The halflife for the reaction below was determined to be 214

The half-life for the reaction below was determined to be 2.14 × 104 s at 800 K. The value of the half-life is independent of the inital concentration of N2O present. The activation energy of the reaction is 226.00 kJ/mol. N2O (g) (arrow) N2(g)+O(g) What would be the half-life at 950.21 K? in s

Solution

half-life is independent of the inital concentration of N2O present

It is first order reaction

t1/2 = 0.6932/k

Rate constant k = 0.6932/2.14 × 10^4 s

k = 3.239 x 10^-5 s-1

Now calculate the rate constant at 950.21 K

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

ln (k2/3.239 x 10^-5) = (226*1000/8.314)*(1/800 - 1/950.21)

ln (k2/3.239 x 10^-5) = 5.3714

(k2/3.239 x 10^-5) = 215.163

k2 = 0.006969 s-1

half-life at 950.21 K

t1/2 = 0.6932/k2

= 0.6932/0.006969

= 99.466 s