For the gas phase decomposition of t-butyl alcohol , the rate constant has been
ID: 1020580 • Letter: F
Question
For the gas phase decomposition of t-butyl alcohol,
the rate constant has been determined at several temperatures. When ln k in s-1 is plotted against the reciprocal of the Kelvin temperature, the resulting linear plot has a slope of -3.30×104 K and a y-intercept of 33.8.
The activation energy for the gas phase decomposition of t-butyl alcohol is kJ/mol?
Now lets say, For the gas phase decomposition of acetic anhydride,
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 -1.73×104 K and a y-intercept of 27.6.
The value of the rate constant for the gas phase decomposition of acetic anhydride at 496 K is ?
Explanation / Answer
Gas phase decomposition of t-butyl alcohol:
(CH3)3C-OH -----------> (CH3)2C=CH2 + H2O
A plot on ln k (in s-1) is plotted against 1/T where T is the Kelvin temperature, the plot has a slope of (-3.30*104)K and the y-intercept is 33.8.
We know that
k = Aexp(-Ea/RT) where A is the Arrhenius constant and R is the gas constant; this is the Arrhenius equation. Taking logarithm on both sides,
ln k = ln A – Ea/RT = ln A – (Ea/R).1/T
Re-arranging,
ln k = (-Ea/R).1/T + ln A ……..(1)
This equation is of the form of a straight line y = mx + c where m is the slope and c is the y-intercept.
Our present problem follows the same y = mx + c equation. We are given m = -3.30*104 K and ln A = 33.8
Now, m = (-Ea/R)
or, (-3.30*104 K) = (-Ea/R)
===> Ea = (3.30*104 K)*R = (3.30*104 K)*(8.314 J/mol.K) = 274,362 J/mol = 274.362 kJ/mol (ans)
Gas phase decomposition of acetic anhydride:
As per equation (1) above, (-Ea/R) = (-1.73*104 K); therefore,
Ea = (1.73*104 K)*R = (1.73*104 K)*(8.314 J/mol.K) = 143,832.2 J/mol = 143.8322 kJ/mol.
Also, ln A = 27.6
====> A = e27.6 = 9.6945*1011
Now, T = 496 K; therefore, (-Ea/RT) (s-1) = (-1.73*104 K/496 K) = -34.879 and exp(-Ea/RT) = e-34.789 = 7.786*10-16
Therefore, at 496 K, k =Aexp(-Ea/RT) = (9.6945*1011)*(7.786*10-16) s-1 = 7.548*10-4 s-1 7.5*10-4 s-1 (ans)