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Lets say we want the activity coefficient of $\ce{Cu^{2+}}$ ions in solution. Would we simply setup one half cell of a $\ce{Cu}$ electrode in a known concentration of $\ce{CuSO4}$ and then connect this to a Standard Hydrogen Electrode.

Using the standard electrode potential of the reaction $\ce{Cu^{2+} + 2e- -> Cu}$ and the Nernst equation could we determine the activity coefficient of $\ce{Cu^{2+}}$ ions ?

Is this all I would need to do ?

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    $\begingroup$ You would not be able to easily separate the activity coefficients of the anion and cation using this method. $\endgroup$ – bobthechemist Apr 17 '14 at 19:26
  • $\begingroup$ You will probably have to do a lot of concentration dependent cross measurements involving a huge set of different ions not only copper. You should also rather use Ag/AgCl electrode. $\endgroup$ – Martin - マーチン May 12 '14 at 11:07
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Sort of 'yes', sort of 'no'. Consider the following points:

  1. Activity coefficients are notorious for changing with $\mathrm{p}\ce{H}$, ionic strength, and concentration (among other things). You might measure the the activity coefficient of $\ce{Cu^{2+}}$ in a $0.7~\mathrm{M}$ $\ce{CuSO4}$ solution and get one value, but try to measure the same thing in a low $\mathrm{p}\ce{H}$ and $1~\mathrm{\mu M}$ $\ce{CuCl2}$ solution and you may get a completely different value. In practice, people usually end up measuring activity coefficients across a range of conditions that are relevant to their specific use-case.

  2. The Standard Hydrogen Electrode is a theoretical device; and actually constructing something similar is difficult. In practice, you would just want to use a commercially available double-junction silver-silver chloride or saturated calomel electrode. The potentials of those two are well-known and fairly stable.

See Chapter 2 of "Electrochemical Methods" 2nd Ed, by Bard and Faulkner for more information.

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