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One useful application of the Nernst
equation is determining ion concentration. If you know the concentrations of
all but one species and the voltage, you can get the concentration of the final
species. This is how pH meters work: the unknown concentration is
[H+], and they simply measure the voltage in the cell.
Example: If the voltage of the cell below is 0.389V in a 0.500 M
solution of Fe+2, 1 atm pressure of H2 at 25oC,
what is the hydrogen concentration in the solution?
- Fe|Fe+2||H+|H2
Solution: First, write out the two half reactions, the balanced
equation and the standard voltages associated with them
- Fe(s) -> Fe+2(aq) + 2e-
E0 = +0.409 V
- 2H+(aq) + 2e- -> H2(g)
E0 = +0.000
The standard cell voltage is thus 0.409 + 0 =
0.409 V. Two electrons are passed during the reaction. The balanced equation is
- Fe(s) + 2H+(aq) -> Fe+2(aq) +
H2(g)
The Nernst equation is
- E = E0 - (RT/nF)ln(Q)
The
reaction
quotient Q has the form and value
- Q =
PH2*[Fe+2]/[H+]2
- Q = 1*0.500/[H+]2
Now simply plug everything
into the Nerst equation and solve for the hydrogen ion concentration. Since
we're doing the reaction at 25oC, the term RT/F is 0.0257 V
- E = E0 - (RT/nF)ln(Q)
- 0.389 = 0.409 - (0.0257/2)*ln(0.5/[H+]2)
- 1.556 = ln(0.5/[H+]2)
- 4.74 = 0.5/[H+]2
- [H+] = 0.325 M
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