Atkins’ Physical Chemistry Eighth Edition Chapter 1 The Properties of Gases Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio de Paula

Homework Set #1 Atkins & de Paula, 8e Chap 1 Exercises: all part (b) unless noted 1, 2, 4, 9, 10, 11, 13, 15, 17, 19, 21

Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. (No solubility rules!) Gases have much lower densities than liquids and solids. Density of a gas given in g/L (vice g/mL for liquids) Physical Characteristics of Gases NO 2

The Perfect Gas Each gas can be described by an equation of state: P = f(T, V, n) Pressure ≡ force / unit area

Fig 1.1

Heat - the transfer of thermal energy between two bodies that are at different temperatures Energy Changes in Chemical Reactions Temperature - a measure of the thermal energy 90 °C 40 °C greater thermal energy Temperature = Thermal Energy greater temperature (intensive) (extensive)

Fig 1.2 Temperature ≡ the direction of thermal energy flow through a thermally conducting rigid wall

Thermal equilibrium ≡ no net heat flow between two objects in contact through a diathermic boundary Fig 1.3 Zeroth Law of thermodynamics

K = ° C Temperature Scales Perfect gas temperature scale

The Gas Laws Pressure - Volume Relationship: Boyle’s Law Pressure - Volume Relationship: Boyle’s Law Temperature - Volume Relationship: Charles’s and Gay-Lussac’s Law Temperature - Volume Relationship: Charles’s and Gay-Lussac’s Law Volume - Amount Relationship: Avogadro’s Law Volume - Amount Relationship: Avogadro’s Law The Perfect (Ideal) Gas Law The Perfect (Ideal) Gas Law

Fig 1.4 Boyle’s Law PV = constant A limiting law

Fig 1.5 Charles’s Law V = constant ∙ T Another limiting law

Fig 1.6 Charles’s Law Variation of volume with temperature at constant P

Variation of pressure with temperature at constant V Fig 1.7 Charles’s Law

Perfect Gas Equation Charles’ law: V ∝ T (at constant n and P) Avogadro’s law: V ∝ n (at constant P and T) V ∝V ∝ nT P V = constant · = R nT P P R is the gas constant PV = nRT What is the value of R? Boyle’s law: V ∝ (at constant n and T) P 1

PV = nRT The conditions 0 ° C and 1 atm are called standard temperature and pressure (STP). Experiments show that at STP, 1 mole of an ideal gas occupies L:

Comparison of Molar Volumes at STP One mole of an ideal gas occupies STP One mole of various real gases at STP occupy:

Fig 1.8 A region of a P-V-T surface of a perfect gas

Fig 1.8 Sections through P-V-T surface of a perfect gas

PV = nRT useful when P, V, n, and T do not change Modify equation when P, V, and/or T change: Initial state (1) of gas: Final state (2) of gas: Eqn [1.12] Combined Gas Law

Gas Mixtures and Partial Pressures V and T are constant P1P1 P2P2 P total = P 1 + P 2 Dalton’s Law of Partial Pressures

Consider a case in which two gases, A and B, are in a container of volume V at a total pressure P T P A = n A RT V P B = n B RT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B X A = nAnA n A + n B X B = nBnB n A + n B P A = X A P T P B = X B P T P i = X i P T mole fraction (X i ) = nini nTnT Dalton’s Law of Partial Pressures