After 71.0 min, 35.0% of a compound has decomposed. What is the half‑life of this reaction assuming first‑order kinetics?

Question

Please help me with this question!

Thank you!

Answer 1

Nothing wrong with the previous answer, but I thought I'd show you an easy way (IMO) to do these problems. Simply use the formula Fraction Remaining (FR) = 0.5ⁿ where n = # of half lives that have elapsed.

In the current problem, FR = 0.65 (0.35 has decomposed leaving 0.65 remaining). Now we will find how many half lives that took.

FR = 0.5n

0.65 = 0.5n

log 0.65 = n*log 0.5

-0.187 = -0.301n

n = 0.622 half lives have elapsed and this is equal to 71.0 minutes

So, 1 half life = 71.0 min / 0.622 half lives = 114 minutes

Answer 2

Step 1: integrated rate law for the 1st order reaction:

ln[reactant]_f = -kt + ln[reactant]_i

Step 2: final concentration of reactant (100%-35%), if the initial quantity 100%

ln65% = -k x 71 min + ln 100% , therefore k = 0.00607 / min

Step 3: half life t_1/2 = ln2/k = 114 min