Chapter 5 Gases

2 Early Experiments Torricelli performed experiments that showed that air in the atmosphere exert pressure. Torricelli designed the first barometer.

3 A torricellian barometer

4 Simple manometer

5 Unit of Pressure 1 standard atmosphere =1 atm =760 mm Hg =760 torr = Pa

6 Boyle’s Experiment

7 Boyle’s Law : PV= k A gas that obeys Boyle’s law is called an ideal gas

8 Charles’s Law: V=bT The volume of a gas at constant pressure increases linearly with the temperature of the gas.

9 Plot V vs. T using kelvin scale

10 Avogadro’s Law : V=an A gas at constant temperature and pressure the volume is directly proportional to the number of moles of gas.

11 Ideal Gas Law Equation of state for a gas PV=nRT P: atm V: Liter n: moles R: L atm K -1 T: K

12 Laws for Gas experiments Boyle’s Law : PV=k Charles’s Law : V=bT Avogadro’s Law : V=an The ideal Gas Law : PV=nRT (so called equation of state for idea gas)

13 Ideal Gas The volume of the individual particles can be assumed to be negligible. The particles are assumed to exert no force on each other. It expresses behavior that real gases approach at low pressure and high temperature.

14 Gas Stoichiometry Standard Temperature and Pressure (STP) T=0 o C P=1 atm V=22.4 L Natural Temperature and Pressure (NTP) T=25 o C P=1 atm V=24.5L

15 Plot of PV versus P for 1 mol of ammonia.

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17 2NaN 3 (s)→2Na(s)+3N 2 (g)

18 Dalton’s Law of Partial Pressures

19 Mole Fraction and Partial Pressure

20 The Model of Ideal Gas in Kinetic- Molecular Theory The volume of the individual particles can be assumed to be negligible. The particles are assumed to exert no force on each other. The particles are in constant motion. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

21 An ideal gas particle in a cube wholse sides are of length L (in meters).

22 The velocity u can be broken down into three perpendicular components, u x, u y, and u 2.

23 Pressure of an Ideal Gas Let the container be a rectangular box with sides of length L x, L y and L z. Let v be the velocity of a given molecule.

24 In the xy plane, v x 2 + v y 2 = v yx 2 by the Pythagorean theorem.

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26 A molecule collide with wall W where W is parallel to the xz plane. Let i have the velocity components v x, v y, v z

27 The integration can be extended over the whole time interval t 1 to t 2. 速度平方之平均值

28 The translational energy E tr = 1/2mv 2 single particle

29 Temperature dependence with translation kinetic energy single particle one mole of particles

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31 Distribution of Molecular Speeds in an Ideal Gas Root mean square speed is assumed that all molecules move at the same speed. The motions of gas molecules should have distribution of molecular speeds in equilibrium.

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33 指數函數 → 機率

34 Plot of O 2 molecules

35 Plot of N 2 molecules

36 Application of The Maxwell Distribution

37 Application of The Maxwell Distribution

38 Velocity distribution for nitrogen

39 Collisions with a Wall v y dt lyly dN w : 粒子撞擊牆壁的數目

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41 H 2 at 25 o C and 1atm 分子量單位 :Kg

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43 Definition of Pressure The pressure of a gas results from collisions between the gas particles and the walls of the container. Each time a gas particle hits the wall, it exerts a force on the wall. An increase in the number of gas particles in the container increases the frequency of collisions with the walls and therefore the pressure of the gas.

44 The effusion of a gas into an evacuated chamber.

45 Suppose there is a tiny hole of area A in the wall and that outside the container is a vacuum. Escape of a gas through a tiny hole is called effusion. collisions × area

46 Diffusion Relative diffusion rates of NH 3 and HCl molecules

47 Molecules Collisions and Mean Free Path Intermolecular collisions are important in reaction kinetics. Assume a molecule as a hard sphere. No intermolecular forces exist except at the moment of collision. z AA : the number of collisions per unit time that one particular A molecule makes with other A molecule [collisions s -1 ]

48 Cylinder swept by gas particles

49 Calculate z AA and z AB (r A +r B =d)

50 AB

51 Since the stationary B molecules are uniformly distributed throughout the container volume V, the number of B molecules with centers in the cylinder equals (V cyl /V)N B.

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53 Mean Free Path  The average distance of a molecule travels between collisions. In a mixture of gases A and B, A differs from B.

54 average distance traveled by an A molecule between collisions In pure gas A, there are no A-B collisions, z AB =0

55 Diameter d of H 2 in the hard-sphere is 1.48 Å

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57 Real Gas No gas exactly follows the ideal gas law. Compression factor ( 壓縮因子 ) Z(P,T)=PV/nRT Z<1, P<P id, V<V id strong intermolecular attraction Z=1, P→0 and T→∞ Z>1, P>P id, V>V id strong intermolecular repulsion

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60 Van der Waals equation

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64 Calculate pressure for 1 mole of CO 2 at 0 o C in containers with 22.4 L P = atm Use idea gas equation Use van der Waals equation

65 Calculate pressure for 1 mole of CO 2 at 0 o C in containers with 0.2 L Use idea gas equation Use van der Waals equation P = 52.6 atm

66 Calculate pressure for 1 mole of CO 2 at 0 o C in containers with 0.05 L Use idea gas equation Use van der Waals equation P = 1620 atm

67 Analysis of the van der Waals Constants~a constant The a constant corrects for the force of attraction between gas particles. attraction between particles↑ a ↑ As the force of attraction between gas particles becomes stronger, we have to go to higher temperatures for the molecules in the liquid to form a gas. Gases with very small values of a, such as H 2 and He, must be cooled to almost absolute zero before they condense to form a liquid.

68 Analysis of the van der Waals Constants~b constant a rough measure of the size of a gas particle the volume of a mole of Ar atoms is L r = 2.3 x cm

69 Chemistry in the Atmosphere

70 The variation of temperature and pressure with altitude.

71 Concentration (in molecules per million molecules of “air”) of some smog components versus time of day.

72 Diagram of the process for scrubbing sulfur dioxide from stack gases in power plants.