Question

Classify each of the following reactions as one of the four possible types summarized in Table \(19.3 :\) (i) spontanous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low \(T\) but not spontaneous at high \(T ;\) (iv) spontaneous at high T but not spontaneous at low \(T .\) $$ \begin{array}{c}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g)} \\ {\Delta H^{\circ}=-249 \mathrm{kJ} ; \Delta S^{\circ}=-278 \mathrm{J} / \mathrm{K}}\\\\{\text { (b) } \mathrm{N}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NCl}_{3}(g)} \\\ {\Delta H^{\circ}=460 \mathrm{kJ} ; \Delta S^{\circ}=-275 \mathrm{J} / \mathrm{K}} \\ {\text { (c) } \mathrm{N}_{2} \mathrm{F}_{4}(g) \longrightarrow 2 \mathrm{NF}_{2}(g)} \\ {\Delta H^{\circ}=85 \mathrm{kJ} ; \Delta S^{\circ}=198 \mathrm{J} / \mathrm{K}}\end{array} $$

Short answer

Reaction (a) is spontaneous at low temperatures but not at high temperatures (Type iii). Reaction (b) is not spontaneous at any temperature (Type ii). Reaction (c) is spontaneous at high temperatures but not at low temperatures (Type iv).

Step-by-step solution

Reaction (a)

For reaction (a), \[\Delta H^{\circ} = -249\mathrm{kJ}, \Delta S^{\circ} = -278\mathrm{J}/\mathrm{K}\] Both \(\Delta H\) and \(\Delta S\) are negative. Therefore, the reaction will be spontaneous at low temperatures but not at high temperatures. So, Reaction (a) is of Type (iii).

Reaction (b)

For reaction (b), \[\Delta H^{\circ} = 460\mathrm{kJ}, \Delta S^{\circ} = -275\mathrm{J}/\mathrm{K}\] \(\Delta H\) is positive and \(\Delta S\) is negative. So, \(\Delta G = \Delta H - T\Delta S\) is always positive, as both terms are positive. Therefore, the reaction is not spontaneous at any temperature. Thus, Reaction (b) is of Type (ii).

Reaction (c)

For reaction (c), \[\Delta H^{\circ} = 85\mathrm{kJ}, \Delta S^{\circ} = 198\mathrm{J}/\mathrm{K}\] \(\Delta H\) is positive, and \(\Delta S\) is positive. Therefore, the reaction will be spontaneous at high temperatures but not at low temperatures. So, Reaction (c) is of Type (iv). In summary: - Reaction (a) is Type (iii): spontaneous at low \(T\), not spontaneous at high \(T\) - Reaction (b) is Type (ii): not spontaneous at any temperature - Reaction (c) is Type (iv): not spontaneous at low \(T\), spontaneous at high \(T\)

Key concepts

Thermodynamics

Thermodynamics is a branch of physics concerned with heat and temperature and their relation to energy and work. It defines macroscopic variables, such as internal energy, entropy, and pressure, that partly describe a body of matter or radiation. It is predicated on the four laws of thermodynamics, which convey empirical facts regarding physical systems at the macroscopic scale.

Within the context of chemical reactions, thermodynamics helps us to determine whether a process is spontaneous—meaning it happens without external intervention. It is important to understand that 'spontaneity' in thermodynamics does not imply that the reaction occurs quickly; rather, it only describes the direction in which the reaction is thermodynamically favored to proceed.

Gibbs Free Energy

Gibbs free energy, symbolized as \( G \), is a thermodynamic quantity that measures the maximum or reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. The change in Gibbs free energy, denoted as \( \Delta G \), is defined by the equation \( \Delta G = \Delta H - T\Delta S \), where \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.

When \( \Delta G \) is negative, the process or reaction is spontaneous. If \( \Delta G \) is positive, the reaction is non-spontaneous. Therefore, we can use the signs of both \( \Delta H \) and \( \Delta S \) to predict the spontaneity of a reaction at a given temperature.

Entropy

Entropy, denoted as \( S \), is a measure of the disorder or randomness in a system. The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. This means that the entropy of the universe, which is considered an isolated system, tends to increase with time.

Detailed explanation of entropy includes its statistical interpretation: in a given macrostate, the entropy is proportional to the number of microstates available. Thus, the higher the number of microstates or configurations that a system can assume, the higher its entropy. Changes in entropy, \( \Delta S \) can significantly influence whether a process is spontaneous. An increase in entropy (\( \Delta S > 0 \) ) often favors the spontaneity of a process, particularly when coupled with a decrease in the system's enthalpy.

Enthalpy

Enthalpy, represented as \( H \), is a concept used in thermodynamics to reflect the total heat content of a system. It’s a measure of energy in a thermodynamic system. It is the sum of the internal energy added to the product of the pressure and volume of the system. \( H = U + pV \).

In reactions where the pressure is constant, the change in enthalpy, \( \Delta H \) correlates with heat absorbed or released. A negative \( \Delta H \) indicates exothermic reactions where heat is released. Conversely, a positive \( \Delta H \) involves endothermic reactions, implying that the reaction absorbs heat from its surroundings. Understanding enthalpy changes allows chemists to predict heat flow during chemical reactions, which is essential for process control and safety.