Question

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.

Answer 1

The activation energy for the gas phase isomerization of cis-cyanostyrene is 193 kJ/mol.

Step-by-step explanation:

The activation energy for the gas phase isomerization of cis-cyanostyrene can be calculated using the slope of the linear plot of ln k in s-1 against the reciprocal of the Kelvin temperature. The activation energy is given by the formula:

Ea = -slope * R

where Ea is the activation energy, slope is the slope of the linear plot (in this case, -2.32×10^4 K), and R is the universal gas constant (8.314 J/Kmol).

Substituting the values:

Ea = -(-2.32×10^4 K) * 8.314 J/Kmol

Ea = 1.93×10^5 J/mol

Converting the activation energy from J/mol to kJ/mol:

Ea = 1.93×10^5 J/mol * (1 kJ/1000 J)

Ea = 193 kJ/mol

Answer 2

The activation energy for the gas phase isomerization of cis-cyanostyrene is 193 kJ/mol.

Step-by-step explanation:

The relation between the rate constant (k) and the absolute temperature (T) is given by the Arrhenius equation:

`k = A.e^(-Ea/R.T)`

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:

`ln k = ln A -(Ea)/(R).(1)/(T)`

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:

`(-Ea)/(R) = -2.32 * 10^(4) K\\Ea = -2.32 * 10^(4) K * -R\\Ea = -2.32 * 10^(4) K * (-8.314 * 10^(-3) (kJ)/(K.mol))\\Ea = 193kJ/mol`