Final answer:
The graph representing the concentration over time for a first-order reaction is an exponential decay curve, halving the concentration every constant half-life period, distinct from the linear concentration decrease observed in a zeroth-order reaction.
Step-by-step explanation:
The graph that best represents the concentration of a reactant over time for a first-order reaction is an exponential decay curve. Since the reaction has a half-life of 120 hours and starts with an initial concentration of 0.04 M, the concentration will decrease by half every 120 hours. Following this pattern, after one half-life, the concentration will be 0.02 M, after two half-lives 0.01 M, and so on. This behaviour is characteristic of a first-order reaction, where the half-life is constant and does not depend on the initial concentration.
The concentration at any time can be calculated using the formula for a first-order reaction: \( [A] = [A]_0 \times (1/2)^n \), where \( [A] \) is the concentration at time \( t \), \( [A]_0 \) is the initial concentration, and \( n \) is the number of half-lives that have passed.
In contrast, a zeroth-order reaction would show a linear decrease in concentration over time, as indicated by a straight line on a concentration vs. time graph, which does not fit the description of this first-order reaction scenario.