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The key point you are missing is that the thermodynamic values you report are for standard conditions, meaning that there would also be 1 M $Zn^{2+}$$\ce{Zn^2+}$ and 1 M $Cu^{2+}$$\ce{Cu^2+}$ in the solutions. The Nernst equation can be used to determine the non-standard condition potential (in your case, sticking a copper wire into a solution with effectively no copper ions. In practice, this would be very hard to do, as adventitious ions (and other reactions not considered) will contribute to the cell potential when the intended ion concentrations are so low.

This concept can be used to determine the concentration of copper ions in solution, and may be of interest in explaining the phenomenon to a general audience. Two $Cu$$\ce{Cu}$/$Cu^{2+}$$\ce{Cu^2+}$ half-cells with the same concentration of copper ions will result in a cell potential of zero; however, if one of the cell concentrations is known (for argument's sake, say 1 M) then the "unknown" ion concentration could be found using the Nernst equation.

The key point you are missing is that the thermodynamic values you report are for standard conditions, meaning that there would also be 1 M $Zn^{2+}$ and 1 M $Cu^{2+}$ in the solutions. The Nernst equation can be used to determine the non-standard condition potential (in your case, sticking a copper wire into a solution with effectively no copper ions. In practice, this would be very hard to do, as adventitious ions (and other reactions not considered) will contribute to the cell potential when the intended ion concentrations are so low.

This concept can be used to determine the concentration of copper ions in solution, and may be of interest in explaining the phenomenon to a general audience. Two $Cu$/$Cu^{2+}$ half-cells with the same concentration of copper ions will result in a cell potential of zero; however, if one of the cell concentrations is known (for argument's sake, say 1 M) then the "unknown" ion concentration could be found using the Nernst equation.

The key point you are missing is that the thermodynamic values you report are for standard conditions, meaning that there would also be 1 M $\ce{Zn^2+}$ and 1 M $\ce{Cu^2+}$ in the solutions. The Nernst equation can be used to determine the non-standard condition potential (in your case, sticking a copper wire into a solution with effectively no copper ions. In practice, this would be very hard to do, as adventitious ions (and other reactions not considered) will contribute to the cell potential when the intended ion concentrations are so low.

This concept can be used to determine the concentration of copper ions in solution, and may be of interest in explaining the phenomenon to a general audience. Two $\ce{Cu}$/$\ce{Cu^2+}$ half-cells with the same concentration of copper ions will result in a cell potential of zero; however, if one of the cell concentrations is known (for argument's sake, say 1 M) then the "unknown" ion concentration could be found using the Nernst equation.

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The key point you are missing is that the thermodynamic values you report are for standard conditions, meaning that there would also be 1 M $Zn^{2+}$ and 1 M $Cu^{2+}$ in the solutions. The Nernst equation can be used to determine the non-standard condition potential (in your case, sticking a copper wire into a solution with effectively no copper ions. In practice, this would be very hard to do, as adventitious ions (and other reactions not considered) will contribute to the cell potential when the intended ion concentrations are so low.

This concept can be used to determine the concentration of copper ions in solution, and may be of interest in explaining the phenomenon to a general audience. Two $Cu$/$Cu^{2+}$ half-cells with the same concentration of copper ions will result in a cell potential of zero; however, if one of the cell concentrations is known (for argument's sake, say 1 M) then the "unknown" ion concentration could be found using the Nernst equation.