Question

Which of the following reactions will be spontaneous at any temperature? (a) \(\Delta H=+, \Delta S=-\) (b) \(\Delta H=-, \Delta S=-\) (c) \(\Delta H=+, \Delta S=+\) (d) \(\Delta H=-, \Delta S=+\)

Short answer

Reaction (d) is spontaneous at any temperature.

Step-by-step solution

Understand Gibbs Free Energy Equation

To determine if a reaction is spontaneous, use the Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \). For a reaction to be spontaneous at any temperature, \( \Delta G \) must always be negative.

Analyze Each Option

Examine each choice based on \( \Delta H \) (enthalpy) and \( \Delta S \) (entropy): (a) \( \Delta H=+, \Delta S=-\): Since both terms are non-favorable, \( \Delta G \) cannot be negative, making the reaction non-spontaneous.(b) \( \Delta H=-, \Delta S=-\): Here \( \Delta H \) is favorable, but \( -T \Delta S \) contributes positively to \( \Delta G \). Therefore, it isn't always spontaneous.(c) \( \Delta H=+, \Delta S=+\): Here \( T \Delta S \) is favorable, but \( \Delta H \) is not, so temperature needs to be a factor; it isn't always spontaneous at any temperature.(d) \( \Delta H=-, \Delta S=+\): Both terms contribute to \( \Delta G \) being negative, ensuring spontaneity at any temperature.

Determine the Spontaneity

From analyzing each option, only option (d) with \( \Delta H=- \) and \( \Delta S=+ \) causes \( \Delta G \) to be negative for all temperature values, confirming its spontaneity at any temperature.

Key concepts

Enthalpy

Enthalpy, represented by the symbol \( \Delta H \), reflects the heat content of a system under constant pressure. It provides insights into the energy absorbed or released during a chemical reaction. When discussing enthalpy, we often talk about exothermic and endothermic reactions.
- **Exothermic reactions** have a negative \( \Delta H \), which means they release energy into the surroundings. These reactions reduce the enthalpy of the system.
- **Endothermic reactions** possess a positive \( \Delta H \), indicating that they absorb energy from their surroundings. This leads to an increase in the system's enthalpy.
In the context of spontaneity, a negative \( \Delta H \) is generally favorable as it naturally releases energy, potentially contributing to negative Gibbs Free Energy \( \Delta G \). Thus, reactions with a negative \( \Delta H \) tend towards being spontaneous, especially when combined with favorable conditions for entropy.

Entropy

Entropy, represented by \( \Delta S \), is a measure of the disorder or randomness in a system. In nature, systems tend to move towards higher entropy, promoting the spread of energy and matter.
- When \( \Delta S \) is positive, a system gains entropy, meaning it becomes more disordered or random.
- Conversely, a negative \( \Delta S \) indicates a decrease in entropy, signifying a move towards a more ordered state.
Changes in entropy are also crucial in determining spontaneity because the term \( T \Delta S \) directly impacts \( \Delta G \) in the Gibbs Free Energy equation: \( \Delta G = \Delta H - T \Delta S \).

• If \( \Delta S \) is positive, the \( T \Delta S \) term becomes negative, aiding the spontaneity of the reaction.
• If \( \Delta S \) is negative, it works against the spontaneity by making \( \Delta G \) more positive.

Understanding entropy's role helps predict whether a process will naturally progress toward a more probable, disordered state.

Spontaneity

The concept of spontaneity in chemistry involves predicting whether a chemical reaction will occur without external influence. A spontaneous process is one that takes place naturally under given conditions, and it's largely determined by the sign of Gibbs Free Energy change \( \Delta G \).
For a reaction to be spontaneous at any temperature, \( \Delta G \) needs to be negative. This occurs when:
- The reaction is exothermic (\( \Delta H \) is negative), which releases energy.
- The entropy change is positive (\( \Delta S \) is positive), increasing disorder.
Using the Gibbs equation \( \Delta G = \Delta H - T \Delta S \):

• A negative \( \Delta H \) and positive \( \Delta S \) will always favor a negative \( \Delta G \), ensuring the process is spontaneous at all temperatures, as seen in reaction type (d) from the exercise.
• Other combinations of \( \Delta H \) and \( \Delta S \) may yield spontaneous conditions only at certain temperatures, or not at all.

Recognizing these patterns is essential for anticipating the natural progression of chemical systems.