Arrhenius Equation Calculations

Question

The activation energy for the gas phase isomerization of cis-1,2-diphenylethene is 179 kJ.

cis-C₆H₅CH=CHC₆H₅trans-C₆H₅CH=CHC₆H₅

The rate constant at 577 K is 3.62×10^-4 /s. The rate constant will be 4.20×10^-3 /s at ______  K.

Answer 1

This question is asking you to find the temperature at which the rate constant (k) = 4.20x10^-3s^-1

The Arrhenius equation can be used to find this value...

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

k1 = 3.62x10^-4 s^-1

k2 = 4.20x10^-3 s^-1

Ea = 179 kJ/mol = 179,000 J/mol (note to change units to match those of R)

R = 8.314 J/Kmol

T1 = 577K

T2 = ?

ln (4.20x10^-3 / 3.62x10^-4) = -179000/8.314 (1/T2 - 1/577)

2.45 = -21530(1/T2 - 0.00173)

2.45 = -21530/T2 + 37.31

-34.86 = -21530/T2

T2 = 618K