Ea or k from Arrhenius Plot Info

Question

For the gas phase isomerization of cis-2-butene,

cis-CH₃CH=CHCH₃trans-CH₃CH=CHCH₃

the rate constant in s^-1 has been determined at several temperatures. When ln k is plotted against the reciprocal of the Kelvin temperature, the resulting linear plot has a slope of -9.06×10³ K and a y-intercept of 0.700.

The value of the rate constant for the gas phase isomerization of cis-2-butene at 1.19×10³ K is ______  s^-1.

(Enter your answer to one significant figure.)

Answer 1

slope = -Ea/R

-9.06x10³K = -Ea/8.314 J/Kmol

Ea = 75,325 J/mol = 75.3 kJ/mol

Arrhenius equation :

ln k = -Ea/RT + lnA

From the y intercept, we have ln A = 0.700, and A = -0.36

Plugging in the values and solving for k, we have...

ln k = -75,325 J/mol / (8.314 J/Kmol)(1.19x10³K) - 0.36

ln k = -75,325 J/mol / 9894 J/mol) - 0.36

ln k = -7.6 -0.36 = -7.97

k = 0.00035 = 4x10^-4 s^-1 (1 sig. fig.)