Accuracy of the Debye-Hückel limiting law Example: The mean activity coefficient in a mol kg -1 MnCl 2 (aq) solution is 0.47 at 25 o C. 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 to calculate the mean activity coefficient. From eq. 10.4, I = ½(2 2 * *(2*0.1)) = 0.3 From eq. 10.3log(γ) = -|2*1|A*(0.3) 1/2 ; = - 2*0.509* = so γ = Error = ( )/0.47 * 100% = 41%

Extended Debye-Hückel law (10.5) B is an adjustable empirical parameter.

Calculating parameter B Example : The mean activity coefficient of NaCl in a diluted aqueous solution at 25 o C is (at 10.0mmol kg -1 ). Estimate the value of B in the extended Debye-Huckel law. Solution: First calculate the ionic strength I = ½(1 2 * *0.01) = 0.01 From equation 10.5 log(0.907) = - (0.509|1*1|*0.01 1/2 )/(1+ B*0.01 1/2 ) B =

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.

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

Typical Electrodes

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

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: Cu 2+ (aq) + 2e - → Cu(s) Left-hand electrode: Zn 2+ (aq) + 2e - → Zn(s) The overall cell reaction can be obtained by subtracting left-hand reaction from the right-hand reaction: Cu 2+ (aq) + Zn(s) → Cu(s) + Zn 2+ (aq)

Expressing a reaction in terms of half-reactions Example : Express the formation of H 2 O from H 2 and O 2 in acidic solution as the difference of two reduction half- reactions. Redox couple: the reduced and oxidized species in a half- reaction such as Cu 2+ /Cu, Zn 2+ /Zn…. Ox + v e - → Red The quotient is defined as: Q = a Red /a Ox Example: Write the half-reaction and the reaction quotient for a chlorine gas electrode.

Varieties of cells

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.

Cell Potential Cell potential: the potential difference between two electrodes of a galvanic cell (measured in volts V). Maximum electrical work : w e,max = ΔG Electromotive force, E, Relationship between E and Δ r G: Δ r G = -νFE where ν is the number of electrons that are exchanged during the balanced redox reaction and F is the Faraday constant, F = eN A. At standard concentrations at 25 o C, this equation can be written as Δ r G θ = -νFE θ