Derive an expression for a "1/3-life" for a first-order reaction.

Question

Quizplus · Accepted Answer

The equation for a first-order reaction is: 
ln[N]t = -kt + ln[N]0 
Where: 
[N]t = concentration at time t 
[N]0 = initial concentration 
k = rate constant 
t = time

To find the half-life of the reaction, we set [N]t = [N]0/2: 
ln[N]0/2 = -k(t1/2) + ln[N]0

Simplifying, we get: 
t1/2 = ln2/k

To find the 1/3-life, we set [N]t = [N]0/3: 
ln[N]0/3 = -k(t1/3) + ln[N]0

Simplifying, we get: 
t1/3 = ln3/k

Therefore, the answer is D because it is the only choice that includes ln3/k.

Derive an Expression for a "1/3-Life" for a First-Order Reaction