Problem 12 - Chemistry: The Central Science in SI Units, Global Edition

Question

Which of the following processes are spontaneous: (a) the evaporation of water at \(\$ T P\) to form water vapor of 101.3 kPa pressure; (b) separation of a mixture of water and oil into two separate phases; (c) the souring of milk; (d) the neutralization of hydrochloric acid with sodium hydroxide at \(\mathrm{STP} ;(\mathbf{e})\) the formation of ice from water at \(20^{\circ} \mathrm{C}\) and \(101.3 \mathrm{kPa} ?\)

Step-by-Step Solution

Answer

(a) Spontaneous, since evaporation increases entropy and the process is endothermic; (b) Spontaneous, since the separation increases entropy; (c) Spontaneous, due to an exothermic reaction and an increase in entropy; (d) Spontaneous at STP, because it is an exothermic reaction with an increase in entropy; (e) Not spontaneous, as it is an endothermic process with a decrease in entropy.

Step 1: 1. Evaporation of water at T P to form water vapor of 101.3 kPa pressure

In this process, water changes from a liquid to a gaseous state (water vapor). This change leads to an increase in entropy because the molecules in the gaseous state are more disordered than in the liquid state. Also, the evaporation process is endothermic because it absorbs energy from the surroundings. However, as long as the temperature is not below the boiling point of water, the entropy increase will outweigh the energy absorbed, making the process spontaneous.

Step 2: 2. Separation of a mixture of water and oil into two separate phases

When a mixture of water and oil separates into two phases, it is due to the immiscible nature of water and oil. The separation process increases the overall entropy of the system because the molecules in each phase are more disordered than they were in the mixed state. The process does not require an external source of energy, so separating water and oil is a spontaneous process.

Step 3: 3. Souring of milk

The souring of milk is a complex process, involving the conversion of lactose (a sugar) into lactic acid by bacteria present in the milk. This conversion is accompanied by a release of energy, making it an exothermic process. The presence of a spontaneous chemical reaction, as well as an increase in the number of particles from lactose to lactic acid and gases, results in an increase in entropy. Thus, the souring of milk is a spontaneous process.

Step 4: 4. Neutralization of hydrochloric acid with sodium hydroxide at STP

The neutralization reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH) involves the transfer of a proton from the acid to the base, forming water and sodium chloride. This reaction is exothermic, meaning it releases energy, and leads to an overall increase in entropy because it forms more stable products. Therefore, the neutralization process is spontaneous at standard temperature and pressure (STP).

Step 5: 5. Formation of ice from water at 20°C and 101.3 kPa

The formation of ice from water at 20°C involves cooling the water molecules and changing their state from liquid to solid. This process requires the removal of heat from the system, making it an endothermic process. Additionally, the entropy decreases as the water molecules become more ordered in the solid state (ice). To be spontaneous, the entropy change and the energy change should favor the process. In this case, since the process requires energy input and the entropy decreases, the formation of ice from water at 20°C and 101.3 kPa is not a spontaneous process.

Key Concepts

Understanding Entropy

Entropy is a measure of the disorder or randomness in a system. It's a central concept in thermodynamics, often associated with the second law, which states that the total entropy of an isolated system can never decrease over time. Entropy tends to increase as systems naturally progress towards equilibrium.

When a process leads to an increase in entropy, it indicates that the matter and energy in the system are more spread out and disordered. For example, when water evaporates to form vapor, the molecules, which are more ordered in the liquid state, become much more disordered in the gaseous state. This is why the increase in entropy is noted.

• Liquid to gas: More entropy.
• Solid to liquid: More entropy.
• Gas to solid: Less entropy.

Understanding how entropy changes in a reaction can help determine whether a process is spontaneous. Processes that increase the overall entropy of the system are usually spontaneous. However, it is important to also consider energy changes in the system, as described by Gibbs free energy, to fully assess spontaneity.

Endo/Exothermic Reactions

In thermodynamics, reactions can either absorb energy from the surroundings (endothermic) or release energy into the surroundings (exothermic). These energy exchanges are fundamental in determining the spontaneity of a process.

Endothermic reactions require energy input to proceed. During these reactions, the system absorbs energy (heat), typically resulting in a higher energy product state. A common example is the melting of ice, which requires heat to break the structured ice bonds, turning into water.

• Ice melting: Endothermic.
• Water boiling: Endothermic.

Exothermic reactions release energy as they proceed. They often involve a transformation to a more stable state, which releases excess energy. For example, when hydrochloric acid neutralizes sodium hydroxide, energy is released, showing that the products are more stable than the reactants.

• Souring of milk: Exothermic.
• Combustion of wood: Exothermic.

The nature of a reaction being either endothermic or exothermic can influence the entropy change and ultimately the spontaneity of the process.

Spontaneous Processes

A spontaneous process is one that occurs on its own without needing continuous energy input. Understanding spontaneous processes is crucial in the study of thermodynamics, as they provide insight into how energy transformations occur naturally.

Processes can be spontaneous even if they require some initial energy input (like activation energy), as long as they eventually lead to a state of higher entropy or lower energy free energy. Volcanic eruptions, a solid dissolving in water, or milk souring are examples of spontaneous processes.

Whether a process is spontaneous depends on various conditions like temperature and pressure, and is often predicted using Gibbs free energy (\( \Delta G = \Delta H - T \Delta S \)). If \(\Delta G < 0 \), the process is spontaneous under the given conditions.

• Processes with \( \Delta G < 0 \): Spontaneous.
• Processes with \( \Delta G > 0 \): Non-spontaneous.

In an exercise context, understanding which processes are spontaneous involves examining both entropy changes and whether the energy changes favor the process naturally.