Step 1: Arrhenius dependence.
The rate constant \(k\) varies with temperature as \(k = A e^{-E_a/RT}\). Hence \(k\) primarily depends on temperature.
Step 2: Eliminate others.
Mass, weight, and time do not directly determine the value of \(k\) (for a given reaction and medium).
Step 3: Conclusion.
Therefore, the correct answer is (A) Temperature.