Ethene (C₂H₄) can be halogenated by the reaction: C₂H₄(g) + X₂(g) → C₂H₄X₂(g) where X₂ can be Cl₂, Br₂, or I₂. Use the thermodynamic data given to calculate ΔH°, ΔS°, ΔG°, and Kp for the halogenation reaction by each of the three halogens at 25 °C. 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?
Compound ΔH°_f (kJ/mol) S° (J/mol·K)
C₂H₄Cl₂(g) -129.7 308.0
C₂H₄Br₂(g) +38.3 330.6
C₂H₄I₂(g) +66.5 347.8

Verified step by step guidance

1. Identify the thermodynamic data needed for the reactants and products: ΔH°f and S° for C2H4, Cl2, Br2, I2, C2H4Cl2, C2H4Br2, and C2H4I2.
2. Calculate ΔH° for each reaction using the formula: ΔH° = ΣΔH°f(products) - ΣΔH°f(reactants).
3. Calculate ΔS° for each reaction using the formula: ΔS° = ΣS°(products) - ΣS°(reactants).
4. Calculate ΔG° for each reaction using the formula: ΔG° = ΔH° - TΔS°, where T is the temperature in Kelvin (298 K for 25 °C).
5. Determine Kp for each reaction using the relationship: ΔG° = -RTlnKp, where R is the gas constant (8.314 J/mol·K). Compare ΔG° values to assess spontaneity and discuss the effect of temperature on spontaneity.

Key Concepts

Thermodynamics

Thermodynamics is the study of energy transformations and the relationships between heat, work, and energy. In chemical reactions, it helps determine the favorability of a reaction through parameters like enthalpy (ΔH°), entropy (ΔS°), and Gibbs free energy (ΔG°). Understanding these concepts is crucial for predicting whether a reaction will occur spontaneously under given conditions.

Gibbs Free Energy

Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The change in Gibbs free energy (ΔG°) during a reaction indicates its spontaneity: if ΔG° is negative, the reaction is spontaneous; if positive, it is non-spontaneous. This concept is essential for comparing the spontaneity of different halogenation reactions.

Equilibrium Constant (Kp)

The equilibrium constant (Kp) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is influenced by the Gibbs free energy change (ΔG°) of the reaction, where a more negative ΔG° corresponds to a larger Kp, indicating a greater tendency for products to form. Understanding Kp is vital for assessing the extent of the halogenation reactions and their spontaneity.