1) If k = 0.022 sec-1 for a first order reaction, what will be the final concentration after 30. seconds if the initial concentration is 0.10 M? 2) How long will it take for the [ ] to drop from 1.00 mol/L to 0.040 mol/L?
3) What is the half-life of the reaction above?

1. [A] = 0.0517M

2. t = 146.3s

3. t (1/2) = 31.5s

Explanation:

The general kinetic law for a first-order reaction is:

ln[A] = -kt + ln [A]₀

Where [A] is actual concentration after time t, k is rate constant and [A]₀ is initial concentration of the reactant.

1. Replacing with the values of the first point:

ln[A] = -kt + ln [A]₀

ln[A] = -0.022sec⁻¹*30s + ln [0.10]

ln[A] = -2.9626

2. Now, with the values of the second point:

ln[A] = -kt + ln [A]₀

ln[0.04] = -0.022s⁻¹t + ln [1]

3. Half-life is the time the reaction need to decrease the initial concentration to the half:

ln[A] = -kt + ln [A]₀

ln[1/2] = -0.022s⁻¹t + ln [1]