Question

Fill in the blanks: (a) At equilibrium, \(\Delta G\) is ________ (b) For \(\mathrm{C}_{6} \mathrm{H}_{6}(l) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(g), \Delta H^{\circ}\) is ________ \((+,-, 0)\) (c) When a pure solid melts, the temperature at which liquid and solid are in equilibrium and \(\Delta G^{\circ}=0\) is called ________

Short answer

_ Answer: Zero Question: For the phase transition C6H6(l) ⇌ C6H6(g), the standard enthalpy change (∆H°) is _?_ Answer: + Question: The temperature at which liquid and solid are in equilibrium and ∆G° = 0 during the melting of a pure solid is called the _?_ Answer: Melting point

Step-by-step solution

a) At equilibrium, ∆G is:

At equilibrium, the Gibbs free energy, ∆G, is equal to zero. This happens because, at equilibrium, there are no further net changes in the system; therefore, there is no driving force for any spontaneous process. So, the answer is zero.

b) For C6H6(l) ⇌ C6H6(g), ∆H° is:

In the given reaction, benzene (C6H6) is changing from the liquid phase to the gaseous phase. This process is referred to as vaporization or evaporation. For any substance, the enthalpy change associated with vaporization is always positive, as energy is absorbed to break intermolecular forces present in the liquid phase so that molecules can move freely in the gaseous phase. Thus, for the given reaction, the standard enthalpy change (∆H°) is positive. So, the answer is "+".

c) When a pure solid melts, the temperature at which liquid and solid are in equilibrium and ∆G° = 0 is called:

When a solid melts into a liquid, the equilibrium that exists between these two phases represents the phase transition. The specific temperature at which a pure solid melts, such that the liquid and solid are in equilibrium, and there is no free energy change (∆G° = 0), is called the melting point of the substance. Hence, the answer is "melting point."

Key concepts

Gibbs Free Energy

Understanding the significance of Gibbs free energy, denoted by \( \Delta G \), is crucial in the context of chemical reactions and thermodynamics. This quantity determines spontaneity in a system, essentially predicting whether a process will occur without energy input from its surroundings. Specifically, \( \Delta G \) combines the system's enthalpy (heat content) with its entropy (degree of disorder) to calculate the amount of useful work that can be obtained during a process at constant temperature and pressure.

When a system is at equilibrium, \( \Delta G \) is equal to zero. This means there's no net change occurring within the system as the forward and reverse reactions are happening at the same rate. In such cases, the system has reached a state of balance, and no external energy is required to maintain this state. This is crucial for students to understand because it explains why systems do not spontaneously change when they are at equilibrium.

Enthalpy Change

Enthalpy change, represented as \( \Delta H \), is one of the fundamental concepts in thermodynamics, specifically relating to the heat transfer during chemical reactions. \( \Delta H \) indicates how much heat is absorbed or released by the system. A positive value for \( \Delta H \) suggests that the system absorbs heat from its surroundings, known as an endothermic process, while a negative value indicates the release of heat to the surroundings, or an exothermic process.

In the context of phase changes, when a substance like benzene \( \mathrm{C}_{6} \mathrm{H}_{6} \) transitions from a liquid to a gas, the process is endothermic. This requires the consumption of energy to overcome intermolecular attractions which is evidenced by a positive \( \Delta H \). This concept is pivotal in understanding how substances absorb energy to change phases, transforming from more ordered to less ordered states.

Melting Point

The melting point of a substance is a distinct temperature at which it changes from solid to liquid form. At this temperature, both the solid and liquid phases coexist in equilibrium, and the Gibbs free energy change for the phase transition is zero \( (\Delta G^\circ = 0) \). This phenomenon is essential for comprehending how purity and temperature influence a substance's state.

The melting point is not only a unique identifier for pure substances but also serves as an indicator for assessing purity. Impurities alter the melting point, causing it to deviate from the standard value expected for the pure substance. Knowledge of melting points is extensively used in chemistry for identifying compounds and assessing their purity, which underlines the students' learning of phase transitions and the conditions under which they take place.