For the endothermic gaseous reaction \text{PCl}_5(g) \rightarrow \text{PCl}_3(g) + \text{C… — JAMB UTME

For the endothermic gaseous reaction $\text{PCl}_5(g) \rightarrow \text{PCl}_3(g) + \text{Cl}_2(g)$ , the standard enthalpy change ( $\Delta H$ ) is $+92\text{ kJ mol}^{-1}$ . The activation energy for the reverse reaction without a catalyst is $58\text{ kJ mol}^{-1}$ . If a catalyst is introduced that lowers the activation energy of the forward reaction by $35\text{ kJ mol}^{-1}$ , what is the activation energy for the catalyzed forward reaction in $\text{kJ mol}^{-1}$ ?

Answer: 115 kJ mol^{-1}

Answer

The activation energy for the catalyzed forward reaction is

115\text{ kJ mol}^{-1}

For an endothermic reaction, the enthalpy change is the difference between the forward and reverse activation energies:

\Delta H = E_{a,\text{forward}} - E_{a,\text{reverse}}

. Rearranging gives the uncatalyzed forward activation energy as

92\text{ kJ mol}^{-1} + 58\text{ kJ mol}^{-1} = 150\text{ kJ mol}^{-1}

. A catalyst lowers the activation energy by

35\text{ kJ mol}^{-1}

, resulting in a catalyzed forward activation energy of

150\text{ kJ mol}^{-1} - 35\text{ kJ mol}^{-1} = 115\text{ kJ mol}^{-1}

Step-by-Step Solution

Determine the activation energy of the uncatalyzed forward reaction

E_{a,\text{forward, uncatalyzed}} = 150\text{ kJ mol}^{-1}

For an endothermic reaction,

\Delta H = E_{a,\text{forward}} - E_{a,\text{reverse}}

. Substituting

\Delta H = +92\text{ kJ mol}^{-1}

and

E_{a,\text{reverse}} = 58\text{ kJ mol}^{-1}

gives

E_{a,\text{forward, uncatalyzed}} = 92 + 58 = 150\text{ kJ mol}^{-1}

Apply the effect of the catalyst on the forward activation energy

E_{a,\text{forward, catalyzed}} = 115\text{ kJ mol}^{-1}

The catalyst lowers the energy barrier for the forward reaction by

35\text{ kJ mol}^{-1}

, so

E_{a,\text{forward, catalyzed}} = 150 - 35 = 115\text{ kJ mol}^{-1}

Key Concept

Calculation of activation energy for catalyzed and uncatalyzed reactions using enthalpy change and reverse activation energy on an energy profile.

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