Answer:
The activation energy for the gas phase isomerization of cis-cyanostyrene is 193 kJ/mol.
Explanation:
The relation between the rate constant (k) and the absolute temperature (T) is given by the Arrhenius equation:
[tex]k = A.e^{-Ea/R.T}[/tex]
where,
A is a preexponential factor
Ea is the activation energy
R is the ideal gas constant
T is the absolute temperature
This expression can be re-written like:
[tex]ln k = ln A -\frac{Ea}{R}.\frac{1}{T}[/tex]
The plot of ln k against 1/T gives a linear plot where ln A is the intercept and -Ea/R is the slope.
Since we know the slope is -2.32 × 10⁴ K, we can find Ea:
[tex]\frac{-Ea}{R} = -2.32 \times 10^{4} K\\Ea = -2.32 \times 10^{4} K \times -R\\Ea = -2.32 \times 10^{4} K \times (-8.314 \times 10^{-3} \frac{kJ}{K.mol})\\Ea = 193kJ/mol[/tex]
