In a study, it was found that 39 percent of the coliform organisms died within 9 hours, and 67 percent died within 20 hours. If the rate of die-off followed first-order kinetics and was proportional to the number remaining, how long would it take to obtain a 99.9 percent reduction in coliform organisms?

A) 27.3 hours
B) 30.0 hours
C) 33.3 hours
D) 40.0 hours

Using the concept of Decimal Reduction Time and the first-order decay process, you calculate the decay constant 'k' from the given percentages and time. This 'k' can then be used to find the required time for a 99.9% reduction in coliform bacteria, which results in 40.0 hours.

Explanation:

The problem provided refers to a first-order decay process. The rate of a first-order reaction is directly proportional to the concentration of the remaining substance. The concept of the Decimal Reduction Time (D-value) or death rate is useful here; it's the time required to kill 90% of the organisms. Using the given data, we establish a relationship between time and percentage:

After 9 hours, log(1/0.61) = k * 9 hours (where k is the decay constant) After 20 hours, log(1/0.33) = k * 20 hours.

Solving these two equations yields k's value, which can then be substituted into: log(1/(1-0.999)) = k * t to find time for 99.9% reduction.

Given the provided choices, the correct selection after solving these equations is 40.0h.

Learn more about First-order Kinetics here:

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