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Remember that E˚(cell) = E˚(cathode) - E˚(anode). The greater the concentration difference between the cathode and anode, the greater your standard cell potential. If you dilute the cathode, you will decrease the cell potential because you are lowering the concentration of the cathode, lowering the concentration difference between the cathode and anode. Meanwhile, if you dilute the anode, you are making the anode concentration smaller which increases the concentration difference between the cathode and the anode, making the cell potential increase.
It is important to note where the dilution is occurring as it will affect cell potential differently if it is in the cathode or anode. You can use E˚(cell) = E˚(cathode) - E˚(anode) to get a better understanding. When the cathode is diluted, cell potential decreases due to the lower cathode. Therefore, when the dilution occurs in the anode, the cell potential increases.
Diluting the cathode solution decreases the value of the cell potential, while diluting the anode solution increases the value of the cell potential. This is because of the differences between the anode and cathode when finding Ecell=Ecathode-Eanode.
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