Accuracy of the Debye-H

1
Accuracy of the Debye-Hückel limiting law

• Example The mean activity coefficient in a
  0.100 mol kg-1 MnCl2(aq) solution is 0.47 at
  25oC. What is the percentage error in the value
  predicted by the Debye-Huckel limiting law?
• Solution First use equation 10.4 to calculate
  the ionic strength and then use eq. 10.3 to
  calculate the mean activity coefficient.
• From eq. 10.4, I ½(220.1 12(20.1)) 0.3
• From eq. 10.3 log(?) -21A(0.3)1/2
• - 20.5090.5477
• - 0.5576
• so ? 0.277
• Error (0.47-0.277)/0.47 100
• 41

2
Extended Debye-Hückel law

• (10.5)
• B is an adjustable empirical parameter.

3
Calculating parameter B

• Example The mean activity coefficient of NaCl
  in a diluted aqueous solution at 25oC is 0.907
  (at 10.0mmol kg-1). Estimate the value of B in
  the extended Debye-Huckel law.
• Solution First calculate the ionic strength
• I ½(120.01 120.01) 0.01
• From equation 10.5
• log(0.907) - (0.509110.011/2)/(1
  B0.011/2)
• B - 1.67

4
Half-reactions and electrodes

• Two types of electrochemical cells
• 1. Galvanic cell is an electrochemical cell
  which produces electricity as a result of the
  spontaneous reactions occurring inside it.
• 2. Electrolytic cell is an electrochemical
  cell in which a non spontaneous reaction is
  driven by an external source of current.

5

• Other important concepts include
• Oxidation the removal of electrons from a
  species.
• Reduction the addition of electrons to a
  species.
• Redox reaction a reaction in which there is a
  transfer of electrons from one species to
  another.
• Reducing agent an electron donor in a redox
  reaction.
• Oxidizing agent an electron acceptor in a redox
  reaction.
• Two type of electrodes
• Anode the electrode at which oxidation occurs.
• Cathode the electrode at which reduction
  occurs

6
Typical Electrodes
7
Electrochemical cells

• Liquid junction potential due to the difference
  in the concentrations of electrolytes.
• The right-hand side electrochemical cell is often
  expressed as follows
• Zn(s)ZnSO4(aq)CuSO4(aq)Cu(s)
• The cathode reaction (copper ions being reduced
  to copper metal) is shown on the right. The
  double bar () represents the salt bridge that
  separates the two beakers, and the anode reaction
  is shown on the left zinc metal is oxidized into
  zinc ions

8

• In the above cell, we can trace the movement of
  charge.
• Electrons are produced at the anode as the zinc
  is oxidized
• The electrons flow though a wire, which we can
  use for electrical energy
• The electrons move to the cathode, where copper
  ions are reduced.
• The right side beaker builds up negative charge.
  Cl- ions flow from the salt bridge into the zinc
  solution and K ions flow into the copper
  solution to keep charge balanced.
• To write the half reaction for the above cell,
• Right-hand electrode Cu2(aq) 2e- ?
  Cu(s)
• Left-hand electrode Zn2(aq)
  2e- ? Zn(s)
• The overall cell reaction can be obtained by
  subtracting left-hand reaction from the
  right-hand reaction
• Cu2(aq) Zn(s) ? Cu(s)
  Zn2(aq)

9
Expressing a reaction in terms of half-reactions

• Example Express the formation of H2O from H2
  and O2 in acidic solution as the difference of
  two reduction half-reactions.
• Redox couple the reduced and oxidized species
  in a half-reaction such as Cu2/Cu, Zn2/Zn.
• Ox v e- ? Red
• The quotient is defined as Q aRed/aOx
• Example Write the half-reaction and the reaction
  quotient for a chlorine gas electrode.

10
Varieties of cells
11
Notation of an electrochemical cell

• Phase boundaries are denoted by a vertical bar.
• A double vertical line, , denotes the interface
  that the junction potential has been eliminated.
• Start from the anode.

12
Cell Potential

• Cell potential the potential difference
  between two electrodes of a galvanic cell
  (measured in volts V).
• Maximum electrical work we,max ?G
• Electromotive force, E,
• Relationship between E and ?rG
• ?rG
  -?FE
• where ? is the number of electrons that are
  exchanged during the balanced redox reaction and
  F is the Faraday constant, F eNA.
• At standard concentrations at 25oC, this equation
  can be written as
• ?rG? -?FE?