Chapter 10: Properties of Gases: The Air We Breathe

Transcription

1 Chapter 10: Properties of Gases: The Air We Breathe South Pole Sept 24, February

2 Chapter Outline The Properties of Gases Effusion and the Kinetic Molecular Theory of Gases Atmospheric Pressure 10.4 Relating P,T, and V: The Gas Laws 10.5 The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubilities of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases 2

3 The Properties of Gases Neither definite shape nor definite volume The Properties of Gases Gases can be compressed. 3

4 The Properties of Gases All gases are miscible with all other gases. Chapter Outline The Properties of Gases Effusion and the Kinetic Molecular Theory of Gases Atmospheric Pressure 10.4 Relating P,T, and V: The Gas Laws 10.5 The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubilities of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases 4

5 Kinetic Molecular Theory of Gases 1. Gas particles have tiny volumes compared with their container s volume Kinetic Molecular Theory of Gases 2. They don t interact with other gas molecules, e.g. no intermolecular forces. X 5

6 Kinetic Molecular Theory of Gases 3. They move randomly and constantly Kinetic Molecular Theory of Gases 4. Elastic collisions with walls of container and other gas molecules 6

7 Kinetic Molecular Theory of Gases 5. Have average kinetic energy that is proportional to absolute Kelvin temperature: KE avg = ½ mu 2 rms rms velocity 1/M = 32 g/mol = 28 = 18 = 4 7

8 Graham s Law of Effusion, p. 415 Effusion is the process where a gas escapes through a small pore in the container wall into a region of lower pressure. Sample Exercise 10.1: Calculating Relative Rates of Effusion An odorous gas emitted by a hot spring was found to effuse at times the rate at which helium effuses. What is the molar mass of the emitted gas? 8

9 Chapter Outline The Properties of Gases Effusion and the Kinetic Molecular Theory of Gases Atmospheric Pressure Relating P,T, and V: The Gas Laws The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubilities of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases Pressure = force/unit area Molecules collide with the inside surface of the container. The force of the collision is measured as pressure. Pressure at Sea Level Pounds/in 2 (psi) 14.7 psi Atmospheres (atm) 1 atm Pascals (N/m 2 ) X 10 3 Pa Torr (mmhg) 760 mmhg 9

10 Torricelli s Barometer 760 mm Hg vacuum Column of mercury Atmospheric pressure The pressure of the atmosphere on the surface of the mercury in the dish is balanced by the downward pressure exerted by the mercury in the column. Elevation and Atmospheric Pressure 0.35 atm 0.62 atm 0.83 atm Sea level 10

11 Chapter Outline The Properties of Gases Effusion and the Kinetic Molecular Theory of Gases Atmospheric Pressure Relating P,T, and V: The Gas Laws The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubilities of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases State Variables for a Gas P = pressure T = temperature V = volume n = number of moles 11

12 Boyle s Law: P and V (n and T held constant) Gases are compressible Pressure as Volume Boyle s Law: P 1/V (T and n fixed) or, P V = constant or, P 1 V 1 = P 2 V 2 Decreasing volume increases number of collisions/area; P (KMT Postulates #3 & 4) Boyle s Law and Respiration 12

13 Applying Boyle s Law Example A bubble of oxygen at the bottom of a lake floats up to the surface. The pressure at the bottom of the lake is 4.75 atm and the volume is 5.65 ml. At the surface, the new volume is 5.65 ml. Assuming that the temperature and number of moles remained constant, what is the final volume of the bubble? Explaining Boyle s Law Using Kinetic Molecular Theory 13

14 Charles s Law: Charles s Law: V and T (n and P held constant) V T (P, n constant) or, V 1 T 1 = V 2 T 2 Volume of a gas extrapolates to zero at absolute zero (0 K = 273 C). Kinetic energy as T ; force of collisions increases and gas expands to maintain constant P (KMT Post. #3, 4 & 5). Jacques Alexandre Charles ( ) The French chemist Charles was most famous in his lifetime for his experiments in ballooning. The first such flights were made by the Montgollier brothers in June 1783, using a large spherical balloon made of linen and paper and filled with hot air. In August 1783, however, a different group. supervised by Jacques Charles, tried a different approach. Exploiting his recent discoveries in the study of gases, Charles decided to inflate the balloon with hydrogen gas. Because hydrogen would escape easily from a paper bag, Charles made a bag of silk coaled with a rubber solution. Inflating the bag to its final diameter took several days and required nearly 500 pounds of acid and 1000 pounds of iron to generate the hydrogen gas. A huge crowd watched the ascent on August 27, The balloon stayed aloft for almost 45 minutes and travelled about 15 miles. When it landed in a village, however, the people were so terrified they tore if to shreds. 14

15 Sample Exercise 10.4: Applying Charles Law Several students at a northern New England campus are hosting a party celebrating the mid-january start of spring semester classes. They decide to decorate the front door of their apartment building with party balloons. The air in the inflated balloons is initially 70 o F. After an hour outside, the temperature of the balloons is -12 o F. Assuming no air leaks from the balloons and the pressure in them does not change significantly, how much does their volume change? Express your answer as a percentage of the initial volume. Explaining Charles Law Using Kinetic Molecular Theory 15

16 Avogadro s Law: V and n (T and P held constant) Volume is directly proportional to the number of moles of gas, V n (T, P constant) V n or, constant V n 1 1 V n 2 2 Increasing n increases the number of collisions, gas expands to keep pressure constant (KMT Post. #3 & 4). Explaining Avogadro s Law Using Kinetic Molecular Theory 16

17 Amonton s Law: P and T (n and V held constant) P T (n, V constant) P T = constant or, P 1 T 1 = P 2 T 2 Increasing T will increase force of collisions if volume is kept constant; P will increase (KMT Post. #3, 4 & 5). Sample Exercise 10.5: Applying Amonton s Law Labels on aerosol cans caution against their incineration because the cans may explode when the pressure inside them exceeds 3.00 atm. At what temperature in degrees Celcius might an aerosol can burst if its internal pressure is 2.00 atm at 25 o C? 17

18 Explaining Amonton s Law Using Kinetic Molecular Theory Chapter Outline The Properties of Gases Effusion and the Kinetic Molecular Theory of Gases Atmospheric Pressure 10.4 Relating P,T, and V: The Gas Laws 10.5 The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubilities of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases 18

19 The Combined Gas Law Combining Boyle s and Charles Law (where n is held constant) Sample Exercise 10.6: Applying the Combined Gas Law The pressure inside a weather balloon as it is released is 798 mmhg. If the volume and temperature of the balloon are 131 L and 20 o C, what is the volume of the balloon when it reaches an altitude where its internal pressure is 235 mmhg and T = -52 o C? 19

20 Chapter Outline The Properties of Gases Effusion and the Kinetic Molecular Theory of Gases Atmospheric Pressure Relating P,T, and V: The Gas Laws The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubilities of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases Ideal Gas Equation Boyle s law: V (at constant n and T) 1 P Charles law: V T (at constant n and P) Avogadro s law: V n (at constant P and T) 20

21 Standard Temperature and Pressure (STP). Experiments show that at STP, 1 mole of an ideal gas occupies L. PV = nrt Sample Exercise 10.7: Applying the Ideal Gas Law Bottles of compressed O 2 carried by climbers ascending Mt. Everest are designed to hold one kilogram of the gas. What volume of O 2 can one bottle deliver to a climber at an altitude where the temperature is -38 o C and the atmospheric pressure is 0.35 atm? Assume that each bottle contains 1.00 kg of O 2. 21

22 Chapter Outline 10.1 The Properties of Gases 10.2 Effusion and the Kinetic Molecular Theory of Gases 10.3 Atmospheric Pressure 10.4 The Gas Laws 10.5 The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubility of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases Densities and Molecular Weights of Gases Using PV = nrt PV = nrt 22

23 Sample Exercise 10.8: Calculating the Density of a Gas According to the U.S National Weather Service, the air temperature in Phoenix, AZ reached 78 o F on January 1, 2012, when the atmospheric pressure was 1024 millibars. What is the density of the air? Assume the average molar mass of air is 28.8 g/mol, which is the weighted average of the molar masses of the various gases in dry air. Example: Calculating the Molecular Weight from PV = nrt g of Freon-113 gas is trapped in a 145 ml container at 760 mmhg and 50.0 C. What is the molar mass of Freon-113? 23

24 Chapter Outline 10.1 The Properties of Gases 10.2 Effusion and the Kinetic Molecular Theory of Gases 10.3 Atmospheric Pressure 10.4 The Gas Laws 10.5 The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubility of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases Gas Laws & Stoichiometry 24

25 Example: Combining Stoichiometry and the Ideal Gas Law Chlorine gas can be prepared in the laboratory by the reaction of manganese dioxide with hydrochloric acid: MnO 2 (s) + 4 HCl(aq) MnCl 2 (aq) + 2 H 2 O(l) + Cl 2 (g) How many grams of MnO 2 should be added to excess HCl to obtain 275 ml of chlorine gas at 5.0 C and 650 mmhg? Chapter Outline The Properties of Gases Effusion and the Kinetic Molecular Theory of Gases Atmospheric Pressure 10.4 Relating P,T, and V: The Gas Laws 10.5 The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubilities of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases 25

26 Dalton s Law of Partial Pressures For a mixture of gases in a container: P total = P 1 + P 2 + P Total pressure depends only on total number moles of gas, not on their identities Mole Fraction & Partial Pressure Mole Fraction: Ratio of the # of moles of a given component in a mixture to the total # of moles in a mixture: x 1 n1 n1 n n n n... total Mole Fraction in Terms of Pressure: When V and T are constant, P n 26

27 Mole Fraction & Partial Pressure Since P n And: x x 1 1 n n 1 1 total P1 P total P P total Then P x P 1 1 total Sample Exercise 10.11: Calculating Mole Fractions and Partial Pressures Scuba divers who dive to depths below 50 meters may breathe a gas mixture called Trimix during the deepest parts of their dives. One formulation of the mixture, called Trimix 10/70, is 10% oxygen, 70% helium, and 20% nitrogen by volume. What is the mole fraction of each gas in this mixture, and what is the partial pressure of oxygen in the lungs of a diver at a depth of 60 meters (where the ambient pressure is 7.0 atm)? 27

28 Collecting a Gas over Water 2 KClO 3 (s) 2 KCl(s) + 3 O 2 (g) Gases collected: O 2 (g) and H 2 O(g) P P P total O H O 2 2 Sample Exercise 10.12: Calculating the Quantity of a Gas Collected by Water Displacement During the decomposition of KClO 3, 92.0 ml of gas is collected by the displacement of water at 25.0 o C. If atmospheric pressure is 756 mmhg, what mass of O 2 is collected? 28

29 Chapter Outline 10.1 The Properties of Gases 10.2 Effusion and the Kinetic Molecular Theory of Gases 10.3 Atmospheric Pressure 10.4 The Gas Laws 10.5 The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubility of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases Solubility of Gases Solubility of gases depends on T and P Solubility as Pressure Solubility as Temperature 29

30 Henry s Law Henry s Law: The higher the partial pressure of the gas above a liquid, the more soluble C gas P gas C gas k H P gas Solubility of Oxygen in Water 30

31 Sample Exercise 10.13: Calculating Gas Solubility Using Henry s Law Lake Titicaca is located high in the Andes Mountains between Peru and Bolivia. Its surface is 3811 m above sea level, where the average atmospheric pressure is atm. During the summer, the average temperature of the water s surface rarely exceeds 15 o C. What is the solubility of oxygen in Lake Titicaca at that temperature? Express your answer in molarity and in mg/l. 31

32 Chapter Outline The Properties of Gases Effusion and the Kinetic Molecular Theory of Gases Atmospheric Pressure Relating P,T, and V: The Gas Laws The Combined Gas Law 10.6 Ideal Gases and the Ideal Gas Law 10.7 Densities of Gases 10.8 Gases in Chemical Reactions 10.9 Mixtures of Gases Solubilities of Gases and Henry s Law Gas Diffusion: Molecules Moving Rapidly Real Gases Gas Diffusion: Molecules Moving Rapidly u rms = 3RT M R = J/mol K 32

33 Practice Exercise 10:14 Calculating Root-Mean-Square Speeds Calculate the root-mean-squared speed of nitrogen molecules at 25 o C. Graham s Law of Effusion: Same for Diffusion! U rms,a effusion rate A diffusion rate A = = U rms,b effusion rate B diffusion rate B = M B M A Problem A flask of ammonia is connected to a flask of an unknown acid HX by a 1.00 m glass tube. As the two gases diffuse down the tube, a white ring of NH 4 X forms 68.5 cm from the ammonia flask. Identify element X. 33