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.

I would use the first but add the article "a" where shown: A negative electrode in the galvanic cell is a cathode where -a- cathodic reaction takes place. This means that different cathodic reactions are possible