91Ó°ÊÓ

Gibbs free energy, denoted as \( \Delta G \), is a thermodynamic quantity crucial for determining the spontaneity of a reaction. It involves the balance of enthalpy, entropy, and temperature to predict whether a reaction will proceed without external intervention. The formula for Gibbs free energy change under standard conditions is:\[ \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \]where:

• \( \Delta H^\circ \) is the change in enthalpy,
• \( T \) is the temperature in Kelvin,
• \( \Delta S^\circ \) is the change in entropy.

To relate Gibbs free energy specifically to reaction conditions, we often use the formula \( \Delta G = \Delta G^\circ + RT \ln Q \), where \( Q \) is the reaction quotient. However, at equilibrium, this simplifies to \( \Delta G^\circ = -RT \ln K \), with \( K \) being the equilibrium constant. This is pertinent to the exercise, as \( \Delta G \), \( T \), and \( K \) remain constant, indicating that the Gibbs free energy does not change during the reaction.

Reaction kinetics deals with the speeds or rates at which chemical reactions occur. The decomposition of hydrogen sulfide (\( \mathrm{H}_2\mathrm{S} \)) into hydrogen (\( \mathrm{H}_2 \)) and sulfur (\( \mathrm{S}_2 \)) represents a reaction whose kinetics are essential in understanding how quickly equilibrium is reached.

• Kinetic factors such as temperature, concentration, and presence of catalysts can influence a reaction rate.
• The rate law expression, which is derived experimentally, details how these factors affect the speed of the reaction.

Knowing that the reaction temperature is constant, it's clear that kinetic parameters will stay uniform, keeping the rate steady. This kinetic stability supports the condition that the reaction's Gibbs free energy will remain unchanged at equilibrium.

A decomposition reaction involves a single compound breaking down into two or more simpler substances. In the given exercise, \( 2 \mathrm{H}_2\mathrm{S} \rightarrow 2 \mathrm{H}_2 + \mathrm{S}_2 \) represents such a decomposition.

• Decomposition reactions are typically endothermic, requiring energy input to break the chemical bonds.
• These reactions are often influenced by factors such as heat, light, or electricity.

At 1000 K, the decomposition of \( \mathrm{H}_2\mathrm{S} \) progresses under thermal conditions, driving the reaction forward until equilibrium is achieved. Monitoring the decomposition helps us understand why equilibrium constants like \( K_c \) do not change once the reaction stabilizes.

Chemical equilibrium occurs when the forward and reverse reactions occur at the same rate, resulting in the concentration of reactants and products remaining constant over time. For the decomposition of \( \mathrm{H}_2\mathrm{S} \), when equilibrium is reached, the rate of formation of \( \mathrm{H}_2 \) and \( \mathrm{S}_2 \) equals the rate of their recombination to form \( \mathrm{H}_2\mathrm{S} \).

• At equilibrium, the reaction quotient \( Q \) equals the equilibrium constant \( K \), indicating a balance in the reaction.
• This state of balance means that thermodynamic parameters such as Gibbs free energy are steady.

The concept of equilibrium is crucial for predicting the outcome and positions of chemical reactions in closed systems at constant temperature and pressure, as shown by the constancy of \( \Delta G^\circ \) in the given problem.