Question

The normal freezing point of \(n\) -octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) is \(-57{ }^{\circ} \mathrm{C}\). (a) Is the freezing of \(n\) -octane an endothermic or exothermic process? (b) In what temperature range is the freezing 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 solid \(n\) -octane are in equilibrium? Explain.

Short answer

(a) The freezing of n-octane is an exothermic process. (b) Freezing of n-octane is spontaneous when the temperature is below its normal freezing point of -57°C. (c) Freezing becomes nonspontaneous when the temperature is above -57°C. (d) Liquid and solid n-octane are in equilibrium at the normal freezing point, -57°C.

Step-by-step solution

(a) Endothermic or Exothermic Process

To determine if the freezing of n-octane is endothermic or exothermic, we need to recall that an endothermic process absorbs heat, while an exothermic process releases heat. Now, we know that freezing is a phase transition from liquid to solid, and in this process, energy is released as the particles slow down and form a more ordered, solid structure. Hence, the freezing of n-octane is an exothermic process as energy is released in the form of heat.

(b) Temperature Range for Spontaneous Freezing

The temperature range for the spontaneous freezing of n-octane can be determined by thinking about where the energy released during the phase change can dissipate into the surroundings. As the temperature of the surroundings decreases, the process of freezing becomes more spontaneous because the energy released during freezing can be more easily absorbed by the surrounding environment. So, in general, the spontaneous freezing of n-octane occurs when the temperature is below its normal freezing point, which is -57°C.

(c) Temperature Range for Nonspontaneous Freezing

As mentioned earlier, the freezing process becomes more spontaneous as the temperature decreases. Therefore, it implies that freezing becomes less spontaneous or nonspontaneous when the temperature is higher. Hence, the nonspontaneous freezing of n-octane occurs when the temperature is above its normal freezing point, that is, greater than -57°C.

(d) Equilibrium Temperature for Liquid and Solid n-Octane

The temperature at which liquid n-octane and solid n-octane are in equilibrium is known as the normal freezing point. At equilibrium, the rate of freezing equals the rate of melting, and both phases can coexist without changing the overall composition. In this case, the equilibrium temperature is given: -57°C. At this temperature, both liquid and solid n-octane coexist in equilibrium.

Key concepts

Understanding Freezing

Freezing is a fundamental phase transition that occurs when a liquid turns into a solid. This transformation happens because the particles in the liquid slow down as they lose energy, becoming fixed in a structured, ordered form typical of solids. The process of freezing involves releasing energy as the substance changes state. This released energy is crucial as it reduces the temperature of the molecules and helps them settle into a more rigid shape. The normal freezing point is the specific temperature at which a substance freezes under atmospheric pressure. For n-octane, this point is (-57°C). At or below this temperature, the molecules of n-octane will transition from a liquid to a solid state, causing freezing.

The Exothermic Nature of Freezing

In simple terms, an exothermic process releases heat to its surroundings, unlike an endothermic process which absorbs heat. When n-octane freezes, it undergoes an exothermic process. This is because energy is released in the form of heat as the liquid turns into a solid. As the molecules of n-octane slow down and arrange themselves into a fixed position, they release the heat that was previously keeping them in the liquid state. This released heat can be observed as a warm feeling when you touch the container in which freezing occurs. The key takeaway is that during freezing, heat flows out of the n-octane, signifying it's an exothermic process.

When Freezing is a Spontaneous Process

A spontaneous process is one that occurs naturally without the need for added energy. For freezing to be spontaneous, the conditions must allow it to happen naturally, without external force. For n-octane, freezing is spontaneous below its freezing point of (-57°C). This means that at lower temperatures, the conditions are favorable for the molecules to lose energy and form a solid without additional input. At these temperatures, the environment can readily absorb the released heat, making the transition smooth and self-sustaining. It is essential to remember that spontaneity doesn't imply immediate freezing but rather readiness of conditions for it to happen.

Finding Equilibrium Between Liquid and Solid

Equilibrium is a state where two phases of a substance coexist without changing the overall system's composition. For n-octane, equilibrium occurs at its normal freezing point of (-57°C). At this specific temperature, the rate at which n-octane melts (liquid to solid) is equal to the rate it freezes (solid to liquid). This balance means that neither phase dominates, allowing both to exist together. In practical scenarios, achieving equilibrium requires stabilized conditions where no external heat is added or removed. This is important in understanding processes like melting and freezing, as it shows nature's ability to reach a self-sustained balance.