Atkins Chapter01.Lect01

Atkins’ Physical ChemistryEighth Edition

Chapter 1The Properties of Gases

Copyright © 2006 by Peter Atkins and Julio de Paula

Peter Atkins • Julio de Paula

Homework Set #1Homework Set #1

Atkins & de Paula, 8eAtkins & de Paula, 8e

Chap 1 Exercises: all part (b) unless Chap 1 Exercises: all part (b) unless notednoted

1, 2, 4, 9, 1, 2, 4, 9,

10, 11, 13, 10, 11, 13,

15, 17, 19, 2115, 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

NO2

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 °C40 °C

greater thermal energy

Temperature = Thermal Energy

greater temperature

(intensive) (extensive)

Fig 1.2 Temperature ≡ thedirection of thermal energy flowthrough a thermally conductingrigid wall

Thermal equilibrium ≡ no net heat flow between two objectsin contact through a diathermic boundary

Fig 1.3 Zeroth Law ofthermodynamics

K = °C + 273.15

Temperature Scales

Perfect gas temperature scale

The Gas LawsThe Gas Laws

Pressure - Volume RelationshipPressure - Volume Relationship: Boyle’s Law: Boyle’s Law

Temperature - Volume RelationshipTemperature - Volume Relationship: Charles’s : Charles’s and Gay-Lussac’s Lawand Gay-Lussac’s Law

Volume - Amount RelationshipVolume - Amount Relationship: Avogadro’s Law: Avogadro’s Law

The Perfect (Ideal) Gas LawThe Perfect (Ideal) Gas Law

Fig 1.4 Boyle’s LawFig 1.4 Boyle’s Law

• PV = constant

• A limiting law

Fig 1.5 Charles’s LawFig 1.5 Charles’s Law

• V = constant ∙ T

• Another limiting law

Fig 1.6 Charles’s LawFig 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 LawFig 1.7 Charles’s Law

Perfect Gas EquationPerfect Gas Equation

Charles’ law: V ∝ T (at constant n and P)

Avogadro’s law: V ∝ n (at constant P and T)

V ∝ nT

P

V = constant · = RnT

P

nT

PR 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).

K) 5mol)(273.1 (1.000L) 4atm)(22.41 (1.000

nTPV

R

Experiments show that at STP,1 mole of an ideal gasoccupies 22.414 L:

KmolatmL

08206.0R

Comparison of Molar Volumes at STP

• One mole of an ideal gas occupies 22.414 L @ STP

• One mole of various real gases at STP occupy:

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

RTn

VP

11

11

• Initial state (1) of gas:

• Final state (2) of gas:

RTn

VP

22

22

22

22

11

11

Tn

VP

Tn

VP

Eqn [1.12]

Combined Gas Law

Gas Mixtures and Partial Pressures

V and T are

constant

P1 P2 Ptotal = P1 + P2

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 PT

PA = nART

V

PB = nBRT

V

nA is the number of moles of A

nB is the number of moles of B

PT = PA + PB XA = nA

nA + nB

XB = nB

nA + nB

PA = XA PT PB = XB PT

Pi = Xi PT mole fraction (Xi) = ni

nT

Dalton’s Law of Partial Pressures