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.

Short answer

(a) The condensation of gaseous n-octane to liquid n-octane is an exothermic process. (b) The temperature range for spontaneous boiling of n-octane is above \(125 ^{\circ}{\rm C}\). (c) The temperature range for nonspontaneous boiling of n-octane is below \(125 ^{\circ}{\rm C}\). (d) Liquid n-octane and gaseous n-octane are in equilibrium at the normal boiling point of \(125 ^{\circ}{\rm C}\).

Step-by-step solution

(a) Identify the process type

To determine whether the condensation of gaseous n-octane to liquid n-octane is endothermic or exothermic, we consider energy changes. In an endothermic process, energy is absorbed from the surroundings, while in an exothermic process, energy is released to the surroundings. When a substance condenses, the molecules change from a less ordered, high-energy (gaseous) state to a more ordered, low-energy (liquid) state, implying a release of energy to the surroundings. Therefore, the condensation of gaseous n-octane to liquid n-octane is an exothermic process.

(b) Determine the temperature range for spontaneous boiling

Boiling occurs when the liquid phase and gaseous phase are in equilibrium at atmospheric pressure. In the case of n-octane, the normal boiling point is given as \(125 ^{\circ}{\rm C}\). At temperatures above this point, it is energetically favorable for the substance to be in its gaseous state, which means the boiling is spontaneous. Therefore, the temperature range for spontaneous boiling of n-octane is above \(125 ^{\circ}{\rm C}\).

(c) Determine the temperature range for nonspontaneous boiling

On the other hand, if the substance is below its normal boiling point, it will tend to remain in its condensed (liquid) state, as it would not have enough energy to transition to its gaseous state. In this condition, the boiling process is nonspontaneous. Therefore, the temperature range for nonspontaneous boiling of n-octane is below \(125 ^{\circ}{\rm C}\).

(d) Identify the equilibrium temperature

The equilibrium temperature between the liquid and gaseous phases is the normal boiling point, at which the vapor pressure of the liquid is equal to the atmospheric pressure. For n-octane, this occurs at \(125 ^{\circ}{\rm C}\). So, yes, there is a temperature at which liquid n-octane and gaseous n-octane are in equilibrium, and that temperature is the normal boiling point of \(125 ^{\circ}{\rm C}\).

Key concepts

Boiling Point

The boiling point is the specific temperature at which a liquid turns into a gas. At this point, the liquid and the vapor form of the substance exist in a dynamic equilibrium. For example, the normal boiling point of n-octane is 125°C. At this temperature, the added energy allows the molecules enough movement to break free into the gaseous form.
Boiling points can indicate the strength of intermolecular forces in a liquid. Substances with strong intermolecular attractions require more energy to separate the molecules, resulting in a higher boiling point.
The boiling point can also be influenced by external factors, such as atmospheric pressure. At higher altitudes where atmospheric pressure is lower, a liquid will boil at a lower temperature than it would at sea level.

Phase Equilibrium

Phase equilibrium occurs when a substance's liquid and vapor phases exist in harmony at a particular temperature and pressure. At this point, the rate of evaporation of the liquid matches the rate of condensation of vapor.
Using n-octane as an example, at 125°C, the energy balance between the liquid and the gas phases reaches equilibrium. Molecules transition between phases at equal rates, implying no net change in the quantity of liquid or gas over time.
Phase equilibrium is essential in understanding chemical processes, especially when considering changes in state. It's a key concept when calculating energy balance in industrial applications and understanding environmental conditions.

Exothermic Process

In an exothermic process, energy is released into the surroundings. This occurs when a system loses heat due to a process making the surroundings warmer.
For n-octane, when it condenses from a gas to a liquid, it releases energy. This change from the gaseous state—a high-energy state with greater molecular movement—to a liquid state signifies a decrease in energy within the substance itself. Consequently, heat is transferred to the surrounding environment.
Exothermic reactions are common in nature and industrial applications, such as combustion and many types of chemical synthesis. These reactions often make processes more sustainable by leveraging the released energy to drive other reactions.

Spontaneous and Nonspontaneous Processes

Spontaneous processes occur without the need for external energy input, directed by the system's natural tendency to achieve equilibrium. For n-octane, boiling is spontaneous at temperatures greater than 125°C. In this state, the energy required for the phase transition is naturally provided by the environment.
Nonspontaneous processes do not occur under the existing environmental conditions, often requiring energy input to proceed. Below 125°C, n-octane's boiling is nonspontaneous. External energy is needed to help overcome intermolecular forces, prompting the transition from liquid to gas.
Understanding the difference helps in predicting how substances behave under varying temperatures and pressures, aiding in energy use and system design in engineering fields.