Nernst Equation Consider the half reaction NO3 10H 8e NH4 3H2O l We can calculate the Eh if the activities of H NO3 and NH4 are known The general Nernst equation 2 303RT is 0 Eh E n log Q The Nernst equation for this reaction at 25 C is a NH 0 0592 4 Eh E 0 log 10 8 a NO a H 3 Let s assume that the concentrations of NO 3 and NH4 have been measured to be 10 5 M and 3 10 7 M respectively and pH 5 What are the Eh and pe of this water First we must make use of the relationship o G 0 r E n For the reaction of interest rG 3 237 1 79 4 110 8 679 9 kJ mol 1 679 9 E 0 88 volts 8 96 42 0 The Nernst equation now becomes 0 0592 a NH 4 Eh 0 88 log a NO a10 8 H 3 substituting the known concentrations neglecting activity coefficients 0 0592 3 10 7 Eh 0 88 log 0 521 volts 10 10 5 10 5 8 and pe 16 9 Eh 16 9 0 521 8 81 Biology s view upside down Reaction directions for 2 different redox couples brought together More negative potential reductant More positive potential oxidant Example O2 H2O vs Fe3 Fe2 O2 oxidizes Fe2 is spontaneous Stability Limits of Water H2O 2 H O2 g 2eUsing the Nernst Equation 0 0592 1 Eh E log 12 2 n pO2 aH 0 Must assign 1 value to plot in x y space P O2 Then define a line in pH Eh space UPPER STABILITY LIMIT OF WATER Eh pH To determine the upper limit on an Eh pH diagram we start with the same reaction 1 2O2 g 2e 2H H2O but now we employ the Nernst eq 0 0592 1 Eh E log 12 2 n pO2 aH 0 0 0592 1 Eh E log 12 2 2 pO2 aH 0 0 r G 237 1 E 1 23 volts n 2 96 42 0 1 Eh 1 23 0 0296 log pO2 a 2 2 H Eh 1 23 0 0148 log pO2 0 0592 pH As for the pe pH diagram we assume that pO2 1 atm This results in Eh 1 23 0 0592 pH This yields a line with slope of 0 0592 LOWER STABILITY LIMIT OF WATER Eh pH Starting with H e 1 2H2 g we write the Nernst equation 1 2 p 0 0592 H2 0 Eh E log 1 aH We set pH2 1 atm Also Gr 0 so E0 0 Thus we have Eh 0 0592 pH O2 H2 O C2HO Making stability diagrams For any reaction we wish to consider we can write a mass action equation for that reaction We make 2 axis diagrams to represent how several reactions change with respect to 2 variables the axes Common examples Eh pH PO2 pH T x x y x y z etc Construction of these diagrams For selected reactions Fe2 2 H2O FeOOH e 3 H 3 a 0 0592 H 0 Eh E log a 2 1 Fe How would we describe this reaction on a 2 D diagram What would we need to define or assume How about Fe3 2 H2O FeOOH ferrihydrite 3 H Ksp H 3 Fe3 log K 3 pH log Fe3 How would one put this on an Eh pH diagram could it go into any other type of diagram what other factors affect this equilibrium description Redox titrations Imagine an oxic water being reduced to become an anoxic water We can change the Eh of a solution by adding reductant or oxidant just like we can change pH by adding an acid or base Just as pK determined which conjugate acid base pair would buffer pH pe determines what redox pair will buffer Eh and thus be reduced oxidized themselves Redox titration II 100 H2S aq SO4 90 4 Some species w SO umolal Let s modify a bjerrum plot to reflect pe changes 80 70 60 50 4 2 0 2 4 pe 6 8 10 12
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