I've seen E=E(red) - E(ox) and E=E(cathode)+E(anode). What's the difference?
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Difference? None. Only the notation is different, otherwise they represent the same thing.
Here's a little mnemonic I came up with years ago: "A red cat ate an ox."
"red cat" = reduction occurs at the cathode
"an ox" = oxidation occurs at the anode
When referring to the cathode, we use the reduction potential. When referring to the anode, we use the oxidation potential which is the reverse of the reduction reaction. When we reverse a half-reaction, the sign of the voltage is reversed as well. Therefore, the oxidation potential is the negative of the reduction potential, hence the sign change.
Here's a little mnemonic I came up with years ago: "A red cat ate an ox."
"red cat" = reduction occurs at the cathode
"an ox" = oxidation occurs at the anode
When referring to the cathode, we use the reduction potential. When referring to the anode, we use the oxidation potential which is the reverse of the reduction reaction. When we reverse a half-reaction, the sign of the voltage is reversed as well. Therefore, the oxidation potential is the negative of the reduction potential, hence the sign change.