7B.7

[emmaferry2D]

Substance A decomposes in a first-order reaction and its half life is 355 s. How much time must elapse for the concentration of A to decrease to (a) one-eighth of its initial concentration; (b) one-fourth of its initial concentration; (c) 15% of its initial concentration; (d) one-ninth of its initial concentration?


For a question like this how do you determine how much time it takes for a substance to decompose without knowing the concentrations

[Catie Donohue 2K]

For these questions, I used the formula for the half-life of a first order reaction to find k. Then, I manipulated the equation for the linear plot of a first order reaction and assumed that, if we were trying to find the time taken to get to 1/8 of the original concentration, for example, the concentration of A naught was eight and the concentration of A was one. I isolated the t variable on one side, so you should have:

-ln(A/Anaught)/k = t

When you plug in your concentration values, you would get -ln(1/8)/k=t. Just repeat this step by plugging in your concentration ratios in in the ln().

[Carolina 3E]

Since the half-life of a first-order rxn is independent of the initial concentration of A, we can determine how much time it takes by multiplying the amount of half-lives by the half-life.
For example,
a) [A] = (1/8)[A]o, [A]/[A]o = (1/2)^3 which means 3 half-lives have past
t = 3(half-life) = 3(355s)