The Gaseous State
Gases consist of widely separated molecules in rapid
motion.
All gases near room temperatures and normal pressures
show the same quantitative relationships among their
physical properties of pressure, temperature, volume and
molar amount.
force
Pressure =
area
SI unit of pressure: pascal (Pa)
1Pa =
1N
1m2
=
1kg . m/s2
1kg/m. s2
=
1m2
Standard atmosphere:
1 atm = 101325 Pa = 101.325 kPa
Temperature: absolute temperature
scale, Kelvin scale
K = °C + 273.15
T = t + 273
Boyle’s law:
The volume of a sample of gas at a given temperature
is found to vary inversely with the applied pressure
1
V
P
(at fixed temperature for a
given amount of gas)
PV = constant
Pressure – Volume Data for 1.00g O2 at 0°C
P (atm)
V (L)
PV
0.250
0.500
0.750
1.000
2.000
3.000
4.000
5.000
2.801
1.400
0.933
0.699
0.349
0.233
0.174
0.139
0.7003
0.7001
0.6999
0.6998
0.6991
0.6984
0.6977
0.6969
A plot of the volume of 1.000g O2 at 0°C for various
pressures.
3
Volume L
2
1.40 L
1
0.70 L
0
0.25
0.50
Pressure (atm)
0.75
1.00
Charles’ Law
Relationship between the volume and the temperature of a
gas (Jacques Charles, Joseph Gay-Lussac)
Variation of the volume of a sample of gas with
temperature (p=const.)
Temperature
°C
K
0
273
Volume
ml
273
1
274
274
10
273
283
546
283
546
The volume of any sample of a gas varies directly with
absolute temperature if the pressure is held constant.
V
VTor V = kT or
=k
T
The V is not directly proportional to the °C.
Vf Vi
Tf
or Vf = Vi x
=
Tf Ti
Ti
Vi = initial volume
Vf = final volume
Ti = initial temperature
Tf = final temperature
Volume L
Temperature-volume curve for an ideal gas (Charles’ law)
-200
-273.15
-100
0
100
Temperature °C
200
Gay-Lussac’s Law
At constant volume, the pressure of a given mass of gas
varies directly with the absolute temperature.
P
PTor P = kT or T = k
Pf Pi
Tf = Ti
Combined Gas Law
PfVf
Pi Vi
=
Ti
Tf
Avogadro’s Law (see stoichiometry)
V = nVm
n = number of moles
Vm = molar gas volume
(volume of 6.022 x 1023 gas molecules
at a given temperature and pressure)
Standard temperature and pressure (STP)
Temperature : 0°C = 273 K
Pressure: 1 atm = 101.325 kPa
Molar gas volume at STP:
22.41 L/mol
The Ideal Gas Law:
1
V
P
at fixed T, n
Boyle’s Law
VT at fixed P, n Charles’ Law
Vn a fixed T, P Avogadro’s Law
Therefore,
1
V T n
P
PV = nRT
molar gas constant
The Ideal Gas Law:
3
PV
101.325
kPa
x
22.41
dm
=
R=
=
1 mol x 273.15 K
nT
8.314 kPa x dm3 x mol-1x K-1
J
Ideal gas: A hypothetical gas that follows the
behavior described by the equation of
state for an ideal gas.
Gas Mixtures:
Dalton’s law of partial pressures: the total
pressure of a mixture of gases that do not react is
equal to the sum of the partial pressures of all the
gases present.
Ptotal = pA + pB + pC + …
Kinetic Theory of an Ideal Gas
Postulates:
1. Gases are composed of molecules whose size is
negligible compared to the distance between them.
2. Molecules move randomly in linear motion.
3. The collosions are elastic.
4. The average kinetic energy of a molecule is
proportional to the K.
0°C
Relative number
of mulecules
Maxwell's distributions
of molecular speeds (H2)
500°C
1000
2000
3000
4000
5000
(m/s)
Graham’s law of effusion:
The rate of effusion of gas molecules from a particular hole
is inversely proportional to the
square root of the molecular weight of the gas
at constant temperature and pressure.
Rate of effusion 
1
V Mm
Real gases
Van der Waals equation:
n2a
P+
V2
V - nb = nRT
„a” and „b” are
constants