H₂ reacts with the halogens (X₂) according to the reaction: H₂(g) + X₂(g) → 2 HX(g) where X₂ can be Cl₂, Br₂, or I₂. Use the thermodynamic data in Appendix IIB to calculate ΔH°, ΔS°, ΔG°, and K_p for the reaction between hydrogen and each of the three halogens. Which reaction is most spontaneous? Least spontaneous? What is the main factor responsible for the difference in the spontaneity of the three reactions? Does higher temperature make the reactions more spontaneous or less spontaneous?

Verified step by step guidance

1. Identify the thermodynamic data needed for each reaction: \( \Delta H^\circ_f \), \( \Delta S^\circ \), and \( \Delta G^\circ_f \) for each reactant and product from Appendix IIB.
2. Calculate \( \Delta H^\circ \) for each reaction using the formula: \( \Delta H^\circ = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants}) \).
3. Calculate \( \Delta S^\circ \) for each reaction using the formula: \( \Delta S^\circ = \sum \Delta S^\circ(\text{products}) - \sum \Delta S^\circ(\text{reactants}) \).
4. Calculate \( \Delta G^\circ \) for each reaction using the formula: \( \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \), where \( T \) is the temperature in Kelvin.
5. Determine \( K_p \) for each reaction using the relationship: \( \Delta G^\circ = -RT \ln K_p \), and compare the spontaneity of the reactions by analyzing \( \Delta G^\circ \) and \( K_p \).