Question

For the reaction \(\mathrm{NaCl}(s) \stackrel{\text { Watr }}{\longrightarrow} \mathrm{Na}^{+}(a q)+\mathrm{Cl}^{-}(a q)\) $$ \Delta H=+4.184 \mathrm{~kJ} / \mathrm{mol} $$ (a) Is this process endothermic or exothermic? (b) Does entropy increase or decrease in this process? (c) Table salt ( \(\mathrm{NaCl}\) ) readily dissolves in water. Explain, based on your answers to parts (a) and (b).

Short answer

(a) The process is endothermic. (b) Entropy increases. (c) NaCl dissolves because the entropy increase makes the process favorable.

Step-by-step solution

Determine if the Process is Endothermic or Exothermic

An endothermic reaction absorbs heat from the surroundings, while an exothermic reaction releases heat. The given reaction has \( \Delta H = +4.184 \ \text{kJ/mol} \), indicating a positive change in enthalpy. A positive \( \Delta H \) means the reaction absorbs heat, thus this reaction is endothermic.

Analyze the Change in Entropy

Entropy is a measure of disorder or randomness. In the given reaction, \( \mathrm{NaCl} \) transitions from a solid state to dissociated ions in aqueous solution. Solids have lower entropy than solutions because the ions in solution are more dispersed and have greater freedom of movement. Therefore, entropy increases during this process.

Explain Why NaCl Dissolves in Water

Despite being endothermic, NaCl dissolves readily in water because the increase in entropy is favorable. The dissolution process involves both enthalpy and entropy changes. The increase in entropy (more disorder) often overcomes the endothermic nature of the reaction, especially at higher temperatures, making the process spontaneous.

Key concepts

Endothermic Reaction

An endothermic reaction is one in which the system absorbs energy from its surroundings in the form of heat. This process requires energy input to proceed, as it feels cold to the touch since heat is taken in. This concept can be identified by the sign of the enthalpy change, \(\Delta H\). In chemical reactions, when \(\Delta H\) is positive, it indicates that the reaction is endothermic.

For example, in the dissolution of sodium chloride \(\mathrm{NaCl}\) in water, we see \(\Delta H = +4.184 \, \mathrm{kJ/mol}\). This positive value reveals that energy is absorbed, classifying this as an endothermic reaction.

Understanding this concept helps us comprehend why some reactions, like this one, require a constant supply of energy to proceed.

Entropy Increase

Entropy is a term that refers to the level of disorder or randomness in a system. In chemical processes, increasing entropy often leads to more spontaneous reactions due to greater disorder.

When sodium chloride dissolves in water, we observe an increase in entropy. Initially, \(\mathrm{NaCl}\) is in a solid crystal lattice, which is orderly. Upon dissolving, it separates into \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\) ions that are freely moving in the solution.

This transition to a more disordered state, indicated by the dispersion of ions in water, signifies an increase in entropy.

• The ions have more freedom to move.
• The system experiences more randomness.
• The overall disorder of the solution increases.

This increase in entropy can provide a driving force for the process, aiding in the dissolution despite its endothermic nature.

Dissolution Process

The dissolution process refers to the transformation where a solute integrates homogeneously into a solvent. For sodium chloride (\(\mathrm{NaCl}\)) dissolving in water, it involves breaking ionic bonds in the solid and forming new interactions with water molecules.

Despite being endothermic, \(\mathrm{NaCl}\) dissolves easily because of the favorable increase in entropy. During dissolution, the structured \(\mathrm{NaCl}\) solid becomes hydrated ions, \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\), dispersed throughout the water, resulting in entropy gain.

The energy absorbed to break ionic bonds is balanced by increased disorder when ions are solvated. This dissolution process is often spontaneous because the energetic cost (endothermic nature) is outweighed by the significant entropy increase.

Enthalpy Change

Enthalpy change, symbolized as \(\Delta H\), reflects the heat absorbed or released during a chemical reaction at constant pressure. In thermodynamics of reactions, it indicates whether a process is endothermic or exothermic.

In the given exercise of dissolving \(\mathrm{NaCl}\), the positive \(\Delta H\) value of \(+4.184 \, \mathrm{kJ/mol}\) signifies that energy is absorbed from the surroundings. This means the environment loses heat, making the enthalpy change a crucial aspect to consider.

The interaction of enthalpy and entropy dictates whether such processes occur spontaneously. Even with the endothermic enthalpy change, the substantial increase in entropy in NaCl dissolution can drive the reaction forward. Understanding \(\Delta H\) helps predict how temperature changes might affect the reaction direction and balance of a system.