(a) Show by suitable integration of the first order rate equation that the half
ID: 509022 • Letter: #
Question
(a) Show by suitable integration of the first order rate equation that the half life tau_1/2 is independent of the initial reactant concentration C_0 and is given by tau_1/2 = ln 2/k where k denotes the first order rate constant. What are the units of k? (b) The Arrhenius parameters which define the Arrhenius equation for the decomposition reaction of Cyclobutane C_4H_8(g) rightarrow 2C_2H_4 (g), are In(A/s^-1) = 15.6 and E_A = 261 kJmol^-1. Determine the ratio of the half lives of cyclobutane at the temperatures 293 K and 773 K.Explanation / Answer
1. for 1st order reaction, -dCA/dt= KCA, CA= concentration of reactant at any time , t
K= rate constant
when integrated with the condition at t=0, CA=CAO( initial concentration of A)
lnCA= lnCAO-Kt
half life is defined as the time required for the concentration to drop to 50% of its initial value
CA=CAO/2
ln(CAO/2)= lnCAO-K* half life
K* half life= lnCAO-ln(CAO/2)
K* half life= ln2
half life= 0.693/K
b) lnK= lnA- Ea/RT
K= rate constant, lnA= 15.6, Ea= 261 KJ/mol= 261*1000 J/mole
at T1= 293 K
lnK1= ln(15.6)- 261*1000/(8.314*293)
at T2= 773K
lnK2= ln(15.6) -261*1000/(8.314*773)
lnK2-lnK1= {261*1000/8.314}(1/293-1/773)
ln(K2/K1)= 66.53
K2/K1= 7.8*1028
but K= 0.693/half life
0.693/t1/0.693/t2= 7.8*1028
t1 and t2 are half lifes fot reaction at 293K and 773K respectively
t2/t1= 7.8*1028
t1/t2= 1.3*10-29
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