Question

The activation energy for the gas phase isomerization of vinyl allyl ether is 128 kJ.

CH2CH-O-CH2CH=CH2----------->CH2CHCH2CH2CHO

The rate constant at 450 K is 2.81×10-4 /s.

The rate constant will be 2.24×10-3 /s at ____________ K.

Answer 1

From Ahrrenius equation;

K1 = A*exp(-Ea/(RT1))

K2 = A*exp(-Ea/(RT2))

Note that A and Ea are the same, they do not depend on Temperature ( in the range fo temperature given)

Then

Divide 2 and 1

K2/K1 = A/A*exp(-Ea/(RT2)) / exp(-Ea/(RT1))

Linearize:

ln(K2/K1) = -Ea/R*(1/T2-1/T1)

get rid of negative sign

ln(K2/K1) = Ea/R*(1/T1-1/T2)

ln((2.24*10^-3)/(2.81*10^-4)) = 128000/8.314*(1/450 -1 /(T2))

ln((2.24*10^-3)/(2.81*10^-4))/128000 *8.314 - 1/450 = -1/T2

T2 = (0.0020873^-1)

T2 = 479.087 K