The rate constant for a reaction depends upon each of the following, EXCEPT:

The rate constant ($k$) is a proportionality constant in the rate law that relates the rate of a reaction to the concentrations of reactants. It is specific to a given reaction under specific conditions.

Let's analyze each option:

• (a) solvent for solutions: The solvent can affect the rate constant by influencing the activation energy or the frequency of collisions, especially in reactions involving ions or polar molecules.
• (b) temperature: The rate constant is highly dependent on temperature, as described by the Arrhenius equation. An increase in temperature generally increases the rate constant.
• (c) concentration of reactants: The rate constant is independent of the concentration of reactants. While the rate of reaction changes with reactant concentrations, the rate constant itself remains constant for a given reaction at a specific temperature.
• (d) nature of reactants: The chemical identity and structure of the reactants fundamentally determine the activation energy and the collision frequency, thus affecting the value of the rate constant.

Therefore, the rate constant does not depend on the concentration of reactants.

The final answer is $\boxed{\text{(c) concentration of reactants}}$.