John C Kotz Paul M Treichel John Townsend

Important – Read Before Using Slides in Class Instructor: This Power. Point presentation contains

BEHAVIOR OF GASES Chapter 11 © 2009 Brooks/Cole - Cengage 3

Importance of Gases PLAY MOVIE • Airbags fill with N 2 gas in an

5 Hot Air Balloons — How Do They Work? PLAY MOVIE © 2009 Brooks/Cole

6 THREE STATES OF MATTER PLAY MOVIE © 2009 Brooks/Cole - Cengage

General Properties of Gases • There is a lot of “free” space in a

8 Properties of Gases Gas properties can be modeled using math. Model depends on—

Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643) ©

Pressure Hg rises in tube until force of Hg (down) balances the force of

Pressure Column height measures P of atmosphere • 1 standard atm = 760 mm

IDEAL GAS LAW P V = n R T Brings together gas properties. Can

13 Boyle’s Law If n and T are constant, then PV = (n. RT)

Boyle’s Law A bicycle pump is a good example of Boyle’s law. As the

15 Charles’s Law If n and P are constant, then V = (n. R/P)T

16 Charles’s original balloon Modern long-distance balloon © 2009 Brooks/Cole - Cengage

17 Charles’s Law Balloons immersed in liquid N 2 (at -196 ˚C) will shrink

Charles’s Law PLAY MOVIE © 2009 Brooks/Cole - Cengage 18

Avogadro’s Hypothesis Equal volumes of gases at the same T and P have the

20 Avogadro’s Hypothesis f PLAY MOVIE The gases in this experiment are all measured

21 Combining the Gas Laws • • • V proportional to 1/P V prop.

Using PV = n. RT How much N 2 is req’d to fill a

24 Gases and Stoichiometry 2 H 2 O 2(liq) f 2 H 2 O(g)

25 Gases and Stoichiometry 2 H 2 O 2(liq) f 2 H 2 O(g)

26 Gases and Stoichiometry 2 H 2 O 2(liq) f 2 H 2 O(g)

Gases and Stoichiometry 2 H 2 O 2(liq) f 2 H 2 O(g) +

29 Dalton’s Law of Partial Pressures 2 H 2 O 2(liq) f 2 H

Dalton’s Law John Dalton 1766 -1844 © 2009 Brooks/Cole - Cengage 30

GAS DENSITY PLAY MOVIE Higher Density air © 2009 Brooks/Cole - Cengage 31 Low

GAS DENSITY PV = n. RT and density (d) = m/V d and M

The Disaster of Lake Nyos • Lake Nyos in Cameroon was a volcanic lake.

34 USING GAS DENSITY The density of air at 15 o. C and 1.

KINETIC MOLECULAR THEORY (KMT) Theory used to explain gas laws. KMT assumptions are •

Kinetic Molecular Theory Because we assume molecules are in motion, they have a kinetic

Kinetic Molecular Theory At the same T, all gases have the same average KE.

Kinetic Molecular Theory Maxwell’s equation Root mean square speed where u is the speed

Distribution of Gas Molecule Speeds PLAY MOVIE © 2009 Brooks/Cole - Cengage • Boltzmann

Velocity of Gas Molecules of a given gas have a range of speeds. ©

Velocity of Gas Molecules Average velocity decreases with increasing mass. © 2009 Brooks/Cole -

42 GAS DIFFUSION AND EFFUSION DIFFUSION is the gradual mixing of molecules of different

GAS EFFUSION is the movement of molecules through a small hole into an empty

44 GAS DIFFUSION AND EFFUSION Molecules effuse thru holes in a rubber balloon, for

GAS DIFFUSION AND EFFUSION Graham’s law governs effusion and diffusion of gas molecules. Rate

Gas Diffusion relation of mass to rate of diffusion PLAY MOVIE See Active Figure

47 Using KMT to Understand Gas Laws Recall that KMT assumptions are • Gases

Avogadro’s Hypothesis and Kinetic Molecular Theory PLAY MOVIE P proportional to n — when

49 Gas Pressure, Temperature, and Kinetic Molecular Theory PLAY MOVIE P proportional to T

Boyle’s Law and Kinetic Molecular Theory PLAY MOVIE P proportional to 1/V — when

Deviations from Ideal Gas Law • Real molecules have volume. • There are intermolecular

Deviations from Ideal Gas Law Account for volume of molecules and intermolecular forces with

Deviations from Ideal Gas Law Cl 2 gas has a = 6. 49, b

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John C. Kotz Paul M. Treichel John Townsend http: //academic. cengage. com/kotz Chapter 11 Gases and Their Properties John C. Kotz • State University of New York, College at Oneonta

Important – Read Before Using Slides in Class Instructor: This Power. Point presentation contains photos and figures from the text, as well as selected animations and videos. For animations and videos to run properly, we recommend that you run this Power. Point presentation from the Power. Lecture disc inserted in your computer. Also, for the mathematical symbols to display properly, you must install the supplied font called “Symb_chm, ” supplied as a cross-platform True. Type font in the “Font_for_Lectures” folder in the "Media" folder on this disc. If you prefer to customize the presentation or run it without the Power. Lecture disc inserted, the animations and videos will only run properly if you also copy the associated animation and video files for each chapter onto your computer. Follow these steps: 1. Go to the disc drive directory containing the Power. Lecture disc, and then to the “Media” folder, and then to the “Power. Point_Lectures” folder. 2. In the “Power. Point_Lectures” folder, copy the entire chapter folder to your computer. Chapter folders are named “chapter 1”, “chapter 2”, etc. Each chapter folder contains the Power. Point Lecture file as well as the animation and video files. For assistance with installing the fonts or copying the animations and video files, please visit our Technical Support at http: //academic. cengage. com/support or call (800) 423 -0563. Thank you.

General Properties of Gases • There is a lot of “free” space in a gas. • Gases can be expanded infinitely. • Gases occupy containers uniformly and completely. • Gases diffuse and mix rapidly. © 2009 Brooks/Cole - Cengage 7

8 Properties of Gases Gas properties can be modeled using math. Model depends on— • • © 2009 Brooks/Cole - Cengage V = volume of the gas (L) T = temperature (K) n = amount (moles) P = pressure (atmospheres)

Pressure Column height measures P of atmosphere • 1 standard atm = 760 mm Hg = 29. 9 inches Hg = about 34 feet of water SI unit is PASCAL, Pa, where 1 atm = 101. 325 k. Pa © 2009 Brooks/Cole - Cengage 11

13 Boyle’s Law If n and T are constant, then PV = (n. RT) = k This means, for example, that P goes up as V goes down. © 2009 Brooks/Cole - Cengage Robert Boyle (1627 -1691). Son of Earl of Cork, Ireland.

Boyle’s Law A bicycle pump is a good example of Boyle’s law. As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire. PLAY MOVIE © 2009 Brooks/Cole - Cengage 14

Avogadro’s Hypothesis Equal volumes of gases at the same T and P have the same number of molecules. V = n (RT/P) = kn V and n are directly related. twice as many molecules © 2009 Brooks/Cole - Cengage 19

21 Combining the Gas Laws • • • V proportional to 1/P V prop. to T V prop. to n Therefore, V prop. to n. T/P V = 22. 4 L for 1. 00 mol when – Standard pressure and temperature (STP) – T = 273 K – P = 1. 00 atm © 2009 Brooks/Cole - Cengage

Using PV = n. RT How much N 2 is req’d to fill a small room with a volume of 960 cubic feet (27, 000 L) to P = 745 mm Hg at 25 o. C? R = 0. 082057 L • atm/K • mol Solution 1. Get all data into proper units V = 27, 000 L T = 25 o. C + 273 = 298 K P = 745 mm Hg (1 atm/760 mm Hg) = 0. 98 atm © 2009 Brooks/Cole - Cengage 22

Using PV = n. RT How much N 2 is req’d to fill a small room with a volume of 960 cubic feet (27, 000 L) to P = 745 mm Hg at 25 o. C? R = 0. 082057 L • atm/K • mol Solution 2. Now calc. n = PV / RT n = 1. 1 x 103 mol (or about 30 kg of gas) © 2009 Brooks/Cole - Cengage 23

24 Gases and Stoichiometry 2 H 2 O 2(liq) f 2 H 2 O(g) + O 2(g) Decompose 0. 11 g of H 2 O 2 in a flask with a volume of 2. 50 L. What is the pressure of O 2 at 25 o. C? Of H 2 O? Bombardier beetle uses decomposition of hydrogen peroxide to defend itself. © 2009 Brooks/Cole - Cengage

25 Gases and Stoichiometry 2 H 2 O 2(liq) f 2 H 2 O(g) + O 2(g) Decompose 0. 11 g of H 2 O 2 in a flask with a volume of 2. 50 L. What is the pressure of O 2 at 25 o. C? Of H 2 O? Solution Strategy: Calculate moles of H 2 O 2 and then moles of O 2 and H 2 O. Finally, calc. P from n, R, T, and V. © 2009 Brooks/Cole - Cengage

26 Gases and Stoichiometry 2 H 2 O 2(liq) f 2 H 2 O(g) + O 2(g) Decompose 0. 11 g of H 2 O 2 in a flask with a volume of 2. 50 L. What is the pressure of O 2 at 25 o. C? Of H 2 O? Solution © 2009 Brooks/Cole - Cengage

Gases and Stoichiometry 2 H 2 O 2(liq) f 2 H 2 O(g) + O 2(g) Decompose 0. 11 g of H 2 O 2 in a flask with a volume of 2. 50 L. What is the pressure of O 2 at 25 o. C? Of H 2 O? Solution P of O 2 = 0. 016 atm © 2009 Brooks/Cole - Cengage 27

Gases and Stoichiometry 2 H 2 O 2(liq) f 2 H 2 O(g) + O 2(g) What is P of H 2 O? Could calculate as above. But recall Avogadro’s hypothesis. V n at same T and P P n at same T and V There are 2 times as many moles of H 2 O as moles of O 2. P is proportional to n. Therefore, P of H 2 O is twice that of O 2. P of H 2 O = 0. 032 atm © 2009 Brooks/Cole - Cengage 28

29 Dalton’s Law of Partial Pressures 2 H 2 O 2(liq) f 2 H 2 O(g) + O 2(g) 0. 032 atm 0. 016 atm What is the total pressure in the flask? Ptotal in gas mixture = PA + PB +. . . Therefore, Ptotal = P(H 2 O) + P(O 2) = 0. 048 atm Dalton’s Law: total P is sum of PARTIAL pressures. © 2009 Brooks/Cole - Cengage

The Disaster of Lake Nyos • Lake Nyos in Cameroon was a volcanic lake. • CO 2 built up in the lake and was released explosively on August 21, 1986. • 1700 people and hundreds of animals died. • See Chapter 14 for more information © 2009 Brooks/Cole - Cengage 33

34 USING GAS DENSITY The density of air at 15 o. C and 1. 00 atm is 1. 23 g/L. What is the molar mass of air? 1. Calc. moles of air. V = 1. 00 L P = 1. 00 atm T = 288 K n = PV/RT = 0. 0423 mol 2. Calc. molar mass/mol = 1. 23 g/0. 0423 mol = 29. 1 g/mol © 2009 Brooks/Cole - Cengage

KINETIC MOLECULAR THEORY (KMT) Theory used to explain gas laws. KMT assumptions are • Gases consist of molecules in constant, random motion. • P arises from collisions with container walls. • No attractive or repulsive forces between molecules. Collisions elastic. • Volume of molecules is negligible. © 2009 Brooks/Cole - Cengage 35

Kinetic Molecular Theory Because we assume molecules are in motion, they have a kinetic energy. KE = (1/2)(mass)(speed)2 At the same T, all gases have the same average KE. As T goes up for a gas, KE also increases — and so does speed. © 2009 Brooks/Cole - Cengage 36

Distribution of Gas Molecule Speeds PLAY MOVIE © 2009 Brooks/Cole - Cengage • Boltzmann plots • Named for Ludwig Boltzmann doubted the existence of atoms. • This played a role in his suicide in 1906. 39

44 GAS DIFFUSION AND EFFUSION Molecules effuse thru holes in a rubber balloon, for example, at a rate (= moles/time) that is • proportional to T • inversely proportional to M. Therefore, He effuses more rapidly than O 2 at same T. © 2009 Brooks/Cole - Cengage He

GAS DIFFUSION AND EFFUSION Graham’s law governs effusion and diffusion of gas molecules. Rate of effusion is inversely proportional to its molar mass. © 2009 Brooks/Cole - Cengage Thomas Graham, 1805 -1869. Professor in Glasgow and London. 45

Gas Diffusion relation of mass to rate of diffusion PLAY MOVIE See Active Figure 11. 18 © 2009 Brooks/Cole - Cengage • HCl and NH 3 diffuse from opposite ends of tube. • Gases meet to form NH 4 Cl • HCl heavier than NH 3 • Therefore, NH 4 Cl forms closer to HCl end of tube. 46

47 Using KMT to Understand Gas Laws Recall that KMT assumptions are • Gases consist of molecules in constant, random motion. • P arises from collisions with container walls. • No attractive or repulsive forces between molecules. Collisions elastic. • Volume of molecules is negligible. © 2009 Brooks/Cole - Cengage

Deviations from Ideal Gas Law Account for volume of molecules and intermolecular forces with VAN DER WAALS’s EQUATION. Measured V = V(ideal) Measured P ( P 2 + n a ----2 V ) V - nb n. RT vol. correction intermol. forces © 2009 Brooks/Cole - Cengage J. van der Waals, 1837 -1923, Professor of Physics, Amsterdam. Nobel Prize 1910. 52

Deviations from Ideal Gas Law Cl 2 gas has a = 6. 49, b = 0. 0562 For 4. 00 mol Cl 2 in a 4. 00 L tank at 100. 0 o. C. P (ideal) = n. RT/V = 30. 6 atm P (van der Waals) = 26. 0 atm © 2009 Brooks/Cole - Cengage 53