Problem 25 - Chemistry in 30 days

Question

If an endothermic reaction is non-spontaneous at freezing point of water and becomes feasible at its boiling point, then (a) \(\Delta H\) is \(-v e, \Delta S\) is \(+\) ve (b) \(\Delta H\) and \(\Delta S\) both are +ve (c) \(\Delta H\) and \(\triangle S\) both are -ve (d) \(\Delta H\) is \(+\mathrm{ve}, \Delta S\) is \(-\mathrm{ve}\)

Step-by-Step Solution

Answer

(b) \( \Delta H \) and \( \Delta S \) both are +ve.

Step 1: Understanding the Question

The problem states an endothermic reaction (which implies that heat is absorbed, i.e., \( \Delta H > 0 \)) and becomes feasible (spontaneous) at the boiling point of water. The task is to determine the sign of \( \Delta H \) and \( \Delta S \) under these conditions.

Step 2: Analyzing Feasibility with Gibbs Free Energy

The process becomes feasible when \( \Delta G < 0 \), where \( \Delta G = \Delta H - T\Delta S \). At freezing (0°C/273K), \( \Delta G > 0 \), and at boiling (100°C/373K), \( \Delta G < 0 \). Thus, an increase in temperature makes the reaction feasible.

Step 3: Interpreting ΔH and ΔS signs

For \( \Delta G \) to decrease with increasing temperature (from freezing to boiling), \( T\Delta S \) must increase enough to overcome \( \Delta H \). This means \( \Delta S > 0 \) because we want \( T\Delta S \) to become large enough such that \( \Delta H \) can be overcome as temperature increases.

Step 4: Conclusion on ΔH and ΔS

Since \( \Delta H > 0 \) (endothermic) and \( \Delta S > 0 \) (as calculated for feasibility to increase with temperature), both \( \Delta H \) and \( \Delta S \) are positive in such a reaction.

Key Concepts

Endothermic Reaction

In chemistry, an endothermic reaction is one that absorbs heat from its surroundings. A key characteristic of these reactions is that the enthalpy change, represented by \( \Delta H \), is positive. This means that the system requires an input of energy in the form of heat to proceed. This energy absorption can often result in a drop in temperature of the surroundings, as the heat is being taken in by the reaction itself.

• Endothermic reactions absorb energy
• Temperature of surroundings often decreases
• \( \Delta H > 0 \) signifies a positive enthalpy change

Endothermic reactions play a vital role in many natural and industrial processes. In the context of spontaneity and Gibbs Free Energy, this absorption of heat can impact whether a reaction proceeds under certain conditions.

Spontaneity

Spontaneity in chemical reactions refers to the ability of a process to occur without any external input of energy once started. For a reaction to be spontaneous at constant temperature and pressure, the Gibbs Free Energy change, \( \Delta G \), must be negative.

• Spontaneous reactions have \( \Delta G < 0 \)
• Occurs without the need for extra energy input
• Temperature and pressure can influence spontaneity

In an endothermic reaction, the reaction becomes spontaneous at higher temperatures if the entropy term, \( T\Delta S \), outweighs the positive enthalpy term, \( \Delta H \). Hence, understanding the balance of these components is crucial for predicting reaction behavior under different conditions.

Enthalpy Change (ΔH)

Enthalpy change, denoted as \( \Delta H \), is the heat absorbed or released by a system at constant pressure during a chemical reaction. For endothermic reactions, \( \Delta H \) is positive, indicating that the system absorbs energy from its surroundings as it proceeds.

• Represents the heat change in a reaction
• Positive in endothermic processes (\( \Delta H > 0 \))
• Informs on energy requirement for reactions

This energy relation helps determine whether a reaction may occur spontaneously if other conditions, such as temperature and entropy, are favorable. For example, the positive \( \Delta H \) in endothermic reactions needs to be balanced or outweighed by a favorable entropy change to achieve spontaneity at specific temperatures.

Entropy Change (ΔS)

Entropy change, \( \Delta S \), quantifies the amount of disorder or randomness introduced into a system during a reaction. A positive entropy change suggests an increase in disorder, which can greatly impact the feasibility of a reaction, particularly at varying temperatures.

• Measures disorder or randomness change
• Positive \( \Delta S \) indicates increased disorder
• Influences the spontaneity of a reaction

For an endothermic reaction which becomes feasible at a higher temperature, \( \Delta S \) must be positive. This allows the \( T\Delta S \) term to increase sufficiently to surpass \( \Delta H \) as temperature rises, facilitating the reaction's spontaneity. Hence, the interplay between \( \Delta H \) and \( \Delta S \) plays a critical role in determining reaction conditions.