Ask Question
17 September, 14:02

The half-life (t1/2) for a chemical reaction is the time it takes for the concentration of reactant to decrease to one-half its initial concentration. For a first-order reaction, the half-life is a constant at a given temperature. So the half-life is also the amount of time it takes for the concentration to change from one-half to one-fourth, and from one-fourth to one-eighth, etc. If the half-life for a first-order reaction is 12.0 minutes, what percentage of reactant remains unreacted after 48.0 minutes?

+5
Answers (1)
  1. 17 September, 14:13
    0
    The percentage of reactant that remains unreacted is 6.25%

    Explanation:

    Let's call [A]₀ the initial concentration of reactant A

    In the first 12.0 minutes the concentration of A will drop to [A]₀/2

    In 24.0 minutes the concentration of A will be reduced by half again

    ([A]₀/2 / 2) = [A]₀ / 4

    In 36.0 min the concentration of A will be ([A]₀/4 / 2) = [A]₀ / 8

    And after 48.0 min the concentration of A will be ([A]₀/8 / 2) = [A]₀/16

    If [A]₀ is the 100%, [A]₀ / 16 will be (100 / 16) = 6.25%

    Mathematically, you can express the concentration of A in this way:

    [A] = [A]₀ / 2ⁿ

    where:

    [A] = concentration of A

    [A]₀ = initial concentration of A

    n = t / t (1/2), where t = time and t (1/2) = half-life

    In this case:

    [A] = [A]₀ / 2^ (48 min / 12 min)

    [A] = [A]₀ / 2⁴

    [A] = [A]₀ / 16
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “The half-life (t1/2) for a chemical reaction is the time it takes for the concentration of reactant to decrease to one-half its initial ...” in 📗 Physics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers