Perhaps:
"The negative electrode of a galvanic cell is the _cathode_, on whose surface cathodic reactions take place."
I feel perfectly comfortable about using "whose" here, but some people do not like using "whose" as the possessive of "which." In that case, I think we'd have to write:
"The negative electrode in the galvanic cell is the _cathode_, on the surface of which cathodic reactions take place."
I might consider breaking it into more than one sentence.