Problem 7 - Chemistry in 30 days

Question

In which case, a spontaneous reaction is possible at any temperature ? (a) \(\Delta H-v e, \Delta \bar{S}+v e\) (b) \(\Delta H-v e, \Delta S-v e\) (c) \(\Delta H+\) ve, \(\Delta S+v e\) (d) none of the cases

Step-by-Step Solution

Answer

Option (a) is suitable as it ensures spontaneity at any temperature.

Step 1: Understand Spontaneity Conditions

To determine when a reaction is spontaneous at any temperature, recall that a spontaneous reaction occurs when \[\Delta G = \Delta H - T \Delta S < 0\]For any temperature, this inequality must be satisfied.

Step 2: Evaluate Each Case

Let's analyze each option:- **Option (a):** \( \Delta H < 0, \Delta S > 0 \) - Here, the negative \( \Delta H \) term is favored and \( \Delta S \) is positive, making \( T \Delta S \) positive, which ensures \( \Delta G < 0 \) for any \( T \).- **Option (b):** \( \Delta H < 0, \Delta S < 0 \) - Both \( \Delta H \) and \( \Delta S \) are negative, and the term \( T \Delta S \) will be positive if \( T \) is high enough. Not spontaneous at all temperatures.- **Option (c):** \( \Delta H > 0, \Delta S > 0 \) - \( \Delta G = \Delta H - T \Delta S \) depends on \( T \) being sufficiently high to outweigh \( \Delta H \). Not spontaneous at all temperatures.

Step 3: Identify the Suitable Option

Since only option (a) allows \( \Delta G < 0 \) regardless of the temperature, it is the only option where the reaction is spontaneous at any temperature. In this case, the exothermic nature and positive entropy change both contribute to spontaneity.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy, often represented as \( \Delta G \), is a crucial concept in understanding chemical reactions. It provides a criterion to predict whether a process will occur spontaneously. The equation for Gibbs Free Energy change is:\[ \Delta G = \Delta H - T \Delta S \]Here's a breakdown of its components:

• \( \Delta H \) is the change in enthalpy, or heat content, of the system.
• \( T \) is the absolute temperature measured in Kelvin.
• \( \Delta S \) is the change in entropy, or the disorder of the system.

A reaction is spontaneous if \( \Delta G < 0 \). This means that the total energy required to drive the reaction is released, favoring the reaction's progress.
If \( \Delta G = 0 \), the system is at equilibrium, and if \( \Delta G > 0 \), the reaction is non-spontaneous under the given conditions.

Entropy

Entropy, denoted as \( \Delta S \), is a measure of disorder or randomness in a system. It reflects the number of ways a system's components can be arranged.
As entropy increases, the system becomes more disordered. In thermodynamics, it's important because:

• Spontaneous processes often lead to an increase in the overall entropy of the universe.
• For a process to be spontaneous, the entropy change \( \Delta S \) of the system must contribute positively to \( \Delta G = \Delta H - T \Delta S \).

This means even if a reaction itself lowers entropy, it might still be spontaneous if enough energy is released (negative \( \Delta H \)) or if the surroundings greatly increase in entropy. Hence, understanding \( \Delta S \) helps predict how a reaction progresses.

Enthalpy

Enthalpy, noted as \( \Delta H \), relates to the heat change during a chemical reaction. It indicates whether a reaction absorbs or releases heat:

• **Exothermic reactions** have a negative \( \Delta H \), meaning they release heat.
• **Endothermic reactions** have a positive \( \Delta H \), meaning they absorb heat.

In reaction spontaneity, \( \Delta H \) plays a vital role. For a reaction to be spontaneous at all temperatures, it should preferably be exothermic, as in option (a) from the exercise. This means :

• Releasing energy into the surroundings can make up for any decrease in entropy \( \Delta S \) or help compensate even if entropy doesn't increase.

Thus, knowing the enthalpy change helps predict if a reaction will proceed without external intervention.