Chapter 14 The Behavior of Gases 14.3 Ideal Gases 14.1 Properties of Gases 14.2 The Gas Laws 14.3 Ideal Gases 14.4 Gases: Mixtures and Movements Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

CHEMISTRY & YOU Do Now If I have 25 mL of a gas at 2.1 atm and 300 K, what will the pressure become if I raise the temperature to 400 K and decrease the volume to 10 mL? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Combined Gas Law P1  V1 T1 T2 P2  V2 = This assumes the amount of gas is constant Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Since volume is proportional to number of moles… Ideal Gas Law Since volume is proportional to number of moles… Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

1 mol of every gas occupies 22.4 L at STP (101.3 kPa and 273 K) Ideal Gas Law P  V T  n R = Ideal Gas Constant = 1 mol of every gas occupies 22.4 L at STP (101.3 kPa and 273 K) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law P  V = n  R  T or PV = nRT R = 8.314 LkPa/molK R = 0.08206 Latm/molK Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Assumes all gases behave the same Ideal Gas Law Ideal Gas Assumes all gases behave the same Assumes all gases follow kinetic theory Particles are small No intermolecular forces Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 14.5 Using the Ideal Gas Law At 34oC, the pressure inside a nitrogen-filled tennis ball with a volume of 0.148 L is 212 kPa. How many moles of nitrogen gas are in the tennis ball? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze List the knowns and the unknown. Sample Problem 14.5 Analyze List the knowns and the unknown. 1 KNOWNS UNKNOWN P = 212 kPa V = 0.148 L T = 34oC R = 8.31 (L·kPa)/(K·mol) n = ? mol N2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.5 Calculate Solve for the unknown. 2 Convert degrees Celsius to kelvins. T = 34oC + 273 = 307 K Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.5 Calculate Solve for the unknown. 2 Rearrange the equation to isolate n. P  V = n  R  T Isolate n by dividing both sides by (R  T): = R  T n  R  T P  V n = R  T P  V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.5 Calculate Solve for the unknown. 2 Substitute the known values for P, V, R, and T into the equation and solve. n = R  T P  V n = 8.31 (L·kPa) / (K·mol)  307 K 212 kPa  0.148 L n = 1.23  10–2 mol N2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 14.6 Using the Ideal Gas Law A deep underground cavern contains 2.24 x 106 L of methane gas (CH4) at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many kilograms of CH4 does the cavern contain? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze List the knowns and the unknown. Sample Problem 14.6 Analyze List the knowns and the unknown. 1 Calculate the number of moles (n) using the ideal gas law. Use the molar mass of methane to convert moles to grams. Then convert grams to kilograms. KNOWNS UNKNOWN P = 1.50  103 kPa V = 2.24  103 L T = 315 K R = 8.31 (L·kPa)/(K·mol) molar massCH4 = 16.0 g m = ? kg CH4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.6 Calculate Solve for the unknown. 2 State the ideal gas law. P  V = n  R  T Rearrange the equation to isolate n. n = R  T P  V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.6 Calculate Solve for the unknown. 2 Substitute the known quantities into the equation and find the number of moles of methane. n = 8.31 (L·kPa)/(K·mol)  315 K (1.50  106 kPa)  (2.24  106 L) n = 1.28  106 mol CH4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.6 Calculate Solve for the unknown. 2 Do a mole-mass conversion. 1.28  106 mol CH4  16.0 g CH4 1 mol CH4 = 20.5  106 g CH4 = 2.05  107 g CH4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.6 Calculate Solve for the unknown. 2 Convert from grams to kilograms. 2.05  106 g CH4  1 kg 103 g = 2.05  104 kg CH4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Dalton’s Law It is not safe to put aerosol canisters in a campfire, because the pressure inside the canister gets very high and can explode. If I have a 1.0 L canister that holds 2.0 moles of gas, and the campfire temperature is 1400 deg C, what is the pressure inside the can (in atmospheres)? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

END OF 14.3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.