Half Life Question. Need help asap!?
What is the half-life of a compound if 89 percent of a given sample of the compound decomposes in 43 min? Assume first-order kinetics.
k= 2.303/t * log (100/11)
k= 0.051261224 min ^ -1
t 1/2 = .693/k
= 13.5 min
The first order rate law is given by
A = A?exp(-kt)
where A? is the initial sample, A is what remains of the initial sample, k is the rate and t is time
To find the half life, we first determine k.
A/A? = 0.11 = (1.00 - 0.89)
t = 43 min
So 0.11 = exp(-43k)
ln(0.11) = -43k
k = - ln(0.11)/43
To find the half life, set A/A? = 1/2
Then 1/2 = 0.5 = exp(-kt)
ln(0.5) = -kt
t = - ln(0.5)/k = ln(0.5)/(ln(0.11)/43)
t? = 13.5 min
Hope this helps