GENERAL CHEMISTRY PRINCIPLES AND MODERN APPLICATIONS ELEVENTH EDITION

Gases CONTENTS Slide 6 - 2 6 -1 Properties of Gases: Gas Pressure 6

FIGURE 6 -1 The gaseous state of three halogens (group 17) Slide 6 -

6 -1 Properties of Gases: Gas Pressure The Concept of Pressure Force (N) =

FIGURE 6 -3 The concept of liquid pressure Slide 6 - 5 General Chemistry:

Liquid Pressure P (Pa) = F = W = A A gxm = gx.

Barometric Pressure FIGURE 6 -4 Measurement of atmospheric pressure with a mercury barometer Slide

Manometers FIGURE 6 -5 Measurement of gas pressure with an open-end manometer Slide 6

Units of Pressure: A Summary Slide 6 - 9 General Chemistry: Chapter 6 Copyright

6 -2 Simple Gas Laws FIGURE 6 -6 Relationship between gas volume and pressure

Boyles Law 1 Pa V PV = a (constant) For a fixed amount of

FIGURE 6 -7 Gas volume as a function of temperature Slide 6 - 12

Charles’s Law Va. T V=b. T The volume of a fixed amount of gas

Standard Conditions of Temperature and Pressure Gas properties depend on conditions. We use the

Avogadro’s Law Gay-Lussac 1808 gases react by volumes in the ratio of small whole

Slide 6 - 16 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

FIGURE 6 -8 Formation of Water – actual observation and Avogadro’s hypothesis Slide 6

1 mol gas = 22. 414 L gas (at 0ºC, 1 atm) 1 mol

6 -3 Combining the Gas Laws: The Ideal Gas Equation and the General Gas

The Ideal Gas Equation PV = n. RT PV R= n. T Slide 6

Applying the ideal gas equation Slide 6 - 21 General Chemistry: Chapter 6 Copyright

The General Gas Equation P i. V i P f. V f = ni.

6 -4 Applications of the Ideal Gas Equation Molar Mass Determination PV = n.

Gas Density m d= V KEEP IN MIND m RT PV = M m

6 -5 Gases in Chemical Reactions Stoichiometric factors relate gas quantities to quantities of

6 -6 Mixtures of Gases Dalton’s law of partial pressures Each component of a

The volume that each gase would individually occupy at a pressure equal to Ptot

Pa Ptot = na. RT/Vtot ntot. RT/Vtot = na ntot na = ntot =

FIGURE 6 -12 Dalton’s law of partial pressures illustrated Slide 6 - 29 General

FIGURE 6 -13 Collecting a gas over water Slide 6 - 30 General Chemistry:

Ptot = Pbar = Pgas + PH 2 O Pgas = Pbar − PH

6 -7 Kinetic Molecular Theory of Gases • Particles are point masses in constant,

Distribution of Molecular Speeds FIGURE 6 -15 Pressure and Molecular Speed Slide 6 -

Maxwell-Boltzmann distribution of speeds Slide 6 - 34 General Chemistry: Chapter 6 Copyright ©

FIGURE 6 -17 Distribution of molecular speeds – an experimental determination Slide 6 -

FIGURE 6 -16 Distribution of molecular speeds – the effect of mass and temperature

Meaning of Temperature The Kelvin temperature (T) of a gas is directly proportional to

Derivation of Boyles Law FIGURE 6 -18 A model for calculating the pressure exerted

Derivation of Boyle’s Law stated mathematically PV = a Pressure of a single molecule

Derivation of Molecular Speeds Basic equation of KMT Boyle’s Law from KMT Since PV=n.

6 -8 Gas Properties Relating to the Kinetic-Molecular Theory FIGURE 6 -20 Diffusion and

Graham’s Law The rate of effusion of a gas is inversely proportional to the

Ratio of Slide 6 - 43 Rate of effusion Molecular speeds Effusion times =

Derivation of Graham’s Law Slide 6 - 44 General Chemistry: Chapter 6 Copyright ©

6. 9 Nonideal (Real) Gases FIGURE 6 -21 The behavior of real gases –

The van der Waals Equation n 2 a P+ V 2 V – nb

Slide 6 - 47 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

FIGURE 6 -23 Intermolecular forces of attraction Slide 6 - 48 General Chemistry: Chapter

FIGURE 6 -22 The effect of finite molecular size Slide 6 - 49 General

End of Chapter Slide 6 - 50 General Chemistry: Chapter 6 Copyright © 2017

Slides: 50

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GENERAL CHEMISTRY PRINCIPLES AND MODERN APPLICATIONS ELEVENTH EDITION PETRUCCI HERRING MADURA BISSONNETTE 6 Gases PHILIP DUTTON UNIVERSITY OF WINDSOR DEPARTMENT OF CHEMISTRY AND BIOCHEMISTRY Slide 6 - 1 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Gases CONTENTS Slide 6 - 2 6 -1 Properties of Gases: Gas Pressure 6 -2 The Simple Gas Laws 6 -3 Combining the Gas Laws: The Ideal Gas Equation and The General Gas Equation 6 -4 Applications of the Ideal Gas Equation 6 -5 Gases in Chemical Reactions 6 -6 Mixtures of Gases 6 -7 Kinetic—Molecular Theory of Gases 6 -8 Gas Properties Relating to the Kinetic —Molecular Theory 6 -9 Nonideal (Real) Gases General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

6 -1 Properties of Gases: Gas Pressure The Concept of Pressure Force (N) = g (m/s 2) x m (kg) Pressure P (Pa) = Force (N) Area (m 2) FIGURE 6 -2 Illustrating the pressure exerted by a solid Slide 6 - 4 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Liquid Pressure P (Pa) = F = W = A A gxm = gx. Vxd = gxhx. Axd A A A = gxhxd liquid pressure is directly proportional to the liquid density and the height of the liquid column Slide 6 - 6 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Boyles Law 1 Pa V PV = a (constant) For a fixed amount of gas at a constant temperature, the gas volume is inversely proportional to the gas pressure. Slide 6 - 11 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Charles’s Law Va. T V=b. T The volume of a fixed amount of gas at constant pressure is directly proportional to the Kelvin (absolute) temperature. Slide 6 - 13 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Standard Conditions of Temperature and Pressure Gas properties depend on conditions. We use the definition of STP recommended by the International Union of Pure and Applied Chemistry (IUPAC). Standard Temperature and Pressure (STP) Slide 6 - 14 0ºC and 1 Bar = 105 Pa General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Avogadro’s Law Gay-Lussac 1808 gases react by volumes in the ratio of small whole numbers. Avogadro 1811 At fixed T and P V∝n or V=cn At a fixed temperature and pressure, the volume of a gas is directly proportional to the amount of gas. Slide 6 - 15 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

6 -3 Combining the Gas Laws: The Ideal Gas Equation and the General Gas Equation Boyle’s law Charles’s law Avogadro’s law Slide 6 - 19 V ∝ 1/P V∝T V∝n General Chemistry: Chapter 6 n. T V∝ P Copyright © 2017 Pearson Canada Inc.

The General Gas Equation P i. V i P f. V f = ni. Ti nf. Tf If we hold the amount constant (n = constant): P i. V i P f. V f = Ti Tf Slide 6 - 22 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Gas Density m d= V KEEP IN MIND m RT PV = M m MP =d= V RT Slide 6 - 24 that gas densities are typically much smaller than those of liquids and solids. Gas densities are usually expressed in grams per liter rather than grams per milliliter. General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

6 -5 Gases in Chemical Reactions Stoichiometric factors relate gas quantities to quantities of other reactants or products. Ideal gas equation relates the amount of a gas to volume, temperature and pressure. Law of Combining Volumes can be developed using the gas law. Slide 6 - 25 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

6 -6 Mixtures of Gases Dalton’s law of partial pressures Each component of a gas mixture exerts a pressure that it would exert if it were in the container alone. The total pressure of a mixture of gases is the sum of the partial pressures of the components of the mixture. Ptot = Pa + Pb +… Slide 6 - 26 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

The volume that each gase would individually occupy at a pressure equal to Ptot is Va = and na. RT Ptot , Vb = nb. RT Ptot , …. . Vtot = Va + Vb +… Percent by volume can be expressed as: volume % A = Slide 6 - 27 Va Vtot ✕ 100% volume % B = General Chemistry: Chapter 6 Vb Vtot ✕ 100% Copyright © 2017 Pearson Canada Inc.

Pa Ptot = na. RT/Vtot ntot. RT/Vtot = na ntot na = ntot = χa Pa = Ptot Va Vtot = ntot. RT/Ptot = na ntot = χa Va = χa Vtot Va = χa. Vtot Pa = χa. Ptot Slide 6 - 28 na. RT/Ptot General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

6 -7 Kinetic Molecular Theory of Gases • Particles are point masses in constant, random, straight line motion. • Molecules are separated by great distances. • Molecules collide only fleetingly, and most of the time are not colliding. • Assumed to be no forces between molecules. • Individual molecules may gain or lose energy but total energy remains constant. FIGURE 6 -14 Visualizing Molecular Motion Slide 6 - 32 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Meaning of Temperature The Kelvin temperature (T) of a gas is directly proportional to the average translational kinetic energy (Ek) of its molecules: T ∝ Ek. Slide 6 - 37 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Derivation of Boyle’s Law stated mathematically PV = a Pressure of a single molecule Pressure of N molecules Average speed in each direction and overall average speed Slide 6 - 39 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Graham’s Law The rate of effusion of a gas is inversely proportional to the square root of its molar mass. Rateeffusion 1 MW Only for gases at low pressure (natural escape, not a jet). Tiny orifice (no collisions) Does not apply to diffusion. Slide 6 - 42 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

Ratio of Slide 6 - 43 Rate of effusion Molecular speeds Effusion times = Distances traveled by molecules Amounts of gas effused. General Chemistry: Chapter 6 ratio of two molar masses (6. 25) Copyright © 2017 Pearson Canada Inc.

6. 9 Nonideal (Real) Gases FIGURE 6 -21 The behavior of real gases – compressibility factor as a function of pressure at 0ºC Slide 6 - 45 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.

The van der Waals Equation n 2 a P+ V 2 V – nb = n. RT The van der Waals equation reproduces the observed behavior of gases with moderate accuracy. It is most accurate for gases comprising approximately spherical molecules that have small dipole moments. Slide 6 - 46 General Chemistry: Chapter 6 Copyright © 2017 Pearson Canada Inc.