Question

The decomposition of X is the first-order reaction. After 60 minutes, X loses its 50% in weight. Find the time it takes to lose 80%.

Answer 1

If 1st order, then:

ln(A) = ln(A0) - kt

A0 = initial concentration, k = rate constant, t = time, A = concentration at time t

so..

t = 60 min, x --> 50% loss so

t 1/2 = ln(2) / K

k = ln(2) / t 1/2 = ln(2) / 60 = 0.011552 1/ min

so..

for 80%:

ln(A) = ln(A0) - kt

80% --> 20% left

ln(0.2*A0) = ln(A0) - 0.011552 * t

ln(0.2*A0) -  ln(A0) =  - 0.011552 * t

ln(0.2) =  - 0.011552 * t

t = ln(0.2) / (-0.011552 ) = 139.321 minutes required