Use the values of of ∆G°f in Appendix B to calculate the stan-dard free-energy change for the synthesis of dichloroethane from ethylene and chlorine: C2H41g2 + Cl21g2S CH2ClCH2Cl1l2 Is it possible to synthesize dichloroethane from gaseous C2H4 and Cl2, each at 25 °C and 1 atm pressure?

Verified step by step guidance

1. Identify the chemical reaction for the synthesis of dichloroethane: \( \text{C}_2\text{H}_4(g) + \text{Cl}_2(g) \rightarrow \text{CH}_2\text{ClCH}_2\text{Cl}(l) \).
2. Use the standard free energy of formation (\( \Delta G^\circ_f \)) values from Appendix B for each compound involved in the reaction: \( \text{C}_2\text{H}_4(g) \), \( \text{Cl}_2(g) \), and \( \text{CH}_2\text{ClCH}_2\text{Cl}(l) \).
3. Apply the formula for the standard free-energy change of the reaction: \( \Delta G^\circ_{\text{reaction}} = \sum \Delta G^\circ_f(\text{products}) - \sum \Delta G^\circ_f(\text{reactants}) \).
4. Substitute the \( \Delta G^\circ_f \) values into the formula to calculate \( \Delta G^\circ_{\text{reaction}} \).
5. Determine if the reaction is spontaneous by checking if \( \Delta G^\circ_{\text{reaction}} \) is negative, which would indicate that the synthesis of dichloroethane is possible under the given conditions.

Key Concepts

Standard Free Energy of Formation (∆G°f)

The standard free energy of formation (∆G°f) is the change in free energy when one mole of a compound is formed from its elements in their standard states. It provides insight into the stability of a compound and the spontaneity of a reaction. A negative ∆G°f indicates that the formation of the compound is thermodynamically favorable under standard conditions.

Gibbs Free Energy and Reaction Spontaneity

Gibbs free energy (G) is a thermodynamic potential that helps predict whether a reaction will occur spontaneously at constant temperature and pressure. The change in Gibbs free energy (∆G) for a reaction is calculated using the equation ∆G = ∆G° + RT ln(Q), where R is the gas constant, T is the temperature in Kelvin, and Q is the reaction quotient. A negative ∆G indicates that the reaction is spontaneous.

Reaction Quotient (Q) and Equilibrium

The reaction quotient (Q) is a measure of the relative concentrations of products and reactants at any point in a reaction. It is used to determine the direction in which a reaction will proceed to reach equilibrium. If Q < K (the equilibrium constant), the reaction will proceed forward to form more products; if Q > K, the reaction will shift to form more reactants.