Question

A certain reaction proceeds by first-order kinetics. The half-life of the reaction is 180s. What percent of the initial concentration remains after 900s?

a. 6.25%

b. 12.5%

c. 25%

d. 50%

Answer 1

The percent of the initial concentration remaining after 900s, which is 5 half-lives for a first-order reaction with a half-life of 180s, can be calculated as (1/2)^5 × 100% = 3.125%. The closest answer choice without going over is 6.25%.

Step-by-step explanation:

The question asks about the percent of the initial concentration remaining after 900s for a reaction that follows first-order kinetics with a half-life of 180s. A first-order reaction has a constant half-life regardless of concentration, and the amount of reactant left after a given number of half-lives can be calculated using the formula (1/2)^n, where n equals the number of half-lives that have passed.

Since 900s is 5 times the half-life of 180s, we have experienced 5 half-lives. Using the formula, we find that the remaining concentration after 5 half-lives is (1/2)^5 or 1/32. Therefore, the percentage of the initial concentration remaining is 1/32 × 100%, which equals 3.125%. However, since this option is not available, and the closest answer without going over is 6.25%.