Question

For the majority of the compounds listed in Appendix \(\mathrm{C},\) the value of \(\Delta G_{f}^{\circ}\) is more positive (or less negative) than the value of \(\Delta H_{f}^{\circ} .\) (a) Explain this observation, using \(\mathrm{NH}_{3}(g), \mathrm{CCl}_{4}(l)\), and \(\mathrm{KNO}_{3}(s)\) as examples. (b) An exception to this observation is \(\mathrm{CO}(g)\). Explain the trend in the \(\Delta H_{f}^{\circ}\) and \(\Delta G_{f}^{\circ}\) values for this molecule.

Short answer

For most compounds, including NH3(g), CCl4(l), and KNO3(s), the value of \(\Delta G_{f}^{\circ}\) is more positive (or less negative) than the value of \(\Delta H_{f}^{\circ}\) because the entropy term (\(T\Delta S\)) is generally positive, which reflects the influence of both enthalpy and entropy changes. However, for CO(g), the trend is different, with \(\Delta G_{f}^{\circ}\) being less positive (or more negative) than \(\Delta H_{f}^{\circ}\), indicating that the entropy term (\(T\Delta S\)) is negative. This suggests that the change in entropy is more significant than the change in enthalpy for the formation of CO(g), resulting in a deviation from the trend observed for a majority of compounds.

Step-by-step solution

Understand Gibbs free energy, enthalpy, and entropy relationships

The relationship between the Gibbs free energy change (\(\Delta G\)), the enthalpy change (\(\Delta H\)), and the entropy change (\(\Delta S\)) can be given by the equation: \[\Delta G = \Delta H - T\Delta S\] Where T is the temperature in Kelvin. Step 2: Analyze the relationship between \(\Delta G_{f}^{\circ}\) and \(\Delta H_{f}^{\circ}\) for NH3(g), CCl4(l), and KNO3(s)

Compare \(\Delta G_{f}^{\circ}\) and \(\Delta H_{f}^{\circ}\) values

For most compounds, \(\Delta G_{f}^{\circ}\) is more positive (or less negative) than \(\Delta H_{f}^{\circ}\). This means that the entropy term (\(T\Delta S\)) is generally positive. For an exothermic reaction, which is when \(\Delta H_{f}^{\circ}\) is negative, this positive entropy term will make the value of \(\Delta G_{f}^{\circ}\) less negative than \(\Delta H_{f}^{\circ}\), as , \(\Delta G_{f}^{\circ}\) reflects both the enthalpy and the entropy changes. Step 3: Explain the exception of CO(g)

Examine the \(\Delta H_{f}^{\circ}\) and \(\Delta G_{f}^{\circ}\) values for CO(g)

The trend in the \(\Delta H_{f}^{\circ}\) and \(\Delta G_{f}^{\circ}\) values for CO(g) is different from the one observed in the previous step. In this case, \(\Delta G_{f}^{\circ}\) is less positive (or more negative) than the \(\Delta H_{f}^{\circ}\). This would indicate that the entropy term (\(T\Delta S\)) is negative, making \(\Delta G_{f}^{\circ}\) more negative than \(\Delta H_{f}^{\circ}\). This suggests that, for the formation of CO(g), the change in entropy is more significant than the change in enthalpy, resulting in a deviation from the trend observed for a majority of compounds.

Key concepts

Enthalpy

Enthalpy is a measure of the total energy of a system. It includes the energy required to create a system as well as the energy needed to displace its surroundings. Often represented by the symbol \(H\), it plays a crucial role in thermodynamics.
Enthalpy changes, noted as \(\Delta H\), are frequently discussed in chemistry and physics as they signify the heat absorbed or released during a process.

• If \(\Delta H\) is negative, the process is exothermic, meaning it releases heat.
• If \(\Delta H\) is positive, it indicates an endothermic process which absorbs heat.

For example, when considering substances like \(\mathrm{NH_3(g)}\) or \(\mathrm{KNO_3(s)}\), the formation enthalpy provides insight into whether their formation releases or absorbs heat. Knowing the enthalpic nature of a reaction helps predict and explain physical and chemical behavior.

Entropy

Entropy is a fundamental concept in thermodynamics, representing the measure of disorder or randomness in a system. It is designated by the symbol \(S\) and is a key player in processes occurring in natural systems.
In thermodynamic terms:

• A positive change in entropy \(T\Delta S\), typically means the system is becoming more disordered.
• A negative change implies that the system is becoming less disordered.

Entropy and enthalpy together determine how energy is dispersed in a system. For reactions involving gases like \(\mathrm{NH_3(g)}\), entropy changes significantly affect their spontaneity since gases are less ordered compared to liquids or solids.

Thermodynamic Stability

Thermodynamic stability refers to the favorability of a compound or a reaction to occur without external energy input. This is often gauged by the value of Gibbs Free Energy \(\Delta G\), which combines both enthalpy \(\Delta H\) and entropy \(T\Delta S\) of the system.
A system is generally considered stable if:

• \(\Delta G\) is negative, indicating a spontaneous reaction or stability under given conditions.
• \(\Delta G\) is positive if a reaction requires energy input, making the compound or reaction unstabile under examined conditions.

For instance, \(\mathrm{CO(g)}\) is an anomaly with \(\Delta G_{f}^{\circ}\) being more negative than \(\Delta H_{f}^{\circ}\). This suggests the entropy component is critical, contributing more significantly to stability than the enthalpic term.
Understanding the thermodynamic stability of molecules aids in predicting reaction paths and equilibrium positions.