Question

Consider a 5.000M solution of the hypotherical compound R. Its decompostition is a second-order reaction and its activation energy is 57.6 kj/mole. At 759^oC, the half-life of the 5.000M solution is 8.49h. What is the half-life of the same solution at 700^oC (3 significant figures)?

Answer 1

Answer– We are given, T1 = 759^oC = 759 + 273.15 = 1032.15 K

T2 = 700+273.15 = 973.15 K, t1 = 8.49 , t2 = ?

Ea = 57.6 kJ/mol

Intergraded Arrhenius equation and need to arrange for half life

ln t2/t1 = - Ea / R *(1/T1-1/T2)

ln t2 / 8.49 = - 5.76*10⁴ J.mol^-1 / 8.314 J/mol.K * (1/1032.15 – 1/973.15)

ln t2 / 8.49 = 0.407

so taking antiln from both side

t2/8.49 hr = 1.50

t2 = 1.50 * 8.49 hr

    = 12.8 hrs

so the half-life of the same solution at 700^oC is 12.8 hrs