Question

The change of state from liquid \(\mathrm{H}_{2} \mathrm{O}\) to gaseous \(\mathrm{H}_{2} \mathrm{O}\) has \(\Delta H=+40.7 \mathrm{~kJ} / \mathrm{mol}\) and \(\Delta S=-109 \mathrm{~J} /(\mathrm{mol} \cdot \mathrm{K})\) (a) Is the change from liquid to gaseous \(\mathrm{H}_{2} \mathrm{O}\) favored or unfavored by \(\Delta H ?\) By \(\Delta S ?\) (b) What are the values of \(\Delta H\) and \(\Delta S\) (in kJ/mol) for the change from gaseous to liquid \(\mathrm{H}_{2} \mathrm{O} ?\)

Short answer

(a) Unfavored by both ΔH and ΔS; (b) ΔH = -40.7 kJ/mol, ΔS = 0.109 kJ/mol·K.

Step-by-step solution

Understanding Favorability of Enthalpy Change (ΔH)

The enthalpy change (ΔH) is given as +40.7 kJ/mol. A positive ΔH indicates that the process requires energy input, thus it is non-spontaneous or energetically unfavored under constant pressure. Therefore, the change from liquid to gaseous water is unfavored by ΔH, as it is endothermic.

Understanding Favorability of Entropy Change (ΔS)

The entropy change (ΔS) is given as -109 J/(mol·K) or -0.109 kJ/(mol·K). A negative ΔS signifies a decrease in disorder, which is typically unfavored for processes progressing spontaneously. Thus, the change from liquid to gaseous water is unfavored by ΔS because gases are generally more disordered than liquids.

Calculating ΔH for the Reverse Process

For the reverse process, which is conversion from gaseous to liquid water, the enthalpy change (ΔH) should be the opposite sign of the forward process. Therefore, ΔH = -40.7 kJ/mol for the gaseous to liquid transition.

Calculating ΔS for the Reverse Process

Similar to ΔH, the ΔS for the reverse reaction will simply flip the sign of the forward process. So, ΔS = 109 J/(mol·K) or 0.109 kJ/(mol·K) for the gaseous to liquid transition.

Key concepts

Enthalpy Change (ΔH)

Enthalpy change, represented by ΔH, is a concept widely used in thermodynamics to describe the energy change in a system during a process at constant pressure. It is an indicator of whether a process is endothermic or exothermic. An endothermic process is characterized by the absorption of energy, meaning ΔH is positive. In contrast, an exothermic process releases energy and thus has a negative ΔH value.

In the case of converting liquid water to vapor, ΔH is given as +40.7 kJ/mol. This indicates an endothermic process where energy is absorbed by the water to transform into gas. This absorption is necessary to break the intermolecular forces holding the liquid molecules together, allowing them to move freely as gas.

• Positive ΔH: energy absorbed, non-spontaneous.
• Negative ΔH: energy released, potentially spontaneous.

Understanding ΔH helps predict the heat energy flow and is crucial when considering reactions and phase transitions in thermodynamics.

Entropy Change (ΔS)

Entropy, symbolized as ΔS, is a measure of disorder or randomness in a system. In general, processes that increase disorder (or have a positive ΔS) tend to be favorable or spontaneous. Conversely, processes that decrease disorder (or have a negative ΔS) tend to be unfavorable or non-spontaneous in nature.

For the state change from liquid \( ext{H}_2 ext{O}\) to gaseous \( ext{H}_2 ext{O}\), the given entropy change is -109 J/(mol·K). A negative entropy change signifies a decrease in disorder, which is counterintuitive for a liquid-to-gas transition since gases are more disordered than liquids. This negative ΔS reflects that within the specific conditions of this process, the overall system becomes less disordered, possibly due to additional constraints or balancing conditions.

• Positive ΔS: increase in disorder, spontaneous tendency.
• Negative ΔS: decrease in disorder, typically non-spontaneous.

Evaluating ΔS is important for understanding the spontaneity and thermodynamic feasibility of a process.

Phase Transition

Phase transitions involve the conversion of a substance from one state of matter to another, such as solid to liquid, liquid to gas, etc. These changes require energy and exhibit particular thermodynamic properties, usually characterized by changes in enthalpy (ΔH) and entropy (ΔS). The process of evaporation, where liquid water turns into steam, is a classic example of a phase transition.

In our example, moving from liquid to gaseous water requires an input of energy (positive ΔH) and, under the given circumstances, results in a decrease in entropy (negative ΔS). This phase transition is not favored naturally due to the positive ΔH and negative ΔS values. However, given a sufficient energy supply, such as heat from the environment, the process can occur.

• Phase transitions involve either endothermic or exothermic enthalpy changes.
• They also influence the system's entropy, which must be evaluated to understand feasibility.

Understanding the intricacies of phase transitions helps in predicting and manipulating physical processes across various scientific and industrial applications.