7B.1 Textbook Problem

[305920501]

I'm confused why in this reaction we need to use the integrated first order reaction instead of the half-life equation? We are given the information to solve the half-life equation, and I thought we could then figure out how many half lives occur in 5 hours. With this information, we could use the (1/2)^n[] equation and plug in 20mg as the mass to discover the remainder after 5 hours. However, this does not give the correct answer, can anyone explain why?

[Lan Wei 3I]

Hi,

we are not given the information to solve for half-life. The half-life equation tells us how much time is needed for the reactant concentration to decrease to one-half its initial value. Usually, questions involving half-life would state the term half-life in the prompt. This question instead asks us how much of a reactant's initial concentration is remaining after t amount of time, which involves the values of [A]0 and [A]after t amount of time. Thus, we must use ln [A]=-kt+ln[A]0. By pluggin in the rate constant 7.6*10^-3 for k and 5.0h=300min for t, we can then get hat 10% of the initial mass was remaining.

[Nicholas_Fink_3A]

For this question, you can't use the 20 mg as n in the equation. The n has to be in moles. So, instead, you have to find the percentage that remains which can be found with just the k and t values.