles. n = (0. 85 atm)(5. 0 L)(mole K) = 0. 18 mole of O 2 (0. 0821 L atm)(293 K) Convert moles to grams using molar mass. n = 0. 18 mole O 2 x 32. 0 g O 2 = 5. 8 g of O 2 1 mole O 2 General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. 13