Nernst Equation Consider the half reaction: NO 3 - + 10H + + 8e - NH 4 + + 3H 2 O(l) We can...
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Transcript of Nernst Equation Consider the half reaction: NO 3 - + 10H + + 8e - NH 4 + + 3H 2 O(l) We can...
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
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)