#### Question

# 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.

#### Answers

k= 2.303/t * log (100/11)

k= 0.051261224 min ^ -1

t 1/2 = .693/k

= 13.5 min

#1

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

#2