Question

Given the following information: Heat of sublimation of \(\operatorname{Li}(s)=166 \mathrm{~kJ} / \mathrm{mol}\) Bond energy of \(\mathrm{HCl}=427 \mathrm{~kJ} / \mathrm{mol}\) Ionization energy of \(\operatorname{Li}(g)=520 . \mathrm{kJ} / \mathrm{mol}\) Electron affinity of \(\mathrm{Cl}(g)=-349 \mathrm{~kJ} / \mathrm{mol}\) Lattice energy of \(\operatorname{LiCl}(s)=-829 \mathrm{~kJ} / \mathrm{mol}\) Bond energy of \(\mathrm{H}_{2}=432 \mathrm{~kJ} / \mathrm{mol}\) Calculate the net change in energy for the following reaction: $$ 2 \mathrm{Li}(s)+2 \mathrm{HCl}(g) \longrightarrow 2 \mathrm{LiCl}(s)+\mathrm{H}_{2}(g) $$

Short answer

The net change in energy for the given reaction is \(3276\text{ kJ}\).

Step-by-step solution

Identify the energy values involved in the reaction

We will first list all the values provided in the exercise for ease of reference. - Heat of sublimation of Li(s): 166 kJ/mol - Bond energy of HCl: 427 kJ/mol - Ionization energy of Li(g): 520 kJ/mol - Electron affinity of Cl(g): -349 kJ/mol - Lattice energy of LiCl(s): -829 kJ/mol - Bond energy of H₂: 432 kJ/mol

Determine energy changes for bond breaking

In the given reaction, bonds in solid lithium and HCl need to be broken. Let's calculate the energy required to break these bonds: Energy to break 2 Li(s) bonds: \(2 \times 166\text{ kJ/mol} = 332\text{ kJ}\) Energy to break 2 HCl bonds: \(2 \times 427\text{ kJ/mol} = 854\text{ kJ}\) Total energy required for bond breaking: \(332\text{ kJ} + 854\text{ kJ} = 1186\text{ kJ}\)

Determine energy changes for bond formation

In the given reaction, new bonds are formed in LiCl and H₂. Let's calculate the energy released during the formation of these bonds: Energy released in the formation of 2 LiCl bonds: \(2 \times (- 829\text{ kJ/mol}) = - 1658\text{ kJ}\) Energy released in the formation of 1 H₂ bond: \(-432\text{ kJ/mol}\) Total energy released for bond formation: \(-1658\text{ kJ} - 432\text{ kJ} = -2090\text{ kJ}\)

Calculate the net change in energy for the reaction

Now, we will calculate the net change in energy by subtracting the energy released for bond formation from the energy required for bond breaking: Net change in energy = Energy required for bond breaking - Energy released for bond formation \(= 1186\text{ kJ} - (- 2090\text{ kJ}) = 1186\text{ kJ} + 2090\text{ kJ} = 3276\text{ kJ}\) So, the net change in energy for the given reaction is \(3276\text{ kJ}\).