General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.1 Chapter 7 Gases 7.7 Volume and Moles (Avogadro’s Law)

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.2 Avogadro's Law: Volume and Moles Avogadro’s law states that  the volume of a gas is directly related to the number of moles (n) of gas  T and P are constant V 1 = V 2 n 1 n 2

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.3 Learning Check If 0.75 mole of helium gas occupies a volume of 1.5 L, what volume will 1.2 moles of helium occupy at the same temperature and pressure? 1) 0.94 L 2) 1.8 L 3) 2.4 L

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.4 Solution 3) 2.4 L STEP 1 Conditions 1 Conditions 2 Know Predict V 1 = 1.5 L V 2 = ? V increases n 1 = 0.75 mole n 2 = 1.2 moles n increases STEP 2 Solve for unknown V 2 : V 2 = V 1 x n 2 n 1 STEP 3 Substitute values and solve for V 2 : V 2 = 1.5 L x 1.2 moles He = 2.4 L 0.75 mole He

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.5 The volumes of gases can be compared at STP (Standard Temperature and Pressure) when they have  the same temperature Standard temperature (T) = 0 °C or 273 K  the same pressure Standard pressure (P) = 1 atm (760 mmHg) STP

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.6 Molar Volume The molar volume of a gas  is measured at STP (standard temperature and pressure)  is 22.4 L for 1 mole of any gas

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.7 Molar Volume as a Conversion Factor The molar volume at STP  has about the same volume as 3 basketballs  can be used to form 2 conversion factors: 22.4 L and 1 mole 1 mole 22.4 L

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.8 Guide to Using Molar Volume

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.9 Using Molar Volume What is the volume occupied by 2.75 moles of N 2 gas at STP? STEP 1 Given: 2.75 moles of N 2 Need: Liters of N 2 STEP 2 Write a plan: Use the molar volume to convert moles to liters.

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.10 Using Molar Volume (continued) STEP 3 Write equalities and conversion factors: 1 mole of gas = 22.4 L 1 mole gas and 22.4 L 22.4 L 1 mole gas STEP 4 Substitute data and solve: 2.75 moles N 2 x 22.4 L = 61.6 L of N 2 1 mole N 2

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.11 What is the volume at STP of 4.00 g of CH 4 ? 1) 5.60 L2) 11.2 L 3) 44.8 L Learning Check

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. Solution 1) 5.6 L STEP 1 Given: 4.00 g of CH 4 Need: liters of CH 4 at STP STEP 2 Write a plan: g of CH 4 moles of CH 4 L of CH 4 (at STP) 12 STEP 3 Write equalities and conversion factors: 1 mole of CH 4 1 mole of gas = 22.4 L 1 mole CH 4 and 16.0 g CH 4 1 mole gas and 22.4 L 16.0 g CH 4 1 mole CH L 1 mole gas STEP 4 Substitute data and solve: 4.00 g CH 4 x 1 mole CH 4 x 22.4 L = 5.6 L of CH 4 (STP) 16.0 g CH 4 1 mole CH 4

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.13 How many grams of He are present in 8.00 L of He at STP? 1) 25.6 g2) g3) 1.43 g Learning Check

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. Solution 3) 1.43 g of He STEP 1 Given: 8.00 L of He Need: grams of He at STP STEP 2 Write a plan: L of He moles of He g of He (at STP) 14 STEP 3 Write equalities and conversion factors: 1 mole of gas = 22.4 L 1 mole of He = 4.00 g of He 1 mole gas and 22.4 L 1 mole He and 4.00 g He 22.4 L 1 mole gas 4.00 g He 1 mole CH 4 STEP 4 Substitute data and solve: 8.00 L He x 1 mole He x 4.00 g He = 1.43 g of He 22.4 L He 1 mole He

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.15 Gases in Chemical Reactions The volume or amount of a gas at STP in a chemical reaction can be calculated from  STP conditions  mole factors from the balanced equation

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. Guide to Problem Solving Reactions Involving Gases 16

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.17 Example of Gases in Equations What volume (L) of O 2 gas is needed to completely react with 15.0 g of aluminum at STP? 4Al(s) + 3O 2 (g) 2Al 2 O 3 (s)

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.18 Solution for Example of Gases in Equations What volume (L) of O 2 gas is needed to completely react with 15.0 g of aluminum at STP? 4Al(s) + 3O 2 (g) 2Al 2 O 3 (s) STEP 1 Find moles of Al using molar mass. STEP 2 Determine moles of O 2 using mole–mole factor. STEP 3 Convert moles of O 2 to L using molar volume. (STEP 1) (STEP 2) (STEP 3) 15.0 g Al x 1 mole Al x 3 moles O 2 x 22.4 L (STP) 27.0 g Al 4 moles Al 1 mole O 2 = 9.33 L of O 2 (at STP)

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.19 What mass of Fe will react with 5.50 L of O 2 at STP? 4Fe(s) + 3O 2 (g) 2Fe 2 O 3 (s) 1) 13.7 g of Fe 2) 18.3 g of Fe 3) 419 g of Fe Learning Check

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.20 STEP 1 Find moles of O 2 using molar volume. STEP 2 Determine moles of Fe using mole–mole factor. STEP 3 Convert moles of Fe to grams using molar mass. (STEP 1) (STEP 2) (STEP 3) 5.50 L O 2 x 1 mole O 2 x 4 moles Fe x 55.9 g Fe 22.4 L O 2 3 moles O 2 1 mole Fe = 18.3 g of Fe Solution