To determine the order of a reaction based on the relationship between the half-life and the concentration of the starting material, you can follow these steps:
1. Understand the concept of reaction order: In chemical kinetics, the order of a reaction refers to the exponent to which the concentration of the reactants is raised in the rate equation of the reaction.
2. Look at the half-life and concentration relationship: In this case, the half-life of the reaction is inversely dependent on the concentration of the starting material. This means that as the concentration of the starting material increases, the half-life decreases, and vice versa.
3. Analyze the possible orders: Based on the information given, the options to consider are zero order, first order, and second order.
a. If the half-life did not depend on the concentration of the starting material (i.e., remained constant), the reaction would be zero order.
b. If the half-life decreased linearly with decreasing concentration of the starting material, the reaction would be first order.
c. If the half-life decreased exponentially with decreasing concentration of the starting material, the reaction would be second order.
4. Apply the information: Since the half-life is inversely dependent on the concentration of the starting material, it means that as the concentration decreases, the half-life increases exponentially. This implies that the reaction is second order.
Therefore, the correct answer is c. the reaction is second order.