Problem 14 - Chemistry: Principles and Reactions

Question

Predict the sign of \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{H}_{2}(g)+\mathrm{Ni}^{2+}(a q) \longrightarrow 2 \mathrm{H}^{+}(a q)+\mathrm{Ni}(s)\) (b) \(\mathrm{Cu}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Cu}^{2+}(a q)\) (c) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\)

Step-by-Step Solution

Answer

Question: Predict the signs of the standard entropy change (\(\Delta S^{\circ}\)) for the following reactions: (a) H\(_{2}\)(g) + Ni\(^{2+}\)(aq) → 2 H\(^{+}\)(aq) + Ni(s) (b) Cu(s) + 2 H\(^{+}\)(aq) → H\(_{2}\)(g) + Cu\(^{2+}\)(aq) (c) N\(_{2}\)O\(_{4}\)(g) → 2 NO\(_{2}\)(g) Answer: (a) For reaction (a), the standard entropy change (\(\Delta S^{\circ}\)) is predicted to be negative: \(\Delta S^{\circ} < 0\). (b) For reaction (b), the standard entropy change (\(\Delta S^{\circ}\)) is predicted to be positive: \(\Delta S^{\circ} > 0\). (c) For reaction (c), the standard entropy change (\(\Delta S^{\circ}\)) is predicted to be positive: \(\Delta S^{\circ} > 0\).

Step 1: Reaction (a) Analysis

In this reaction, hydrogen gas reacts with Ni\(^{2+}\) ions in aqueous solution and forms 2 H\(^{+}\) ions in aqueous solution and solid Ni. The gaseous reactant changes to the solid and aqueous products, which decreases the disorder. Moreover, two moles of products are formed from one mole of hydrogen gas.

Step 2: Predicting the Sign of \(\Delta S^{\circ}\) for Reaction (a)

Since the reaction involves a gas changing to solid and aqueous states, and the number of moles does not significantly increase, it is reasonable to predict that the standard entropy change for reaction (a) will be negative, \(\Delta S^{\circ} < 0\).

Step 3: Reaction (b) Analysis

In this reaction, solid Cu reacts with two moles of H\(^{+}\) ions in aqueous solution and forms hydrogen gas and Cu\(^{2+}\) ion in aqueous solution. The solid reactant changes to gaseous and aqueous products, which increases the disorder. Regarding the number of moles, two moles of reactants change to two moles of products.

Step 4: Predicting the Sign of \(\Delta S^{\circ}\) for Reaction (b)

Since the reaction involves a solid changing to gaseous and aqueous states, and the number of moles remains the same, it is reasonable to predict that the standard entropy change for reaction (b) will be positive, \(\Delta S^{\circ} > 0\).

Step 5: Reaction (c) Analysis

In this reaction, one mole of N\(_2\)O\(_4\) gas decomposes into 2 moles of NO\(_2\) gas. There's no phase change in this reaction; both reactants and products are in gaseous states. However, the number of moles of reactants increases from one to two.

Step 6: Predicting the Sign of \(\Delta S^{\circ}\) for Reaction (c)

Since there is no phase change, but an increase in the number of moles, it is reasonable to predict that the standard entropy change for reaction (c) will be positive, \(\Delta S^{\circ} > 0\).

Key Concepts

Thermodynamics

Thermodynamics is a fundamental branch of physics that deals with the relationships between different forms of energy, emphasizing heat and work. At its core, thermodynamics explains how energy transfers within physical systems. It helps us understand how natural processes occur and predict their outcomes. The laws of thermodynamics outline the principles of energy conservation and entropy.

• The first law, also known as the law of energy conservation, dictates that energy cannot be created or destroyed, only transformed.
• The second law introduces the concept of entropy. It states that energy transfers are not completely efficient, leading to increased disorder or entropy in a closed system.

In chemical reactions, these principles help predict whether a reaction will occur spontaneously. Understanding these energy transformations is vital for grasping more complex concepts in physical and chemical processes.

Chemical Reactions

Chemical reactions are processes where reactants undergo transformation into products. During these reactions, bonds between atoms break and new ones form. This reorganization of atoms releases or absorbs energy. The study of chemical reactions involves examining how substances interact and change at the molecular level. One important aspect of chemical reactions is the concept of equilibrium. Reactions may reach a state where reactants and products exist in a stable ratio without further change.

• Chemical reactions can be exothermic (releasing energy) or endothermic (absorbing energy).
• The classification of reactions (e.g., synthesis, decomposition, single-replacement) provides a framework to predict the behavior of these transformations.

Knowing how these processes work allows chemists to manipulate reactions for various applications, from industrial synthesis to pharmaceutical development.

Entropy Prediction

Entropy refers to the degree of disorder in a system. During chemical reactions, predicting changes in entropy is crucial to understanding the spontaneity and feasibility of a process. Entropy change, denoted as \(\Delta S\), indicates whether a system becomes more ordered or disordered.

• A positive \(\Delta S\) suggests increased disorder, making the process more favorable.
• A negative \(\Delta S\) implies an increase in order, often requiring an input of energy to proceed.

In predicting entropy changes, consider:1. Phase Changes: Transitions from solids to liquids or gases increase entropy, while the opposite decreases it.2. Molecular Complexity: More complicated molecules generally have higher entropy.3. Moles of Gas: An increase in gaseous molecules typically increases entropy.By analyzing these factors, you can predict the sign of \(\Delta S^{\circ}\) for reactions, aiding in understanding reaction spontaneity through the lens of thermodynamic principles.