A certain constant-pressure reaction is nonspontaneous at 45^∘ C. The entropy change for the rea

step 1 If we know some thermodynamic properties about a reaction, we might be able to tell some informa

A certain constant-pressure reaction is nonspontaneous at...

A certain constant-pressure reaction is nonspontaneous at $45^{\circ} \mathrm{C}$. The entropy change for the reaction is $72 \mathrm{~J} / \mathrm{K}$. What can you conclude about the sign and magnitude of $\Delta H ?$

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Key Concepts

Gibbs Free Energy

The Gibbs free energy (?G) is a key thermodynamic quantity that determines the spontaneity of a reaction under constant pressure and temperature conditions. Its relationship is defined by the equation ?G = ?H - T?S, where a positive ?G indicates that the process is nonspontaneous, and a negative ?G signifies that the process is spontaneous.

Enthalpy and Entropy Relationship

Enthalpy (?H) is the heat change at constant pressure, and entropy (?S) reflects the degree of disorder or randomness. In the context of the Gibbs free energy equation, a positive ?S makes the T?S term subtract from ?H. However, if the overall ?G remains positive (nonspontaneous reaction), it implies that the positive ?H (endothermic characteristic) is large enough to outweigh the cooling effect of T?S, thereby preventing spontaneity.

Temperature Dependence of Spontaneity

Temperature influences the weight of the entropy term (T?S) in the Gibbs free energy equation. At higher temperatures, the T?S term has a more pronounced effect on the value of ?G. In a situation where the reaction is nonspontaneous at a given temperature and shows an increase in entropy, the large positive ?H must compensate sufficiently to keep ?G positive, indicating that temperature is a critical factor in balancing the ?H and ?S contributions.

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