Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-1
• Molecular motion in gases
4. Transport properties of a perfect gas
b) Transport parameters
• Molecular motion in liquids
5. Some experimental results
6. Conductivities of electrolyte solutions
• Ch. 21 Molecules in motion
Molecular motion in gases
Molecular motion in liquids
Diffusion: migration of matter down a concentration gradient
Lecture 3
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-2
• According to the kinetic model, the diffusion coefficient is:
dz
dDJN
(matter)
cD 3
1
1. The decreases as the p increases. So D decreases with p.
2. The increases with T. So D also increases with T.
3. Because the increases when the of the molecules
decreases, the D is greater for small molecules than for large
molecules.
p
kT
M
RTc
8
c
* See Further Information 21.1.
*
Higher D at lower p and higher T for smaller molecules!
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-3
dz
dTJ (energy)
• According to the kinetic model, the thermal conductivity of a
perfect gas A having molar concentration [A] (= n/V) is:
A3
1,mVCc
where CV,m is the molar heat capacity at constant volume.
p
kT
M
RTc
8
1. Because the is inversely proportional to p and the [A]
proportional to p, the is independent of p.
2. The is greater for gases with a high CV,m because a given
temperature gradient then corresponds to a greater energy
gradient.
* See Further Information 21.1.
*
• At very low p, why ?? p759. p
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-4
dz
dvJ xmomentum) ofcomponent -(x
• According to the kinetic model, the viscosity of a perfect gas A
having molar concentration [A] (= n/V) is:
A3
1Mc
p
kT
M
RTc
8
*
1. Because the is inversely proportional to p and the [A]
proportional to p, the is independent of p.
2. Because , .
where M is the molar mass of the gas molecules.
Tc T
* See Further Information 21.1.
• For a perfect gas, the viscosity increases with T, but for liquids,
decreases with T. intermolecular interaction (Sec. 21.6)
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-5
• For a molecule to move in a liquid, it must acquire at least a
minimum energy (Ea) to escape from its neighbor.
• The probability that a molecule has at least an energy Ea is
proportional to .
• So the mobility of the molecules in the liquid increases with T.
RTEae/
RTEae/
1
• Because the coefficient of viscosity is
inversely proportional to the mobility of the
particles,
• In liquids, the viscosity decreases sharply
with increasing T.
H2O
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-6
• Consider the motion of ions in solution.
• Because the ions have electric charges, the conductance (G)
of a solution is the inverse of its resistance (R).
RG
1
Vs
CSG
1:
siemens
• The conductance of a sample decreases with its length (l) and
increases with its cross-sectional area (A).
l
AG
where is the conductivity.
m
S:
A
lR
yresistivit :
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-7
• The conductivity of a solution depends on the number of ions
in the solution.
• The molar conductivity (m) is defined as
cm
where c is the molar concentration of the electrolyte.
mol
Sm:
2
m
• The molar conductivity (m) is found to vary with the
concentration of the electrolyte. Why?
1. The number of ions might not be proportional to the
concentration of the electrolyte.
2. The conductivity of a solution is not exactly proportional to the
number of ions, due to the strong interaction between ions.
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-8
• According to experimental observations,
there are two classes of electrolyte.
• Strong electrolyte: its molar conductivity
slightly decreases with increasing the molar
concentration.
• Weak electrolyte: its molar conductivity falls
sharply with increasing the concentration.
strong
weak
• The classification depends on the solvent as well as the solute.
ex) LiCl (aq): strong electrolyte
LiCl in propanone: weak electrolyte
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-9
• Strong electrolytes are fully ionized in solution.
Ex) Ionic solids (e.g. LiCl), strong acids (e.g. HCl)
• Owing to the complete ionization, the number of ions in
solution is proportional to the concentration of electrolyte.
• Friedrich Kohlrausch experimentally found
that the molar conductivities of strong
electrolytes vary linearly with .
co
mm K
c
Kohlrausch’s Law
•The dependence of the molar
conductivity arises from interactions
between ions.
c
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-10
• The constant mo is the limiting molar conductivity at infinite
dilution (then the ions do not interact each other).
• The limiting molar conductivity (mo) can be decomposed into
contributions from the cations (+) and the anions (−) as
where v+ and v− are the numbers of cations and anions in the
formula unit of electrolyte. (e.g. for MgCl2, v+ = 1 and v− = 2)
• The constant K is found to depend more on the stoichiometry
(MX, M2X, MX2, etc) of the electrolyte than on its specific
identity.
vvo
m
co
mm K
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-11
• The limiting molar conductivities (mo) of each ion are
tabulated as below.
Ex) For BaCl2 in water at 298 K,
/molm mS 98.2763.7272.121 2om
vvo
m
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-12
• Weak electrolytes are not fully ionized in solution.
• Ex) Brnsted acids (e.g. CH3COOH) and bases (e.g. NH3)
• Kohlrausch also showed that the molar conductivity is strongly
dependent of the concentration of the weak electrolytes.
(aq) A (aq) OH (l) OH (aq)HA -32
• The strong concentration dependence of their
molar conductivities arises from the
displacement of the equilibrium.
HA
AOH
aa
aaK
3
• For weak acids, Ka < 1. Only a small extent
of deprotonation in water.
Ka = 1.410-5
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-13
• The conductivity depends on the number of ions in solution,
and therefore on degree of ionization () of the electrolyte.
(aq) A (aq) OH (l) OH (aq)HA -32
Initial:
c)1( HA
c HA o
Equilibrium
0 OHo3 0 A o
c OH3 c A
If we ignore activity coefficients, Ka is approximately
11HA
A OH 22233
c
c
c
a
aaK
HA
AOH
a
10
• For the weak acids (HA), the degree of deprotonation ( )
is considered.
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-14
• By rearranging,
1
2cKa
14
12 a
a
K
c
c
K
(aq) A (ag) OH (l) OH (ag)HA -32
• However, the weak acid is also fully deprotonated at infinite
dilution, and its molar conductivity is then mo.
• In real solution of weak acids, only a fraction () is actually
present as ions. So the measured molar conductivity (m) is
given by: omm
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-15
• For 0.01 M CH3COOH (aq) at 298 K, if m = 1.65 mS m2/mol,
52
109.11
cKa
(aq) CH3COO (aq) OH (l) OH (aq) COOHCH 323 Ex)
0423.009.496.34
65.1
om
momm
• To express the acidity of weak acids, the pKa is often used.
aa KpK log
For the acetic acid, 72.4109.1loglog 5 aa KpK
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-16
• Once we know Ka, we can use the following equations to
predict the concentration dependence of the m.
14
12 a
a
K
c
c
Ko
mm
om
a
am
K
c
c
K
14
12
5109.1 aK
/molcm mS 05.39 2om
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-17
• The concentration dependence of m can be used to
determine the mo.
• Rearranging into and into ,
1
2cKa
aK
c
1
1
we obtain the Ostwald’s dilution law:
omm o
mm
11
oma
om
m
om
oma
omm K
c
K
c
111
211
oma
m
omm K
c
• If 1/m is plotted against cm, then the
y-intercept will be 1/mo.
Prof. Yo-Sep Min Physical Chemistry II, Fall 2013 Lecture 3-18
• Next Reading:
8th : p.764 ~ 772
9th : p.760 ~ 766
