Oxidation and Reduction Lecture 9

Law of Mass Action Important to remember our equation describes the equilibrium condition. At non-equilibrium conditions it is called the reaction quotient, Q. Written for the reaction H 2 CO 3 = HCO H + We can see that if the equilibrium constant is to remain constant, addition of H + must drive the reaction to the left (i.e, activity of bicarbonate must decrease and that of carbonic acid must increase). “Changing the concentration of one species in a reaction in a system at equilibrium will cause a reaction in a direction that minimizes that change”.

Le Chatelier’s Principle We can generalize this to pressure and temperature: dG = VdP - SdT An increase in pressure will drive a reaction in a direction such as to decrease volume An increase in temperature will drive a reaction in a direction such as to increase entropy. “When perturbed, a system reacts to minimize the effects of perturbation.”

Temperature and Pressure Dependence Since ∆G r ˚ = ∆H r ˚ - T∆S r ˚ and ∆G r ˚ = -RT ln K then Temperature dependency can be found by taking derivatives of this equation with respect to T and P: o (this is known as the van Hoff equation). For pressure, since

Oxidation and Reduction Oxidation refers to processes in which atoms gain or loss electrons, e.g., Fe 2+  Fe 3+

Valence and Redox We define valence as the charge an atom acquires when it is dissolved in solution. Conventions o Valence of all elements in pure form is 0. o Sum of valences much equal actual charge of species o Valence of hydrogen is +1 except in metal hydrides when it is -1 o Valence of O is -2 except in peroxides when it is -1. Elements generally function as either electron donors or acceptors. o Metals in 0 valence state are electron donors (become positively charged) o Oxygen is the most common electron acceptor (hence the term oxidation) Redox o A reduced state can be thought of as one is which the availability of electrons is high o An oxidized state is one in which the availability of electrons is low. Really idiotic pneumonic: Leo the Lion Says GRR: Loss Equals Oxidation Gain Refers to Reduction Really idiotic pneumonic: Leo the Lion Says GRR: Loss Equals Oxidation Gain Refers to Reduction

Redox in Aqueous Solutions Redox reactions occur over a wide range of conditions: from groundwaters to magma. They are approached differently. We begin with aqueous solutions.

Electrochemical Cells A simple redox reaction would be: o We want to know ∆G of the reaction. Measuring energy of it in electrochemical cell might be good approach. o However, such a cell can only measure exchange of electrons (e.g., between Zn and Cu) o We really want to know are energies for individual redox reactions such as:

Hydrogen Scale Potential We assign a potential of 0 for the reaction: ½H 2(g) = H aq + + e - o in practice one side has Pt electrode in H 2 gas, the other acid with a H+ = 1. Then for the reaction The potential is assigned to Potentials measured in this way are called hydrogen scale potentials, written E H and have units of volts.

Table 3.3 E H ˚ and pe˚ for half-cell reactions The sign convention for E H is that the sign of the potential is positive when the reaction proceeds from left to right. o Thus if a reaction has posi­tive E H, the metal ion will be reduced by hy­drogen gas to the metal. If a reaction has negative E H, the metal will be oxidized to the ion and H + reduced. The reactions are listed so that a species will be oxidized by (and therefore will reduce) all species listed below it. o Thus Li will be oxidized in preference to Ca.

E H and ∆G Electrochemical energy is a form of free energy. E H is related to ∆G r by: ∆G r = -z F E H where F is the Faraday constant (96,485 coulombs) and converts volts to joules. and ∆G r ˚ = -z F E˚ o Values of E˚ available in compilations (e.g., Table 3.3) Since then This is known as the Nernst Equation.

pe Consider again the reaction: The equilibrium constant expression for this reaction is ? In log form: We define pe as: So

Standard State pe and Relation to E H Continuing with the reaction In an aqueous solution, the standard state activities are? Thereforepe˚ = log K More generally, o So for this reaction: pe is related to E H as:

What pe is really telling us We have defined pe as the negative log of the activity of the electron. So a high pe means a low activity and concentration of electrons in our system. A low concentration of electrons implies an oxidized system; a high concentration (and low pe) implies a reduced system. Same is true of E H. So these are parameters that tell us about the redox state of our system (just as pH tells us about acidity).

Speaking of pe and pH… A commonly used diagram to illustrate chemical variation in aqueous solutions is the pe- pH diagram (or E H -pH) Water only stable over limited range, so we start by setting boundaries. ½O 2(g) + 2e - + 2H + = H 2 O o In the standard state: pe = pH o The is a line with intercept of and slope of -1. Similarly: H + + e - = ½H 2(g) and pe = -pH

pe-pH Diagrams To construct the diagrams 1.Write a reaction relating species of interest. 2.Redox reactions should contain e - 3.pH dependent reactions should contain H + 4.Write the equilibrium constant expression. 5.Get in log form, solve for pe with equation of the form pe = a + bpH 5.Find or calculate value of log K.

Drawing stability boundaries Now consider: For equal activities of the two species, pe = log K o (horizontal line with intercept = K) Next Fe(OH) 2+ ⇋ Fe(OH) 2 + : Fe(OH) 2+ + OH – ⇋ Fe(OH) 2 + Fe(OH) 2+ + H 2 O ⇋ Fe(OH) H + Use H + rather than OH - !

Drawing stability boundaries Now consider Fe 3+ ⇋ Fe(OH) 2+ Fe 3+ + H 2 O = Fe(OH) 2+ + H + Next: Fe(OH) 2+ ⇋ Fe 2+ Fe(OH) 2+ +e - + H 2 O ⇋ Fe 2+ + H +

Fe(OH) 2+ –Fe 2+ Our reaction is: Equilibrium constant expression is: In the form we want: We can write it as as the sum of two reactions, o we sum o to yield The log equilibrium constant of the net reaction is the sum of the log equilibrium constants of the two.

Line 5 has a slope of -1 and an intercept of log K. We can also use pe-pH diagrams to illustrate stability of solid phases in presence of solution. In this case, we must choose concentration.

More about pe-pH diagrams pe-pH diagrams are a kind of stability or predominance diagram. They differ from phase diagrams because lines indicate not phase boundaries, but equal concentrations. o There is only 1 phase in this this diagram – an aqueous solution. Regions are regions of predominance. o The aqueous species continue to exist beyond their fields, but their concentrations drop off exponentially.

Environmental Interpretation of pe-pH