1. Electrochemistry & Solutions 1. Solutions and Mixtures
Department of Chemistry
Electrochemistry & Solutions
1. Solutions and Mixtures
Year 1 – Module 3
8 Lectures
Dr Adam Lee

2. Aims
To:
Understand physical chemistry of solutions and their thermodynamic properties
 predict/control physical behaviour
 improve chemical reactions
Link electrochemical properties to chemical thermodynamics
 rationalise reactivity.

3. Synopsis Phase rule Clapeyron & Clausius-Clapeyron Equations
Chemical potential
Phase diagrams
Raoults law (Henry’s law)
Lever rule
Distillation and Azeotropes
Osmosis
Structure of liquids
Interactions in ionic solutions
Ion-ion interactions
Debye-Huckel theory
Electrodes
Electrochemical cells
Electrode potentials
Nernst Equation
Electrode types
Recommended Reading
R.G. Compton and G.H.W. Sanders, Electrode Potentials
Oxford Chemistry Primers No 41.
P. W. Atkins, The Elements of Physical Chemistry,
OUP, 3rd Edition, Chapters 5, 6 & 9.
P. W. Atkins, Physical Chemistry,
OUP, 7th Edition, Chapters 7, 8 & 10 OR 8th Edition, Chapters 4, 5, 6 & 7.

4. Phase Diagrams

6. Vacuum
Pump

9. No. of degrees
of freedom
No. of components
No. of phases

12. Gibbs Free Energy Josiah Willard Gibbs
Josiah Willard Gibbs
Gibbs Free Energy
American mathematical physicist developed theory of chemical thermodynamics. First US engineering PhD…later Professor at Yale.

13.
Benoit Paul Emile Clapeyron
Parisian engineer and mathematician. Derived differential equation for determining heat of melting of a solid

17. Modified eqn. for Liquid/Gas and Solid/Gas Lines: Clausius -
Clapeyron Eqn.
Maths
dx/x = dlnx dp/p = dlnp = ò dx x n 1 + 2 T dT dp V H D
Clapeyron
Equation
Rudolf Julius Emmanuel Clausius

19. Clausius-Clapeyron
Equation

20. 99

25. GA = GoA + nART ln pA, GB = GoB + nBRT ln pB
Consider ideal gas at constant temperature:
dG = Vdp – SdT = Vdp
Since pV = nRT,
If initial state 1 = STP (1 atm)
In general for a mixture AB:
GA = GoA + nART ln pA, GB = GoB + nBRT ln pB
since GA = nAA
A = Ao + RT ln pA

26. p = pA + pB

27. nA nB nA+ nB Ginitial = nAA + nBB = nA[ + RTlnp] + nB[B + RTlnp]yA yA yB yB
Ginitial = nAA + nBB
= nA[ + RTlnp] + nB[B + RTlnp]
Gfinal = nA[ + RTlnyAp] + nB[B + RTlnyBp]
G = Gfinal - Ginitial = RT[nAlnyAp – nAlnp
+ nBlnyBp - + nBlnp] nA nB
nA+ nB A B
Initial
Final ya yb
Gmixing ya yb

28. yA yA yB yB yA yA yB yB
Gmixing
Smixing ya ya 1 yb 1 yb

29.  Chemical Potential (in English!) G  ln(pressure)
Molecules acquire
more spare energy
Gibbs
Free
Energy
Greater “chemical potential” 
G  ln(pressure)
Pressure
Low Pressure
High Pressure
Constant Temperature
Effect of environment
on this free energy
Energy free for molecules
to “do stuff”at STP
Gmolar = G molar + RT lnp

30. Why do we use Chemical Potential?
Gibbs Free Energy (G) is total energy in entire system
available to “do stuff”
- includes all molecules, of all substances, in all phases
G = nAA + nBB
For single component
e.g. pure H2O
For mixtures
e.g. H2O/C2H5OH
No real need to use 
Free energy from 2 sources
G = nH2OH2O
Free energy only comes
from H2O
G = nH2OH2O+nEtOHEtOH
 tells us how much from
H2O versus C2H5OH

31. Why do we different molecules have different Chemical Potentials?
Involatile
Volatile
Ethanol can soak up much more energy in extra vibrational modes and chemical bonds
- will respond differently to pressure/temperature increases
Chemical Potential :
1. A measure of "escaping tendency" of components in a solution
2. A measure of the reactivity of a component in a solution
Free
Energy
(G)
& 
Gas-phase molecule
Liquid-phase
Solid-state
Pressure

32. Raoult's law Volatility eqns. of straight lines passing thru origin
Total pressure above boiling liquid

33. lnxA xA runs between 0 (none present) to 1 (pure solution)
Mixing (diluting a substance) always lowers xA
 this means mixing ALWAYS gives a negative lnxA
lnxA
Mixing always
lowers 
Pure B
Pure A
Dilution xA 1

35. Volatile
Involatile

36. Volatile
Involatile

39. Case 2: -ve deviation A more attracted by B (e.g. CHCl3 + acetone)
mixH = < 0
b.pt. > ideal A B
Case 3: +ve deviation
A less attracted by B
(e.g. EtOH + water)
mixH = > 0
b.pt. < ideal

40. Summary: Raoult’s Law for Solvents
Proportionality constant
pA = xA . pAΘ
Total pressure
Volatile
high vapour pressure
Liquid p o A 1 x
Partial pressure of A
Involatile
low vapour pressure p
pBΘ 1 x o B
Partial pressure of B
pB = xB . pBΘ A B

41. = tendancy of system to increase S
High p0ө(A)
Low p0ө(A)
High order: low S
Less order: higher S A A A A
Strong desire to  S
Less need to  S
Boiling of A
favoured
A happier in liquid
p0ө = vapour pressure
= tendancy of system to increase S

42. Proportionality constant
Amount in solution

43. Dissolution is EXOTHERMIC
For dissolution of oxygen in water, O2(g) O2(aq), enthalpy change under standard conditions is kJ/mole.

44. Consider O2 dissolution in water:
pH2O
pO2
Solvent: H2O
Solute: O2
H2O O2
Henry's law accurate for gases dissolving in liquids when concentrations and partial pressures are low.
As conc. and partial pressures increase, deviations from Henry's law become noticeable
Consider O2 dissolution in water:
Important in Green Chemistry for selective oxidation
Cinnamic Acid
Cinnamaldehyde
Cinnamyl Alcohol
Similar to behavior of gases
- deviate from the ideal gas law at high P and low T.
Solutions obeying Henry's law are therefore often called ideal dilute solutions.
Aspects of Allylic Alcohol Oxidation
Adam F. Lee et al, Green Chemistry 2000, 6, 279

46.  A yA xA

48. Liquid-Gas Distribution
Volatile
Involatile B A
LIQUID
GAS
Lever Rule
Tie-line
LIQUID
GAS A B
A-B Composition
Liquid-Gas Distribution

50. Example Problem
The following temperature/composition data were obtained for a mixture of octane (O) and toluene (T) at 760 Torr, where x is the mol fraction in the liquid and y the mol fraction in the vapour at equilibrium
The boiling points are C for toluene and C for octane. Plot the temperature/composition diagram of the mixture. What is the composition of vapour in equilibrium with the liquid of composition:
1. x(T) = 0.25
2. x(O) = 0.25
Boiling/
Condensation
Temperature
Liquid
Vapour
x(T) = 1, T = C
x(O) = 1, x(T) = 0, T = C
P.W. Atkins, Elements of Phys.Chem. page 141

51. y1
boiling  x1 x2
cool y2

53. Case 2: -ve deviation A more attracted by B (e.g. CHCl3 + acetone)
mixH = < 0
b.pt. > ideal A B
Case 3: +ve deviation
A less attracted by B
(e.g. EtOH + water)
mixH = > 0
b.pt. < ideal

54. azeotropic
composition

55. A B
Residue
Distlllate B A

56. Topics Covered (lectures 2-4)
 Chemical Potential
- A(l) = A(l) + RTlnxA
- A(g) = A(g) + RTlnpA
 Mol fractions
- A = nA / nA+nB
 Raoult’s Law
- pA = poA xA pB = poB xB
- ideal solutions
- +ve/-ve deviations
 Vapour-pressure diagrams
- Tie-lines
- Lever Rule

57. Solutions Equations Phase Rule F = c - p + 2 c = components
degrees of freedom p = no. of phases
Clapeyron Equation
H = enthalpy of phase change
V = volume change associated with phase change
Clausius-Clapeyron Equation or
Mol fractions
xA = nA / nA+nB ni = mols of i
yA = pA / pA + pB pi = partial pressure of i
Raoults Law
pA = poA xA and pB = poB xB
Lever Rule (for tie-line joining phases via point a)
nl =no. moles in liquid phase
nv =no. moles in liquid phase

58. A(solution) < A(solvent)
Contains solute (e.g. NaCl, glucose)
WHY?!!!
Solvent A
A(l) = A(l) + RTlnxA