Calculating the Energy Change for the Formation of LiCl(s) from Its Elements

Q15. Calculate the energy change for the formation of LiCl(s) from its elements in their standard states using the provided tabulated information.

Background

Topic: Thermochemistry – Born-Haber Cycle

This question tests your understanding of the Born-Haber cycle, which is used to calculate the lattice energy and overall enthalpy change for the formation of an ionic compound from its elements.

Key Terms and Formulas

• Born-Haber Cycle: A stepwise method to analyze the formation of ionic compounds using enthalpy changes.

• Lattice Energy: The energy released when ions combine to form an ionic solid.

• Ionization Energy: Energy required to remove an electron from an atom.

• Electron Affinity: Energy change when an atom gains an electron.

• Enthalpy of Formation ($\Delta H_f$): The total energy change for forming a compound from its elements.

General formula for the Born-Haber cycle:

$\Delta H_f = \text{Sublimation energy} + \text{Ionization energy} + \text{Bond dissociation energy} + \text{Electron affinity} + \text{Lattice energy}$

Step-by-Step Guidance

1. Identify the target reaction: $\text{Li}(s) + \frac{1}{2} \text{Cl}_2(g) \rightarrow \text{LiCl}(s)$

2. List all the relevant steps and their enthalpy changes from the table:

   • $\text{Li}(s) \rightarrow \text{Li}(g)$ (sublimation)

   • $\text{Li}(g) \rightarrow \text{Li}^+(g) + e^-$ (ionization energy)

   • $\frac{1}{2} \text{Cl}_2(g) \rightarrow \text{Cl}(g)$ (bond dissociation)

   • $\text{Cl}(g) + e^- \rightarrow \text{Cl}^-(g)$ (electron affinity)

   • $\text{Li}^+(g) + \text{Cl}^-(g) \rightarrow \text{LiCl}(s)$ (lattice energy)

3. Write out the enthalpy values for each step (from the table):

   • Sublimation of Li: $+159.4$ kJ/mol

   • Ionization of Li: $+520.2$ kJ/mol

   • Dissociation of Cl$_2$: $+121.7$ kJ/mol

   • Electron affinity of Cl: $-348.6$ kJ/mol

   • Lattice energy: $-853$ kJ/mol

4. Set up the sum of all these enthalpy changes to find the overall $\Delta H_f$ for the formation of LiCl(s):

   $\Delta H_f = (+159.4) + (+520.2) + (+121.7) + (-348.6) + (-853)$

Try solving on your own before revealing the answer!

Final Answer: -400.3 kJ/mol

$\Delta H_f = (+159.4) + (+520.2) + (+121.7) + (-348.6) + (-853) = -400.3$ kJ/mol$

This value represents the enthalpy change for the formation of LiCl(s) from its elements in their standard states, calculated using the Born-Haber cycle.