The half-life of a first-order reaction is 13 min.If the initial concentration of reactant is it takes for it to decrease to 0.085 M.

Question

The half-life of a first-order reaction is 13 min.If the initial concentration of reactant is  it takes  for it to decrease to 0.085 M.

Quizplus · Accepted Answer

First we need to find the rate constant (k) using the half-life equation: 
t1/2 = ln2/k 
13 min = ln2/k 
k = ln2/13 = 0.0531 min^-1

Next, we can use the first-order rate equation to find the time it takes for the concentration to decrease to 0.085 M: 
ln([reactant]t/[reactant]0) = -kt 
ln(0.085/11) = -0.0531t 
t = 8.0 min

Therefore, the best choice is C (8.0 min).

The Half-Life of a First-Order Reaction Is 13 Min