Question

Predict the sign of \(\Delta S^{\circ}\) for each of the following changes. a. \(\mathrm{Na}(s)+\frac{1}{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NaCl}(s)\) b. \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})\) c. \(\mathrm{NaCl}(s) \longrightarrow \mathrm{Na}^{+}(a q)+\mathrm{Cl}^{-}(a q)\) d. \(\mathrm{NaCl}(s) \longrightarrow \mathrm{NaCl}(l)\)

Short answer

a. \(\Delta S^{\circ} < 0\) b. \(\Delta S^{\circ} < 0\) c. \(\Delta S^{\circ} > 0\) d. \(\Delta S^{\circ} > 0\)

Step-by-step solution

Reaction a:

In this reaction, a solid sodium \(\mathrm{(Na)}\) reacts with gaseous chlorine \(\frac{1}{2}\mathrm{Cl}_2\) to form solid sodium chloride \(\mathrm{(NaCl)}\). The products have a lower entropy than the reactants, because a gas is involved in the reactants and both products are solids. Therefore, the sign of \(\Delta S^{\circ}\) is negative.

Reaction b:

In this reaction, gaseous nitrogen \(\mathrm{(N_{2})}\) reacts with gaseous hydrogen \(\mathrm{(3H_{2})}\) to produce gaseous ammonia \(\mathrm{(2NH_{3})}\). We have 4 moles of gas in the reactants and 2 moles of gas in the products. The decrease in the number of gas moles results in a decrease in entropy. Therefore, the sign of \(\Delta S^{\circ}\) is negative.

Reaction c:

In this reaction, solid sodium chloride \(\mathrm{(NaCl)}\) dissociates into aqueous ions \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\). The dissociation of the solid into separate ions in solution increases the entropy as there is an increase in the number of particles and their freedom of movement. Therefore, the sign of \(\Delta S^{\circ}\) is positive.

Reaction d:

In this reaction, solid sodium chloride \(\mathrm{(NaCl)}\) changes its state to a liquid \(\mathrm{(NaCl(l))}\). A change from a solid to a liquid results in higher entropy, as the particles have more freedom to move and rearrange in the liquid state compared to the solid state. Therefore, the sign of \(\Delta S^{\circ}\) is positive.

Key concepts

Thermodynamics

Thermodynamics is the study of energy, heat, and work. It examines how energy is transferred and transformed in physical and chemical processes.
When we talk about thermodynamics in chemistry, we often refer to concepts like enthalpy, entropy, and Gibbs free energy.

• Energy Transformation: Energy can be converted from one form to another, like potential energy into kinetic energy.
• First Law of Thermodynamics: Energy cannot be created or destroyed in an isolated system.
• Entropy: Often symbolized by "S," entropy is a measure of disorder or randomness in a system.

The second law of thermodynamics tells us that the total entropy of an isolated system can never decrease over time.
This is why processes such as mixing or dissolving tend to increase entropy.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products, changing the chemical structure and energy content.
These reactions often involve the breaking and forming of chemical bonds.

• Endothermic Reactions: Absorb energy, resulting in a positive change in enthalpy ( ΔH > 0 ).
• Exothermic Reactions: Release energy, resulting in a negative change in enthalpy ( ΔH < 0 ).

Catalysts can increase the rate of a reaction without being consumed by lowering the activation energy.
During chemical reactions, we consider the state of reactants and products to predict changes in entropy.

State of Matter

The state of matter refers to the physical form in which a substance exists: solid, liquid, or gas.
Each state has distinct characteristics based on particle arrangement and movement.

• Solids: Particles are tightly packed with little movement, resulting in low entropy.
• Liquids: Particles have more freedom to move, increasing entropy.
• Gases: Particles are far apart and move freely, possessing the highest entropy.

Transitions between these states, such as melting and boiling, involve changes in entropy.
For example, when a solid turns into a liquid, the entropy increases because particles move more freely.

Entropy Change

Entropy change ( ΔS ) measures how the disorder or randomness in a system changes during a process.
For reactions:

• Negative ΔS: Indicates a decrease in entropy, meaning the system becomes more ordered.
• Positive ΔS: Indicates an increase in entropy, meaning the system becomes more disordered.

For the reactions given in the original exercise: 1. The formation of NaCl from Na and Cl yields a negative ΔS because gas turns into a solid. 2. The production of NH₃ decreases entropy due to fewer moles of gas in the products. 3. The dissociation of NaCl into ions results in positive ΔS due to increased particle freedom. 4. The melting of NaCl results in positive ΔS as solids transition to liquids, increasing disorder.