How many half-lives are required for the concentration of reactant to decrease to 3.1% of its original value?

Question

Quizplus · Accepted Answer

To calculate the number of half-lives required, we can use the formula:

final concentration = original concentration * (1/2)^(number of half-lives)

Let's assume the original concentration is 100%, and we want to find the number of half-lives required for the concentration to reach 3.1% or 0.031.

0.031 = 100% * (1/2)^(number of half-lives)

Taking the log of both sides:

log(0.031) = log(100%) - number of half-lives * log(2)

log(0.031) - log(100%) = -number of half-lives * log(2)

number of half-lives = (log(100%) - log(0.031))/ log(2)

number of half-lives = 4.91 or ~5 (rounding up)

Therefore, the answer is C) 5.

How Many Half-Lives Are Required for the Concentration of Reactant