# How do you calculate a half cell potential Copper(II) and Copper Sulfate?

I have to complete an experiment for school where I have copper and zinc electrodes placed into an electrolyte of copper sulfate and I have measured the potential across it at varying temperatures. For example at $$\pu{60°C}$$ ($$\pu{333K}$$) I measured the potential to be $$\pu{0.880 volts}$$ and at $$\pu{75°C}$$ ($$\pu{348K}$$) I measured the potential to be $$\pu{0.780 volts}$$.

Is there a way I can prove this result? I tried using the Nernst Equation, but my reaction quotient is equal to 1, which disproves my finding. I found out about activity coefficients, but I do not know how to apply it or the Nernst Equation to half cell potentials.

Any advice or help is greatly appreciated!

• That's not a Cu(2+)/CuSO4 half cell, it's a Cu/CuSO4 half cell, or Cu/Cu(2+) if you like. – orthocresol Jul 31 '19 at 9:59
• Do you have a single solution vessel containing copper sulfate solution and the two metal electrodes? If so, why not use two vessels and a salt bridge, like in a Daniell cell? Zinc is spontaneously oxidized by copper ions, so a single vessel cell has a short circuit, as it were. – Ed V Jul 31 '19 at 12:08
• @EdV Yes I do have a single solution vessel containing copper sulfate solution and metals copper and zinc as the electrodes. I essentially wanted to make a Daniel cell with two solution vessels, but instead my chemistry teacher suggested to me to use one solution vessel and the two metal electrodes as it would be easier to set up. However, I did not consider whether the Nernst Equation would change accordingly and I have already collected my data using one solution vessel and need to type a lab report using my collected results. How would I configure the equation for my experiment? – Sam Jaber Jul 31 '19 at 12:54
• Unfortunately, I do not see a way to salvage this: using a single vessel was a definite problem, but the electrolyte should at least have contained both zinc ions and copper ions (from, say, the sulfate salts). Then, even though the cell was internally shorted, you could have used the Nernst equation, though not accurately at all. Instead, you start with zero zinc ion concentration, so you have an unknown, but spontaneously increasing, zinc ion concentration in solution. And the copper ion concentration is also unknown after a short time and continues to decline. Sorry! – Ed V Jul 31 '19 at 13:28
• @EdV Thanks for the Advice! I will be changing my experiment then by using two solution vessels insead. – Sam Jaber Jul 31 '19 at 20:36

Note the spelling of the name: it was invented in 1836 by John Frederic Daniell. At $$\pu{25 ^\circ C}$$, and with $$n = \pu{2 equivalents/mole}$$, as correct here, $$(\ln 10)\frac{RT}{nF} = \pu{0.02958 V} = \pu{29.58 mV}$$.