Final answer:
Option a is the correct option. The correct characteristic of a first-order reaction with one reactant is that the rate is proportional to the concentration of that reactant. The rate constant remains constant over time, and while temperature can affect reaction rates, it is not addressed in the specific characteristic mentioned.
Step-by-step explanation:
The characteristic of a first-order reaction having only one reactant is that the rate is proportional to the reactant concentration. In a first-order reaction, such as A → products, the rate at which A is converted into products is directly related to the current concentration of A. As the reaction proceeds, the concentration of A decreases over time, leading to a decrease in the reaction rate. The relationship between reaction rate and concentration can be expressed by the differential rate law: rate = k[A], where k is the rate constant. This depicts that the rate constant is indeed constant during the course of the reaction and does not change over time and is also independent of the concentration of the reactant.
Moreover, this characteristic is not affected by temperature within the context of this question, although in practice, temperature does have an effect on reaction rates and therefore on the value of the rate constant 'k'. The rate is not inversely proportional to time; instead, as time goes by and the reactant concentration decreases, the reaction slows down but does not strictly follow an inverse relationship with respect to time.
Therefore, the correct option for the characteristic of a first-order reaction having only one reactant is a. Rate proportional to reactant concentration.