Question

Isopropenyl allyl ether in the vapor state isomerizes to allyl acetone accord-ing to a first-order rate equation. The following equation gives the influence of tem-perature on the rate constant (in s-1). k = 5.4 x 1011 e-123,000/RT where the activation energy is expressed in J mol-1. At 150 ° C, how long will it take to build up a partial pressure of 0.395 bar of allyl acetone, starting with 1 bar of isopropenyl allyl ether?

Answer 1

we know that for the first order kinetics

we know that for the first order kinetics C = Coe^-kt where C = concentration at any time t Co = initial concentration k = rate Constant, putting the value of R = 8.34 J/mol.K and T = 423 K k = 3.89 times 10^(-4) now we know that using ideal gas law, C = p/RT where p = partial pressure so the concentration equation changes to, P = Poe^-kt where p = initial pressure of the reactant = 1 bar po = partial pressure of reactant at time t = (1 - 0.395) = 0.605 bar putting the values we get t = 1291.842 sec

where C = concentration at any time t

Co = initial concentration

k = rate Constant , putting the value of R = 8.34 J/mol.K and T = 423 K

k= 3.89 X 10^(-4)

now we know that using ideal gas law, C = p/RT

where p= partial pressure

so the concentration equation changes to ,

where p = initial pressure of the reactant = 1 bar

po = partial pressure of reactant at time t = (1 - 0.395) = 0.605 bar

putting the values we get t= 1291.842 sec