Which scenario results in a nonspontaneous reaction, regardless of the temperature?

In thermodynamics, the spontaneity of a reaction is often determined by the change in Gibbs free energy (∆G), which can be predicted using the equation:

[ \Delta G = \Delta H - T \Delta S ]

Where:

• ∆G is the change in Gibbs free energy,
• ∆H is the change in enthalpy,
• T is the temperature in Kelvin,
• ∆S is the change in entropy.

For a reaction to be nonspontaneous, ∆G must be greater than zero.

In the given scenario of a reaction with positive enthalpy change (+∆H) and negative entropy change (-∆S), the reaction is nonspontaneous at all temperatures. Here's why:

1. Positive ΔH: A positive enthalpy change means that the reaction absorbs heat from the surroundings, making it endothermic. This characteristic typically works against the spontaneity.

2. Negative ΔS: A negative entropy change indicates that the degree of disorder in the system decreases during the reaction. An increase in order is thermodynamically unfavorable, as systems tend to favor arrangements that maximize disorder.

When both of these factors are present—an increase in enthal