For the gas phase isomerization of cis-cyanostyrene, cis-c6h5ch=chc --> ntrans-c6h5ch=chcn 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 -2.32×104 k and a y-intercept of 26.7. the activation energy for the gas phase isomerization of cis-cyanostyrene is kj/mol.

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:

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:

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: