Nernst EquationConsider 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

is

The Nernst equation for this reaction at 25°C is

Qn

RTEEh log

303.20

100

3

4log8

0592.0

HNO

NH

aa

aEEh

Let’s assume that the concentrations of NO3- and

NH4+ have been measured to be 10-5 M and

310-7 M, respectively, and pH = 5. What are the Eh and pe of this water?

First, we must make use of the relationship

For the reaction of interest

rG° = 3(-237.1) + (-79.4) - (-110.8)

= -679.9 kJ mol-1

n

GE

or0

volts88.0)42.96)(8(

9.6790 E

The Nernst equation now becomes

substituting the known concentrations (neglecting activity coefficients)

and

10

3

4log8

0592.088.0

HNO

NH

aa

aEh

volts521.01010

103log

8

0592.088.0 1055

7

Eh

81.8)521.0(9.169.16 Ehpe

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!

Biology’s view upside down?

Stability Limits of Water• H2O 2 H+ + ½ O2(g) + 2e-

Using the Nernst Equation:

• Must assign 1 value to plot in x-y space (PO2)

• Then define a line in pH – Eh space

20

21

2

1log

0592.0

HO apn

EEh

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.

20

21

2

1log

0592.0

HO apn

EEh

20

21

2

1log

2

0592.0

HO ap

EEh

As for the pe-pH diagram, we assume that pO2

= 1 atm. This results in

This yields a line with slope of -0.0592.

221

2log0296.023.1

HO apEh

pHpEh O 0592.0log0148.023.12

volts23.1)42.96)(2(

)1.237(00

n

GE r

pHEh 0592.023.1

LOWER STABILITY LIMIT OF WATER (Eh-pH)

Starting with

H+ + e- 1/2H2(g)

we write the Nernst equation

We set pH2 = 1 atm. Also, Gr° = 0, so E0 =

0. Thus, we have

pHEh 0592.0

H

H

a

pEEh

21

2log1

0592.00

O2/H2O

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+

How would we describe this reaction on a 2-D diagram? What would we need to define or assume?

2

30 log

1

0592.0

Fe

H

a

aEEh

• 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

• Let’s modify a bjerrum plot to reflect pe changes

Greg Mon Oct 25 2004

-4 -2 0 2 4 6 8 10 1250

60

70

80

90

100

pe

So

me

sp

eci

es

w/

SO

4-- (

um

ola

l) H2S(aq) SO4--