Problem 16 - Chemistry The Central Science In Si Units

Question

The normal boiling point of \(n\) -octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) is \(125^{\circ} \mathrm{C}\). (a) Is the condensation of gaseous \(n\) -octane to liquid \(n\) -octane an endothermic or exothermic process? (b) In what temperature range is the boiling of \(n\) -octane a spontaneous process? (c) In what temperature range is it a nonspontaneous process? (d) Is there any temperature at which liquid \(n\) -octane and gaseous \(n\) -octane are in equilibrium? Explain.

Step-by-Step Solution

Answer

(a) Exothermic. (b) \(T > 125^\circ\)C. (c) \(T < 125^\circ\)C. (d) Yes, at 125°C.

Step 1: Understanding processes

Identify the nature of the energy exchange for condensation. Condensation is the process where gas turns into a liquid, and typically releases energy into the surroundings. Therefore, condensation is an exothermic process, as heat is released when gas becomes liquid.

Step 2: Identifying spontaneous boiling

Boiling of a liquid is spontaneous when the Gibbs free energy change \( \Delta G \) is negative. For boiling to be spontaneous, temperature must be above the boiling point. Here, the boiling point of \(n\)-octane is 125°C, so boiling is spontaneous for temperatures greater than 125°C.

Step 3: Identifying nonspontaneous boiling

Boiling is nonspontaneous when \( \Delta G \) is positive. For boiling to be nonspontaneous, temperature must be below the boiling point. Therefore, boiling is nonspontaneous for temperatures below 125°C.

Step 4: Considering equilibrium

At equilibrium, the change in Gibbs free energy \( \Delta G \) is zero, meaning the process is neither spontaneous nor nonspontaneous. This occurs exactly at the boiling point of a substance. For \(n\)-octane, this equilibrium temperature is exactly 125°C.

Key Concepts

Boiling Point

The boiling point is the temperature at which a substance transitions from a liquid to a gas. It's an important physical property of a substance. For n-octane, the boiling point is 125°C.
At this temperature, the liquid molecules have enough thermal energy to overcome intermolecular forces holding them together. This allows them to escape into the gaseous phase. When a liquid is at its boiling point, any added energy will be used to convert the substance from liquid to gas rather than increasing its temperature.
Key points about boiling point include:

• It's specific to each substance and determined by intermolecular forces.
• Higher elevation decreases atmospheric pressure, lowering the boiling point.
• A liquid can boil at a lower temperature under reduced pressure.

Understanding boiling points helps predict how a substance behaves at different temperatures.

Gibbs Free Energy

Gibbs free energy, denoted as \( \Delta G \), measures the maximum reversible work a thermodynamic system can perform at constant temperature and pressure. It's crucial for determining the spontaneity of a process.
A negative \( \Delta G \) indicates a spontaneous process, meaning it can occur without outside energy. A positive \( \Delta G \) indicates a nonspontaneous process. If \( \Delta G \) is zero, the process is at equilibrium.

• For n-octane, boiling is spontaneous when temperature exceeds 125°C, making \( \Delta G \) negative.
• When \( \Delta G \) is positive, boiling is nonspontaneous; this occurs below 125°C.
• At 125°C, \( \Delta G \) is zero, indicating equilibrium.

Understanding \( \Delta G \) allows us to predict how temperature influences spontaneity in phase changes.

Exothermic Process

An exothermic process releases heat into its surroundings. This is a common characteristic of many condensation and freezing processes.
When n-octane condenses from gas to liquid, it's an exothermic process because energy is released as heat. As the gaseous molecules slow down and come together to form a liquid, this energy is lost to the environment. Understanding whether a process is exothermic or not is key to grasping how temperature and energy flow in chemical reactions.

• In exothermic reactions, products have lower energy than reactants.
• Heat flows out of the system to the surroundings.
• Condensation of n-octane releases energy, keeping equilibrium dynamic at conditions such as 125°C.

Remember, exothermic processes are not restricted to chemical reactions but are fundamental to physical changes as well.

Phase Equilibrium

Phase equilibrium occurs when two phases of a substance coexist at thermodynamic equilibrium. At this point, there is no net change in the amount of substance in each phase.
For n-octane, phase equilibrium is achieved at its boiling point of 125°C. At this temperature, liquid and gas phases of n-octane coexist. The Gibbs free energy change \( \Delta G \) for this process is zero, meaning the process is neither spontaneous nor nonspontaneous.
During phase equilibrium:

• The rate of evaporation equals the rate of condensation.
• The energy change of the system remains constant.
• The physical properties like temperature and pressure do not change over time.

Understanding phase equilibrium helps predict the behavior of substances during phase changes, and it's essential for designing and understanding various industrial and laboratory processes.