Three (Common) States (Phases) of Matter
Gas Properties
Volume
gas
no fixed volume (V) or shape
liquid fixed V, no fixed shape
solid
V space occupied; container V
L or mL
Temperature T molecule movement; average E K
m
quantity
n moles
kg x
collision force
kg
mass xsa2
Pressure
P =
=
=
area
m2
m s2
fluids (flow)
fixed V and shape
Blaise
●
French
1623 - 1662
vacuum
Lower Falls
Yellowstone NP
June 2011
Yellowstone NP
barometer
air
constant
air
h = 760 mm (average)
Hg
=
Old Faithful
Yellowstone NP
Evangelista Torricelli
Italian
1643
P 
study gases because
stoichiometry: cannot weigh gases  moles
massHg
densityHg x volume

area
area

height x area
area
760 mmHg = 760 torr = 1 atmosphere (atm)
all gases behave alike  physical properties:
systematic study illustrates scientific method
Boyle’s Law
50
Charles’s Law
Robert Boyle
English
1662
Boyle’s Original Data
45
V1
volume ( height)
air
bubble
h1  P1
40
35
V and P inversely related
20
50
70
90
V 
110
pressure ( height)
50
volume
h2  P2
40
P1V1 = P2V2 = P3V3 ...
20
15
V2 < V1
30
V
= constant
T
20
V2
T2 80
oC
V1
0.01
0.02
0.03
0
73
V2
...
T2
373
any gas law calculation; T must be Kelvin!
0.04
T (K) = T(°C) + 273.15
Avogadro’s Law
equal V gas, same P and T,
same moles
248
173
=
Temperature (K)
T2 > T1 V2 > V1
0
T1
1/pressure
3. V– n (constant P, T)
V  T
V = constant x T
PV = constant
30
25
P2 > P1
V and T directly related
40
10
35
10
T1 0 oC
1
P
constant
V =
P
45
V2
William Thomson
(Lord Kelvin)
Scottish
1848
50
25
10
30
Jacques Charles
French
1787
60
V1
30
15
Hg
2. V – T (constant P, n)
Volume (L)
1. V – P (constant T, n)
Combined Laws
Amedeo Avogadro
Italian
1811
V and n directly related
V  n
V1
n1
=
Boyle’s
1
V 
P
V2
Charles’
V  T
V 
n2
V  n
Tn
V1
P
n1
V = R
Benoît Clapeyron
French
1850
Avogadro’s
=
V2
n2
Tn
P
PV = nRT
Ideal-Gas Law
Henri Regnault
French
1842
1
Gas Constant: R
Mole Calculations
PV = nRT
R =
0.08206 L∙atm/mole∙K
g x
liquid, solid: mass, FW
mole
= mole
g
82.06 mL∙atm/mole∙K
62.36 L∙torr/mole∙K
mole
solution:
M, V
gas:
P, V, R, T
L
62,360 mL∙torr/mole∙K
8.314 m3∙Pa/mole∙K
SI unit
8.314 J/mole∙K
P x V is energy
n =
g
FW
PV =
FW =
gRT
FW
g
inverse T; direct FW
=
atm x L
= mole
●
Dalton’s Law of Partial Pressures
gRT
PV
(FW)P
determine FW
gas mixtures: each acts independently, but same V and T
Pgas = ngas
density
V
RT
barometer
thermometer
graduated cylinder
balance
gas out until Pinside = Poutside:
T of gas = water bath T:
V of gas = V of flask:
g of gas = g of condensed ℓ:
= mole
L atm/mole K x K
●
Formula Weight Determination
PV = nRT
x L
pin hole
foil
vaporized sample
V
 Pgas  ngas
sum of partial Pgas = Ptotal
Ptotal
10 molecules
6 red, 4 blue
hot water (> bp)
RT
=
Pred
+
+
=
1.0 atm
Pblue
0.6 atm
0.4 atm
Pgas = fractiongas x Ptotal
liquid sample
Application of Partial Pressures
Gases often collected by water displacement:
2 HgO(s)
HgO
2 Hg(ℓ) + O2(g)
O2(g), H2O(g)
adjust for vapor pressure of water (vpH2O)
Ptotal = Patmosphere = PO2 + vpH2O
352 mL of gas collected at atm P of 766.2 torr and 30.0 oC.
What mass of HgO was reacted?
Vapor Pressure of Water
T(oC)
16
17
18
19
20
21
22
23
24
25
26
27
28
29
P(torr)
13.63
14.53
15.48
16.48
17.54
18.65
19.83
21.07
22.38
23.76
25.21
26.74
28.35
30.04
T(oC)
30
35
40
45
50
55
60
65
70
80
90
92
94
96
P(torr)
31.8
42.2
55.3
71.9
92.5
118.0
149.4
187.5
233.7
355.1
525.8
567.0
610.9
657.6
2