The accompanying diagram shows how ΔH (red line) and T ΔS (blue line) change with temperature fo

step 1 For option A, we are given with the temperature T equals 300 Kelvin. The system is at equilibriu

The accompanying diagram shows how ΔH (red line) and T ΔS...

The accompanying diagram shows how $\Delta H$ (red line) and $T \Delta S$ (blue line) change with temperature for a hypothetical reaction. (a) What is the significance of the point at $300 \mathrm{~K}$, where $\Delta H$ and $T \Delta S$ are equal? (b) In what temperature range is this reaction spontaneous? [Section 19.6$]$

Key Concepts

Gibbs Free Energy

Gibbs free energy, defined as ?G = ?H ? T?S, is a central thermodynamic function that determines whether a reaction will occur spontaneously at a given temperature. Its value incorporates both the enthalpy change (?H) and the entropy change multiplied by temperature (T?S), and a negative ?G indicates that the reaction is spontaneous under constant temperature and pressure.

Temperature Dependence of Thermodynamic Terms

Both ?H and T?S can vary with temperature. In many reactions, while ?H may remain relatively constant or change slowly with temperature, the term T?S increases linearly with temperature. This temperature dependence is crucial in determining at what temperature the entropy term will overcome the enthalpy term, thereby changing the spontaneity of the reaction.

Equilibrium Temperature (Transition Point)

The point where ?H equals T?S corresponds to the temperature at which the Gibbs free energy change (?G) equals zero. This equilibrium or transition temperature marks the boundary between non?spontaneous and spontaneous behavior; at this temperature, the driving forces for the forward and reverse reactions are balanced.

Reaction Spontaneity Criterion

The reaction is spontaneous when ?G is negative, meaning that T?S must exceed ?H. Therefore, understanding the relation between ?H and T?S as functions of temperature helps in determining the temperature range over which a reaction is spontaneous, specifically above or below the transition temperature depending on the signs of ?H and ?S.

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