Which of the following statements about the reduction potentials is true?

The statement that only one value exists for a given half-reaction is true because each half-reaction is defined by its standard reduction potential, which is a measure of the tendency of a species to gain electrons and be reduced. This value is specific to that half-reaction and is standardized under defined conditions (usually 25°C and 1 M concentration for solutes).

Standard reduction potentials are typically reported in volts (V) and provide a consistent basis for comparing the reduction strengths of various chemical species. While the same half-reaction can exhibit different potentials under varying conditions (like concentration or temperature), the standard reduction potential is unique to each specific reaction under standard conditions. Consequently, if you consider a specific half-reaction, it will yield a single, defined reduction potential that can be referenced.

The other statements do not hold true universally. While it's accurate that reduction potentials can vary with temperature, they are not all positive; some can be negative, indicating a lower tendency to gain electrons, and reduction potentials are not extensive properties, which depend on the amount of substance present. Hence, the correct understanding of half-reaction potentials is that each unique reaction possesses a singular standard value under standard conditions, solidifying the correctness of the chosen answer.