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Chapter 10: Properties of Gases: The Air We Breathe

South Pole 15 February 2017 Sept 24, 2006

http://ozonewatch.gsfc.nasa.gov

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Chapter Outline

. 10.1 The Properties of Gases . 10.2 Effusion and the Kinetic Molecular Theory of Gases . 10.3 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 . 10.10 Solubilities of Gases and Henry’s Law . 10.11 Gas Diffusion: Molecules Moving Rapidly . 10.12 Real Gases

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The Properties of Gases

Neither definite shape nor definite volume

The Properties of Gases

Gases can be compressed.

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The Properties of Gases

All gases are miscible with all other gases.

http://catalog.flatworldknowledge.com/bookhub/4309?e=averill_1.0-ch13_s01

Chapter Outline

. 10.1 The Properties of Gases . 10.2 Effusion and the Kinetic Molecular Theory of Gases . 10.3 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 . 10.10 Solubilities of Gases and Henry’s Law . 10.11 Gas Diffusion: Molecules Moving Rapidly . 10.12 Real Gases

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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.

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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

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Kinetic Molecular Theory of Gases

5. Have average kinetic energy that is proportional to absolute Kelvin temperature:

2 KEavg = ½ mu rms

rms velocity  1/M

= 32 g/mol

= 28

= 18

= 4

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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 0.342 times the rate at which helium effuses. What is the molar mass of the emitted gas?

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Chapter Outline

. 10.1 The Properties of Gases . 10.2 Effusion and the Kinetic Molecular Theory of Gases . 10.3 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 . 10.10 Solubilities of Gases and Henry’s Law . 10.11 Gas Diffusion: Molecules Moving Rapidly . 10.12 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/in2 (psi) 14.7 psi

Atmospheres (atm) 1 atm

Pascals (N/m2) 101.325 X 103 Pa

Torr (mmHg) 760 mmHg

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Torricelli’s Barometer

vacuum The pressure of the Column of atmosphere on the surface mercury of the mercury in the dish is balanced by the 760 mm Hg downward pressure exerted by the mercury in Atmospheric the column. pressure

Elevation and Atmospheric Pressure

0.35 atm

0.62 atm

0.83 atm Sea level

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Chapter Outline

. 10.1 The Properties of Gases . 10.2 Effusion and the Kinetic Molecular Theory of Gases . 10.3 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 . 10.10 Solubilities of Gases and Henry’s Law . 10.11 Gas Diffusion: Molecules Moving Rapidly . 10.12 Real Gases

State Variables for a Gas P = pressure V = volume T = temperature n = number of moles

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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, P1V1 = P2V2 • Decreasing volume increases number of collisions/area; P↑ (KMT Postulates #3 & 4)

Boyle’s Law and Respiration

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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

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Charles’s Law: V and T (n and P held constant) . Charles’s Law: • V  T (P, n constant) V V or, 1 = 2 T T 1 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 (1796-1823) 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, 1783. 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.

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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 oF. After an hour outside, the temperature of the balloons is -12 oF. 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

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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  constant n V V or, 1  2 n1 n2 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

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Amonton’s Law: P and T (n and V held constant) . P  T (n, V constant) P = constant T P P or, 1 = 2 T1 T2 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 oC?

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Explaining Amonton’s Law Using Kinetic Molecular Theory

Chapter Outline

. 10.1 The Properties of Gases . 10.2 Effusion and the Kinetic Molecular Theory of Gases . 10.3 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 . 10.10 Solubilities of Gases and Henry’s Law . 10.11 Gas Diffusion: Molecules Moving Rapidly . 10.12 Real Gases

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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 oC, what is the volume of the balloon when it reaches an altitude where its internal pressure is 235 mmHg and T = -52 oC?

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Chapter Outline

. 10.1 The Properties of Gases . 10.2 Effusion and the Kinetic Molecular Theory of Gases . 10.3 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 . 10.10 Solubilities of Gases and Henry’s Law . 10.11 Gas Diffusion: Molecules Moving Rapidly . 10.12 Real Gases

Ideal Gas Equation

Boyle’s law: V  1 (at constant n and T) P Charles’ law: V  T (at constant n and P) Avogadro’s law: V  n (at constant P and T)

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Standard Temperature and Pressure (STP).

Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.

PV = nRT

Sample Exercise 10.7: Applying the Ideal Gas Law

Bottles of compressed O2 carried by climbers ascending Mt. Everest are designed to hold one kilogram of the gas. What volume of O2 can one bottle deliver to a climber at an altitude where the temperature is -38 oC and the atmospheric pressure is 0.35 atm? Assume that each bottle contains 1.00 kg of O2.

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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 10.10 Solubility of Gases and Henry’s Law 10.11 Gas Diffusion: Molecules Moving Rapidly 10.12 Real Gases

Densities and Molecular Weights of Gases Using PV = nRT

PV = nRT

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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 oF 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

1.018 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?

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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 10.10 Solubility of Gases and Henry’s Law 10.11 Gas Diffusion: Molecules Moving Rapidly 10.12 Real Gases

Gas Laws & Stoichiometry

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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:

MnO2(s) + 4 HCl(aq)  MnCl2(aq) + 2 H2O(l) + Cl2(g)

How many grams of MnO2 should be added to excess HCl to obtain 275 mL of chlorine gas at 5.0°C and 650 mmHg?

Chapter Outline

. 10.1 The Properties of Gases . 10.2 Effusion and the Kinetic Molecular Theory of Gases . 10.3 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 . 10.10 Solubilities of Gases and Henry’s Law . 10.11 Gas Diffusion: Molecules Moving Rapidly . 10.12 Real Gases

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Dalton’s Law of Partial Pressures

. For a mixture of gases in a container:

• Ptotal = P1 + P2 + P3 + . . .

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: nn 11 x1  ntotal n 1 n 2  n 3  ... . Mole Fraction in Terms of Pressure:

• When V and T are constant, P  n

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Mole Fraction & Partial Pressure

Since P  n nP11 x1  nPtotal total

P And: x  1 1 P total

Then… P1 x 1 P 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)?

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Collecting a Gas over Water

2 KClO3(s) → 2 KCl(s) + 3 O2(g)

Gases collected:

O2(g) and H2O(g)

PPP total O22 H O

Sample Exercise 10.12: Calculating the Quantity of a Gas Collected by Water Displacement

During the decomposition of KClO3, 92.0 mL of gas is collected by the displacement of water at 25.0 oC. If atmospheric pressure is 756 mmHg, what mass of O2 is collected?

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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 10.10 Solubility of Gases and Henry’s Law 10.11 Gas Diffusion: Molecules Moving Rapidly 10.12 Real Gases

Solubility of Gases

. Solubility of gases depends on T and P

Solubility ↑ as Pressure ↑

Solubility ↓ as Temperature ↑

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Henry’s Law

. Henry’s Law: • The higher the partial pressure of the gas above a liquid, the more soluble

• Cgas  Pgas

• Cgas  kH Pgas

Solubility of Oxygen in Water

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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 0.636 atm. During the summer, the average temperature of the water’s surface rarely exceeds 15 oC. What is the solubility of oxygen in Lake Titicaca at that temperature? Express your answer in molarity and in mg/L.

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Chapter Outline

. 10.1 The Properties of Gases . 10.2 Effusion and the Kinetic Molecular Theory of Gases . 10.3 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 . 10.10 Solubilities of Gases and Henry’s Law . 10.11 Gas Diffusion: Molecules Moving Rapidly . 10.12 Real Gases

Gas Diffusion: Molecules Moving Rapidly

3푅푇 푢 = 푟푚푠 푀

R = 8.314 J/mol K

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Practice Exercise 10:14 Calculating Root-Mean-Square Speeds

Calculate the root-mean-squared speed of nitrogen molecules at 25 oC.

Graham’s Law of Effusion: Same for Diffusion!

푈 푒푓푓푢푠푖표푛 푟푎푡푒 퐴 푑푖푓푓푢푠푖표푛 푟푎푡푒 퐴 푀 푟푚푠,퐴 = = = 퐵 푈푟푚푠,퐵 푒푓푓푢푠푖표푛 푟푎푡푒 퐵 푑푖푓푓푢푠푖표푛 푟푎푡푒 퐵 푀퐴

Problem 10.121 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 NH4X forms 68.5 cm from the ammonia flask. Identify element X.

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