Question

The reaction (CH3)3CBr + OH- ------->(CH3)3COH + Br- In a certain solvent is first order with respect to (CH3)3CBr and zero order with respect to OH-. In several experiments, the rate constant k was determined at different temperatures. A plot of ln(k) versus 1/T was constructed resulting in a straight line with a slope value of -1.10 X10^4 K and y-intercept of 33.5. Assume k as units of s-1. a. Determine the activation energy for this reaction b. Determine the value of the frequency factor A c. Calculate the value of k at 25 degree Celsius.

Answer 1

Rate = k[(CH3)3CBr]

Arrhenius equation: k = A exp(-Ea/RT)

ln k = (-Ea/R) x (1/T) + ln A

=> Plot of ln k vs 1/T gives straight line with slope = (-Ea/R) and y-intercept = ln A

(a) Slope = -Ea/R = -1.10 x 10^4

Activation energy Ea = 1.10 x 10^4 x R

= 1.10 x 10^4 x 8.314

= 91454 J/mol = 91.5 kJ/mol

(b) y-intercept = ln A = 33.5

Frequency factor A = exp(33.5)

= 3.53 x 10^14 s-1

(c) When T = 25 deg C = 298.15 K

ln k = -1.10 x 10^4 x 1/298.15 + 33.5 = -3.394

Rate constant k = exp(-3.394)

= 0.0335s-1 = 3.35 x 10^(-2) s-1