Question

In organic chemistry, cis/trans isomerism describes the relative orientation of functional groups within a molecule. Alkene containing compound but-2-ene can Interconvert from the cis isomer to the trans isomer at 80 degree C with an activation energy of 65.0 kJ/mol. At the same temperature with a nitric oxide (NO) catalyst, the activation energy decreases to 27.5 kJ/mol. Assuming the frequency factor is the same for the catalyzed and uncatalyzed reactions, how many times faster is the catalyzed reaction than the uncatalyzed reaction at 80 degree C? 3.5 Times 10^5 2.8 Times 10^-6 5.1 Times 10^8 1.0 Times 10^10 1.7 Times 10^-2

Answer 1

$lnK_1 = lnA - \frac{Ea_1}{RT}$

$lnK_2 = lnA - \frac{Ea_2}{RT}$

subtracting equation 1 from equation 2 we get

$ln K_2 - lnK_1 = \frac{1}{RT}(Ea_1 - Ea_2)$

$ln \frac{K_2}{K_1} = \frac{1}{RT}(Ea_1 - Ea_2)$

substituting the values we get

$ln \frac{K_2}{K_1} = \frac{1}{8.314 * 353}(65000 - 27500)$

$ln \frac{K_2}{K_1} = 12.7775$

$\frac{K_2}{K_1} = e^{12.7775} = 354165.35 = 3.5 * 10^{5}$

Hence the correct answer is Option A