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Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254 No. 2 (Chapter 22: The rates of chemical reactions) March 6 at Biology building, room 113 March 7 at Dillion Hall, room 254 No. 3 (Chapter 24: Molecular Reaction Dynamics) March 27 at Biology building, room 113 March 28 at Dillion Hall, room 361

Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

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Page 1: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

Tutorial schedule(3:30 – 4:50 PM)

• No. 1 (Chapter 7: Chemical Equilibrium)

January 31 at Biology building, room 113

February 1 at Dillion Hall, room 254

• No. 2 (Chapter 22: The rates of chemical reactions) March 6 at Biology building, room 113

March 7  at Dillion Hall, room 254  • No. 3 (Chapter 24: Molecular Reaction Dynamics)

March 27 at Biology building, room 113

March 28 at Dillion Hall, room 361

Page 2: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

Extended Debye-Hückel law

B is an adjustable empirical parameter. It is different for each electrolyte.

21

21

1 /

/||)log(

BI

IzzA

Page 3: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

Calculating parameter B

Example : The mean activity coefficient of NaCl in a diluted aqueous solution at 25oC is 0.907 (at 10.0 mmol kg-1). Estimate the value of B in the extended Debye-Huckel law.

Solution: First calculate the ionic strength

I = ½[12*0.01 + (-1)2*0.01] = 0.01

From equation

log(0.907) = - (0.509|1*(-1)|*0.011/2)/(1+ B*0.011/2)

B = - 1.67

21

21

1 /

/||)log(

BI

IzzA

Page 4: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

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.

Page 5: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

• 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

Page 6: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

Typical Electrodes

Page 7: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

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

Page 8: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

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)

Page 9: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

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.

(in class discussion)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.

(in class discussion)

Page 10: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

Varieties of cells

Page 11: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

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.

A general format: Solid | gas phase | aqueous phase || aqueous phase | gas phase | solid

Page 12: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

Concentration Cells

• M | M+(aq, L) || M+(aq, R) | M

• Cell reaction: M+(aq, R) → M+(aq, L)

since ΔrGθ = 0 (why?)

QvF

RTEQ

vF

RT

vF

GE r lnln

R

L

b

b

vF

RTE ln

Page 13: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

Cell Potential• Cell potential: the potential difference between two electrodes of a

galvanic cell (measured in volts V).

• Maximum electrical work : we,max = ΔG

• Electromotive force, E,

• Relationship between E and ΔrG:

ΔrG = -νFE

where ν is the number of electrons that are exchanged during the balanced redox reaction and F is the Faraday constant, F = eNA.

• At standard conditions, this equation can be written as

ΔrGθ = -νFEθ

Page 14: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

The cell emf • The emf of a cell can be calculated by the difference of the potentials of

the two electrodes, Ecell = Eright - Eleft

• The potential of an electrode can be calculated from its standard potential. For example

Fe+3(aq) + e- → Fe+2(aq)

Cu+2(aq) + 2e- → Cu(s)

• Consider: Ag(s)|Ag+(aq) || Cl-(aq) |AgCl(s)| Ag(s) Ecell = E(AgCl/Ag, Cl-) – E(Ag+/Ag) = Eθ - ??

3

2

lnFe

Fe

b

b

vF

RTEE

2

lnCu

Cu

b

a

vF

RTEE

Page 15: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

• In the lead storage battery (used in automobiles), Pb | PbSO4 | H2SO4 | PbSO4|PbO2 | Pb

would the voltage change if you changed the concentration of H2SO4? (yes/no)

• Answer ... • Yes, because• The net cell reaction is Pb + PbO2 + 2HSO4

- + 2H+ → 2 PbSO4 + 2 H2O • The Nernst equation E = E° - (0.0594/2)log{1/{[HSO4

-]2[H+]2}}.

Page 16: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

Previous two examples involve the same number of electron transfer at the cathode and anode, how to calculate emf if the number of electrons transferred at the two electrodes are different?

Example: What is the emf for the cell : Mn(s)|Mn+2||Fe+3|Fe+2|Pt(s)

Solution: The two reduction half reactions Right: Fe+3(aq) + e- → Fe+2(aq)

Left: Mn+2(aq) + 2e- → Mn(s)

It shows that the above two half reactions have different number of electrons being transferred!

The cell reaction is obtained via 2*R – L, 2Fe+3(aq) + Mn(s) → 2Fe+2(aq) + Mn+2(aq)

should the standard cell potential be calculated as 2*Eө(R) - Eө(L) ?

Answer: NO! it is still calculated with Ecell = Eright - Eleft

Consider: ΔrGθ = 2ΔrGθ (R) - ΔrGθ(L) 2FE θ = 2(1*F* E θ (R) – 2*F* E θ (L)

it leads to Eөcell = Eө(R) - Eө(L)

= 0.769 - (- 1.182) = 1.951 V

Page 17: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

Standard Cell emf• Eθcell = Eθ (right) – Eθ(Left)

• Calculating equilibrium constant from the standard emf : Evaluate the solubility constant of silver chloride, AgCl, from cell potential

data at 298.15K. Solution: AgCl(s) → Ag+(aq) + Cl-(aq) Establish the electrode combination: Right: AgCl + e- → Ag(s) + Cl-(aq) Eθ = 0.22V Left: Ag+(aq) + e- → Ag(s) Eθ = 0.80V The standard cell emf is : Eθ (right) – Eθ(Left) = - 0.58V

K = 1.6x10-10

• The above example demonstrates the usefulness of using two half reactions to represent a non redox process. What would be the two half reactions for the autoprotolysis of H2O?

0257.0

58.0ln

RT

vFEK

Page 18: Tutorial schedule (3:30 – 4:50 PM) No. 1 (Chapter 7: Chemical Equilibrium) January 31 at Biology building, room 113 February 1 at Dillion Hall, room 254

The measurement of standard potentials

• The potential of standard hydrogen electrode: Pt(s)|H2(g)|H+(aq)

is defined as 0 at all temperatures.• The standard potential of other electrodes can be obtained by

constructing an electrochemical cell, in which hydrogen electrode is employed as the left-hand electrode (i.e. anode)

• Example: the standard potential of the AgCl/Ag couple is the standard emf of the following cell:

Pt(s)|H2(g)|H+(aq), Cl-(aq)|AgCl(s)|Ag(s)or

Pt(s)|H2(g)|H+(aq) || Cl-(aq)|AgCl(s)|Ag(s)

with the cell reaction is: ½ H2(g) + AgCl(s) → H+(aq) + Cl-(aq) + Ag(s)