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 enthalpy change for the formation of an ionic compound from its elements. You will use several steps involving ionization energy, electron affinity, and lattice energy.

Key Terms and Formulas

• Born-Haber Cycle: A series of steps that breaks down the formation of an ionic solid into individual processes.

• Lattice Energy: The energy released when ions come together to form a solid.

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

• Electron Affinity: The energy change when an atom gains an electron.

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

Step-by-Step Guidance

1. Write out the overall reaction: $\text{Li(s) + \frac{1}{2} Cl_2(g) \rightarrow LiCl(s)}$

2. Identify the individual steps and their associated enthalpy changes from the table:

   • Li(s) → Li(g): $+159.4$ kJ/mol

   • Li(g) → Li+(g) + e-: $+520.2$ kJ/mol

   • 1/2 Cl2(g) → Cl(g): $+121.7$ kJ/mol

   • Cl(g) + e- → Cl-(g): $-348.6$ kJ/mol

   • Li+(g) + Cl-(g) → LiCl(s): $-853$ kJ/mol

3. Arrange the steps in the correct order to form LiCl(s) from Li(s) and Cl2(g). Each step represents a physical or chemical process in the Born-Haber cycle.

4. Add up the enthalpy changes for each step to set up the calculation for the overall energy change:

   $\Delta H_f = \text{(Li(s) → Li(g))} + \text{(Li(g) → Li^+(g) + e^-)} + \text{(1/2 Cl_2(g) → Cl(g))} + \text{(Cl(g) + e^- → Cl^-(g))} + \text{(Li^+(g) + Cl^-(g) → LiCl(s))}$

Try solving on your own before revealing the answer!

Final Answer: -400.3 kJ/mol

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

By summing the enthalpy changes for each step, you find the overall energy change for the formation of LiCl(s) from its elements. The negative value indicates that the process is exothermic.