A reaction has ΔH°rxn = -112 kJ and ΔS°rxn = 354 J/K. At what temperature is the change in entropy for the reaction equal to the change in entropy for the surroundings?

Verified step by step guidance

1. Identify the relationship between the change in entropy for the system (ΔS°_rxn) and the surroundings. The change in entropy for the surroundings (ΔS_surroundings) is given by the formula ΔS_surroundings = -ΔH°_rxn / T.
2. Set the change in entropy for the system equal to the change in entropy for the surroundings: ΔS°_rxn = -ΔH°_rxn / T.
3. Rearrange the equation to solve for the temperature (T): T = -ΔH°_rxn / ΔS°_rxn.
4. Substitute the given values into the equation. Remember to convert ΔH°_rxn from kJ to J by multiplying by 1000, so ΔH°_rxn = -112,000 J.
5. Calculate the temperature (T) using the rearranged equation with the substituted values.

Key Concepts

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. It is defined by the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates a spontaneous process, which is crucial for understanding the conditions under which a reaction will occur.

Entropy and the Second Law of Thermodynamics

Entropy (S) is a measure of the disorder or randomness in a system. The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time, and processes occur in the direction that increases the total entropy. In the context of reactions, the change in entropy for the surroundings can be calculated using the formula ΔS_surroundings = -ΔH/T, which relates the heat exchanged with the surroundings to the temperature.

Temperature and its Role in Thermodynamics

Temperature (T) is a measure of the average kinetic energy of the particles in a substance and plays a critical role in thermodynamic equations. In the context of the question, it is essential to determine the temperature at which the change in entropy for the reaction equals the change in entropy for the surroundings. This relationship is pivotal in understanding how temperature influences the spontaneity and direction of chemical reactions.