Problem 63 - Chemistry: The Central Science in SI Units, Global Edition

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 \(T\). $$ \begin{array}{l} \text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{~F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g) \\ \Delta H^{\circ}=-249 \mathrm{~kJ} ; \Delta S^{\circ}=-278 \mathrm{~J} / \mathrm{K} \\ \text { (b) } \mathrm{N}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NCl}_{3}(g) \\ \Delta H^{\circ}=460 \mathrm{~kJ} ; \Delta S^{\circ}=-275 \mathrm{~J} / \mathrm{K} \\ \text { (c) } \mathrm{N}_{2} \mathrm{~F}_{4}(g) \longrightarrow 2 \mathrm{NF}_{2}(g) \\ \Delta H^{\circ}=85 \mathrm{~kJ} ; \Delta S^{\circ}=198 \mathrm{~J} / \mathrm{K} \end{array} $$

Step-by-Step Solution

Answer

In summary, reaction (a) is spontaneous at all temperatures, reaction (b) is not spontaneous at any temperature, and reaction (c) is spontaneous at high \(T\), but not spontaneous at low \(T\).

Step 1: Reaction (a)

As given, for reaction (a), \(\Delta H^{\circ} = -249 kJ\) and \(\Delta S^{\circ} = -278 J/K\). Therefore, for reaction (a), the Gibbs free energy change, \(\Delta G^{\circ}\), equation will look like: $$ \Delta G^{\circ} = (-249 kJ) - T(-278 J/K) $$ Since both \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are negative, their signs will become positive when they are multiplied, and overall \(\Delta G^{\circ} < 0\). Hence, reaction (a) is spontaneous at all temperatures.

Step 2: Reaction (b)

As given, for reaction (b), \(\Delta H^{\circ} = 460 kJ\) and \(\Delta S^{\circ} = -275 J/K\). Therefore, for reaction (b), the Gibbs free energy change, \(\Delta G^{\circ}\), equation will look like: $$ \Delta G^{\circ} = (460 kJ) - T(-275 J/K) $$ Since \(\Delta H^{\circ}\) is positive and \(\Delta S^{\circ}\) is negative, their signs will become positive when they are multiplied, making the overall \(\Delta G^{\circ} > 0\). Hence, reaction (b) is not spontaneous at any temperature.

Step 3: Reaction (c)

As given, for reaction (c), \(\Delta H^{\circ} = 85 kJ\) and \(\Delta S^{\circ} = 198 J/K\). Therefore, for reaction (c), the Gibbs free energy change, \(\Delta G^{\circ}\), equation will look like: $$ \Delta G^{\circ} = (85 kJ) - T(198 J/K) $$ Since \(\Delta H^{\circ}\) is positive and \(\Delta S^{\circ}\) is positive, their signs will cancel each other when they are multiplied, making the overall \(\Delta G^{\circ}\) become more negative as \(T\) increases. Hence, reaction (c) is spontaneous at high \(T\), but not spontaneous at low \(T\).

Key Concepts

Spontaneity of Reactions

Chemical reactions can either be spontaneous or non-spontaneous, meaning they either occur on their own or require external energy, respectively. Spontaneity does not equate to speed; rather, it indicates the natural tendency for a process to occur.

• If a reaction is spontaneous at all temperatures, it means that under any condition, the reaction will proceed without external intervention. This typically happens when both enthalpy change (\( \Delta H^{\circ} \)) and entropy change (\( \Delta S^{\circ} \)) are favorable, such as negative \( \Delta H^{\circ} \) indicating exothermic reactions, and positive \( \Delta S^{\circ} \) suggesting increased disorder.
• If a reaction is not spontaneous at any temperature, it means it would never occur without external energy input, often characterized by positive \( \Delta H^{\circ} \) and negative \( \Delta S^{\circ} \).
• Reactions spontaneous at high temperatures but not low temperatures become more feasible with increased heat, as a positive \( \Delta S^{\circ} \) dominates the process.
• On the flip side, reactions spontaneous at low temperatures typically have negative \( \Delta H^{\circ} \), releasing energy that drives the process forward.

Understanding spontaneity is key to predicting whether or not a chemical reaction will happen without continuous input of energy.

Thermodynamics in Chemistry

Thermodynamics is the branch of chemistry that studies the exchange of energy and matter. It provides the framework for understanding chemical reactions and processes. The three laws of thermodynamics lay down the rules for these exchanges.

• The First Law states that energy cannot be created or destroyed but can be transformed. This means the total energy of the universe remains constant.
• The Second Law introduces the concept of entropy (\( S \)), which is the degree of disorder in a system. It states that in any spontaneous process, the total entropy of a system and its surroundings always increases over time.
• The Third Law asserts that as temperature approaches absolute zero, the entropy of a perfect crystal approaches zero. This underlines that perfect order is only achieved at absolute zero.

In chemistry, applying these laws helps to predict how energy changes occur during reactions and to better understand why some reactions are spontaneous, while others are not. Gibbs free energy, a derived thermodynamic quantity, merges these concepts for more precise predictions.

Enthalpy and Entropy

Enthalpy (\( H \)) and entropy (\( S \)) play crucial roles in predicting reaction behavior. Both concepts are part of the equation for Gibbs free energy (\( \Delta G = \Delta H - T\Delta S \)), a pivotal equation in thermodynamics.

• Enthalpy (\( \Delta H \)) reflects the heat exchange of a reaction at constant pressure. It tells us if a reaction absorbs heat (endothermic, positive \( \Delta H \)) or releases heat (exothermic, negative \( \Delta H \)). Reactions tend to be spontaneous when \( \Delta H \) is negative.
• Entropy (\( \Delta S \)) indicates the change in disorder within the system. A positive \( \Delta S \) implies greater disorder (favorable for spontaneity), while a negative \( \Delta S \) suggests increased order (less favorable for spontaneity).

The interplay of enthalpy and entropy is crucial. A reaction can be pushed towards spontaneity either by a favorable enthalpy or an increase in entropy, particularly at varying temperatures. Overall, understanding these two concepts provides insights into the feasibility and direction of chemical reactions.