Reaction; Rate Constant

Question

Consider the following reaction.

aA +bB →cC

whose first and second half-lives are 48.6 and 97.2 minutes respectively. If the rate constant is equal to 0.001956 and [A]₀ = 10.52, calculate the [A] at t = 34.05 minutes. 

What does K = at t = 34.05

Answer 1

Hi Justin G.,

There's some error in the terminology of your question. Half-lives refers to the inherent deterioration process of independent, randomly-decaying particles (usually radioactive nuclei). O.K., since the two given values are in 1:2 proportion, let's assume that there's an exponential decay of each item, and that "one half-life and two half-lives" is what is meant (not, "first half-life and second half-life"; do you see the issue?).

Then, you actually have excess data (the "rate constant") here; all you need is [A0] and the respective times (34.05 and 48.6) to calculate. I'm assuming you can set up and solve the exponential decay expression?

This incidentally forces both a and b to be 1, I think -- otherwise non-exponential behavior results ....

-- Cheers, --Mr. d.