Question

The decomposition of urea in 0.1M HCl follows first order kinetics. the rate constant increases from 7.13 x 10^(-6) min^(-1) at 61.05 degrees celsius to 2.77 x 10^(-5) min^(-1) at 71.25 degrees celsius. calculate the half life of uread in 0.1M HCl at 37 degrees celsius.

Answer 1

Using Arrhenius equation,

ln(k2/k1) = Ea/R[1/T1-1/T2]

with,

k1 = 7.13 x 10^-6 min-1

k2 = 2.77 x 10^-5 min-1

T1 = 61.05 + 273 = 334.05 K

T2 = 71.25 + 273 = 344.25 K

Ea = activation energy

R = 8.314 J/K.mol

we get,

ln(2.77 x 10^-5/7.13 x 10^-6) = Ea/8.314[1/334.05 - 1/344.25]

Ea = 127207.85 J/mol = 127.208 kJ/mol

Now, for 37 oC,

k1 = ? at 37 oC

k2 = 7.13 x 10^-6 min-1

T1 = 37 + 273 = 310 K

T2 = 61.05 + 273 = 334.05 K

we get,

ln(7.13 x 10^-6/k1) = 127207.85/8.314[1/310 - 1/334.05]

k1 = 2.04 x 10^-7 min-1

half life at 37 oC will be thus,

t1/2 = 0.693/k = 0.693/2.04 x 10^-7 = 3395250.1 min = 2357.81 d