Peter Atkins • Julio de Paula
Atkins’ Physical Chemistry
Eighth Edition
Chapter 1
The Properties of Gases
Copyright © 2006 by Peter Atkins and 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
Physical Characteristics of Gases
•
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)
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
Energy Changes in Chemical Reactions
Heat - the transfer of thermal energy between two bodies that
are at different temperatures
Temperature - a measure of the thermal energy
Temperature = Thermal Energy
(intensive)
90 °C
greater temperature
(extensive)
40 °C
greater thermal energy
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
Temperature Scales
Perfect gas temperature scale
K = °C + 273.15
The Gas Laws
 Pressure - Volume Relationship: Boyle’s Law
 Temperature - Volume Relationship: Charles’s
and Gay-Lussac’s Law
 Volume - Amount Relationship: Avogadro’s 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
Fig 1.7 Charles’s Law
• Variation of pressure with
temperature at constant V
Perfect Gas Equation
1
Boyle’s law:
V∝
Charles’ law:
V∝T
(at constant n and P)
Avogadro’s law:
V∝n
(at constant P and T)
(at constant n and T)
P
V ∝ nT
P
V = constant ·
nT
P
nT
=R
P
R is the gas constant
PV = nRT
What is the value of R?
PV = nRT
PV (1.000 atm)(22.41 4 L)
R

nT (1.000 mol)(273.1 5 K)
L  atm
R  0.08206
mol  K
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 22.414 L:
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 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:
P1V1
R
n1T1
Combined Gas Law
• Final state (2) of gas:
P1V1 P2 V2

n1T1 n2 T2
P2 V2
R
n2 T2
Eqn [1.12]
Gas Mixtures and Partial Pressures
V and T
are
constant
P1
P2
Dalton’s Law of Partial Pressures
Ptotal = P1 + P2
Consider a case in which two gases, A and B, are in a
container of volume V at a total pressure PT
nART
PA =
V
nA is the number of moles of A
nBRT
PB =
V
nB is the number of moles of B
PT = PA + PB
PA = XA PT
nA
XA =
nA + nB
nB
XB =
nA + nB
PB = XB PT
Pi = Xi PT
mole fraction (Xi) =
Dalton’s Law of Partial Pressures
ni
nT