NERNST

1
NERNST!!!

• How do we use the Nernst Equation?

The first thing we need to work with the Nernst
Equation is a balanced Galvanic
Cell xocell 2 Fe3 (aq) 2 e-
? 2 Fe 2 (aq) 0.77 V Cu2
(aq) 2 e- ? Cu (s) 0.34 V Which is the
cathode? Which means the copper reaction will be
the oxidation at the anode, so we need to switch
the reaction and the sign of the xcell.
2
NERNST!!!

• How do we use the Nernst Equation?

• The first thing we need to work with the Nernst
  Equation is a balanced Galvanic Cell
• xocell
• 2 Fe3 (aq) 2 e- ? 2 Fe 2 (aq)
  0.77 V
• Cu (s) ? Cu2 (aq) 2 e- -0.34 V
• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Lets assume that we start with a cell where all
  solutions are at an initial concentration of 1 M
  (standard conditions).
• Even though we are at standard conditions we are
  going to use the Nernst Equation to determine the
  cell potential to make sure we understand where
  everything is coming from.
• Remind me, the Nernst equation is
• xo RT ln(Q)
• nF

3
NERNST!!!

• How do we use the Nernst Equation?

• xocell
• 2 Fe3 (aq) 2 e- ? 2 Fe 2 (aq)
  0.77 V
• Cu (s) ? Cu2 (aq) 2 e- -0.34 V
• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Under standard conditions, all aqueous reagents
  will be 1 M, so lets start to plug in some data
  to the Nernst Equation
• xo RT ln(Q)
• nF
• xo 0.43 V
• x 0.43 V -

4
NERNST!!!

• How do we use the Nernst Equation?

• xocell
• 2 Fe3 (aq) 2 e- ? 2 Fe 2 (aq)
  0.77 V
• Cu (s) ? Cu2 (aq) 2 e- -0.34 V
• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Under standard conditions, all aqueous reagents
  will be 1 M, so lets start to plug in some data
  to the Nernst Equation
• xo RT ln(Q)
• nF
• R 8.314 J/mol K, T 298 K
• x 0.43 V 8.314 J x 298 K x
• mol K

5
NERNST!!!

• How do we use the Nernst Equation?

• xocell
• 2 Fe3 (aq) 2 e- ? 2 Fe 2 (aq)
  0.77 V
• Cu (s) ? Cu2 (aq) 2 e- -0.34 V
• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Under standard conditions, all aqueous reagents
  will be 1 M, so lets start to plug in some data
  to the Nernst Equation
• xo RT ln(Q)
• nF
• Where do we get n from? n the number of mols
  electrons that are involved in the cell (the of
  the e- that is cancelled out in balancing the
  equation) 2x 0.43 V 8.314 J x 298 K x
  x
• mol K 2

6
NERNST!!!

• How do we use the Nernst Equation?

• xocell
• 2 Fe3 (aq) 2 e- ? 2 Fe 2 (aq)
  0.77 V
• Cu (s) ? Cu2 (aq) 2 e- -0.34 V
• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Under standard conditions, all aqueous reagents
  will be 1 M, so lets start to plug in some data
  to the Nernst Equation
• xo RT ln(Q)
• nF
• F Faradays constant 96,485 C/mol
• x 0.43 V 8.314 J x 298 K x x
  mol x
• mol K 2 96,485 C

7
NERNST!!!

• How do we use the Nernst Equation?

• xocell
• 2 Fe3 (aq) 2 e- ? 2 Fe 2 (aq)
  0.77 V
• Cu (s) ? Cu2 (aq) 2 e- -0.34 V
• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Under standard conditions, all aqueous reagents
  will be 1 M, so lets start to plug in some data
  to the Nernst Equation
• xo RT ln(Q)
• nF
• ln(Q)we get this by determining Q for this
  reaction (which is why it is so important to have
  a balanced equation).
• How do we determine Q?
• prodm/reactn

8
NERNST!!!

• How do we use the Nernst Equation?

• xocell
• 2 Fe3 (aq) 2 e- ? 2 Fe 2 (aq)
  0.77 V
• Cu (s) ? Cu2 (aq) 2 e- -0.34 V
• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Under standard conditions, all aqueous reagents
  will be 1 M, so lets start to plug in some data
  to the Nernst Equation
• xo RT ln(Q)
• nF
• What is Q for this reaction?
• Q Cu2Fe22 / Fe32
• Why isnt Cu (s) involved?
• Only aqueous solutions or gasses are considered
  in Q/K calculations.

9
NERNST!!!

• How do we use the Nernst Equation?

• xocell
• 2 Fe3 (aq) 2 e- ? 2 Fe 2 (aq)
  0.77 V
• Cu (s) ? Cu2 (aq) 2 e- -0.34 V
• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Under standard conditions, all aqueous reagents
  will be 1 M, so lets start to plug in some data
  to the Nernst Equation
• xo RT ln(Q)
• nF
• Under standard conditions all solutions are 1 M,
  so Q 1 and ln(Q) 0.
• x 0.43 V 8.314 J x 298 K x x
  mol x 0 0.43 V
• mol K 2 96,485 C
• Do the units work??? Yes! 1 V J/C

10
NERNST!!!

• How do we use the Nernst Equation?

Lets calculate what the potential of the cell
will be after the reaction has gone to 10
completion. xocell 2 Fe3 (aq) Cu
(s) ? Cu2 (aq) 2 Fe2 (aq) 0.43 V I 1.0 M
-- 1.0 M 1.0 M C -0.1
M -- 0.05 M 0.1 M E 0.9
M -- 1.05 M 1.1 M Make sure to
make sure you pay attention to coefficients when
working with the ICE tablefailure to do so is
bad! What will our value of Q be?
1.051.12/0.92 1.5685 (again, watch the
coefficients) ln(Q) 0.450
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NERNST!!!

• How do we use the Nernst Equation?

• We can now plug our value of ln(Q) into the
  previous equation to get
• x 0.43 V 8.314 J x 298 K x x
  mol x 0.450 0.424 V
• mol K 2 96,485 C
• We can continue to track the reaction as it
  would proceed over time.
• The only thing that will be changing is the
  values of Q and ln(Q).
• Lets go through one more real quickly

12
NERNST!!!

• How do we use the Nernst Equation?

Lets calculate what the potential of the cell
will be after the reaction has gone to 30
completion. xocell 2 Fe3 (aq) Cu
(s) ? Cu2 (aq) 2 Fe2 (aq) 0.43 V I 1.0 M
-- 1.0 M 1.0 M C -0.3
M -- 0.15 M 0.3 M E 0.7
M -- 1.15 M 1.3 M What will our
value of Q be? 1.151.32/0.72 3.966
ln(Q) 1.378 x 0.43 V 8.314 J x 298 K x
x mol x 1.378 0.412 V
mol K 2 96,485 C
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NERNST!!!

• How do we use the Nernst Equation?

What would happen if we kept on going? This is
one of the great things about the Nernst
Equation, it allows us to calculate what the
potential of a cell would be as a battery went
dead. What do we mean by dead? Ecell 0 (no
more potential) What is another way we can think
about this? When we have a dead battery, the
system is happy, it has reached
equilibrium Which means that a cell works by
trying to reach equilibrium(this will be
important very soon) So lets actually look at
what happens when we keep on going
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NERNST!!!

• How do we use the Nernst Equation?

• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Now what will happen as we move away from the
  standard conditions?

15
NERNST!!!

• How do we use the Nernst Equation?

• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Now what will happen as we move away from the
  standard conditions?

16
NERNST!!!

• How do we use the Nernst Equation?

• 2 Fe3 (aq) Cu (s) ? Cu2 (aq) 2 Fe2
  (aq) 0.43 V
• Now what will happen as we move away from the
  standard conditions?
• This system would make for a decent battery, the
  Ecell stays pretty constant until almost all of
  the Fe3 has reacted.