Which of the following graphs best represents the relationship between the concentration of a reactant and the rate of a first-order reaction?

• A. A curve that increases rapidly at first and then levels off
• B. A horizontal line indicating a constant rate regardless of concentration
• C. A straight line with a positive slope passing through the origin
• D. A straight line with a negative slope

Answer: (C)

Verified step by step guidance

1. Recall that for a first-order reaction, the rate law is given by \(\text{rate} = k [A]\), where \(k\) is the rate constant and \([A]\) is the concentration of the reactant.
2. Since the rate is directly proportional to the concentration of the reactant, the graph of rate versus concentration should be a straight line.
3. The line should have a positive slope equal to the rate constant \(k\), because as concentration increases, the rate increases proportionally.
4. The line must pass through the origin because if the concentration is zero, the rate must also be zero (no reactant means no reaction).
5. Therefore, the graph that best represents this relationship is a straight line with a positive slope passing through the origin.