Question

Ethyl chloride \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\right)\) boils at \(12^{\circ} \mathrm{C}\). When liquid \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) under pressure is sprayed on a room-temperature \(\left(25^{\circ} \mathrm{C}\right)\) surface in air, the surface is cooled considerably. (a) What does this observation tell us about the specific heat of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(g)\) as compared with that of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(l) ?\) (b) Assume that the heat lost by the surface is gained by ethyl chloride. What enthalpies must you consider if you were to calculate the final temperature of the surface?

Short answer

The observation tells us that the specific heat of ethyl chloride in its gaseous state (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(g)\)) is larger than that in its liquid state (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(l)\)), as it can absorb more heat to evaporate and cool the surface. To calculate the final temperature of the surface, we must consider three enthalpy changes: (1) enthalpy of vaporization of liquid ethyl chloride, (2) enthalpy change of liquid ethyl chloride, and (3) enthalpy change of gaseous ethyl chloride.

Step-by-step solution

(a) Comparing specific heats

When ethyl chloride is sprayed onto the room-temperature surface, the surface cools down. This means that ethyl chloride absorbs a significant amount of heat from the surface as it evaporates. In this situation, the specific heat of ethyl chloride in its gaseous state must be larger than that in its liquid state, because it can absorb more heat from the surface to change its temperature, which allows it to evaporate and cool the surface.

(b) Enthalpies to consider

To calculate the final temperature of the surface, we need to consider the enthalpy changes involved in the process. There are three main enthalpy changes when ethyl chloride absorbs heat from the surface: 1. The enthalpy of vaporization of liquid ethyl chloride, which describes the energy required to change its state from liquid to gas at its boiling point (\(12^{\circ} C\)). This energy is taken away from the surface, causing it to lose heat. 2. The enthalpy change of liquid ethyl chloride, which accounts for the energy required to heat ethyl chloride from its initial temperature up to its boiling point. This heat is also taken away from the surface. 3. The enthalpy change of the gaseous ethyl chloride, which describes the energy absorbed by ethyl chloride in its gaseous state after it has vaporized. This energy gain is also at the expense of the surface. By considering these enthalpies, we can use energy conservation principles to calculate the final temperature of the surface after ethyl chloride is sprayed on it.

Key concepts

Specific Heat

Specific heat is a measure of how much heat energy is required to change the temperature of a substance by a given amount. When ethyl chloride is sprayed onto a surface at room temperature, it quickly begins to evaporate. This process cools the surface down, suggesting that it absorbs a significant amount of heat.

The specific heat of ethyl chloride in its gaseous state is larger than in its liquid state. This is because gaseous ethyl chloride can absorb more heat from the surface, providing it with the energy needed to transition from one state to another. Having a higher specific heat means it can store more thermal energy per unit temperature change. This property is crucial when considering substances that undergo phase changes, as it aids in explaining their cooling effects.

Vaporization

Vaporization refers to the process of a liquid turning into a gas. One of the essential concepts here is the enthalpy of vaporization. Enthalpy of vaporization is the heat required to convert a liquid into a vapor without changing its temperature.

For ethyl chloride to evaporate, it needs to overcome the enthalpy of vaporization at its boiling point. The heat energy required for this transition is absorbed from the surrounding surface. This is why when ethyl chloride is sprayed on a surface, it causes the surface to lose heat and cool down. It's important to note that different substances have different enthalpies of vaporization, affecting how much heat they require to turn into a gas.

Heat Absorption

Heat absorption is the process by which a substance absorbs heat energy from its surroundings. This absorption plays a crucial role in cooling applications. When ethyl chloride is introduced to a warmer surface, it absorbs heat to undergo a phase change from liquid to gas.

In our scenario, ethyl chloride absorbs heat initially to reach its boiling point and then to vaporize. Both these steps involve the transfer of energy, which is absorbed from the surface, leading to cooling. This process is efficient because the heat taken from the surface helps meet the energy requirements of the liquid ethyl chloride, facilitating its conversion to gas.

Energy Conservation

Energy conservation in thermodynamics refers to the principle where the total energy of an isolated system remains constant. In the context of ethyl chloride spraying, we analyze the interaction between the ethyl chloride and the surface.

According to energy conservation, the heat lost by the surface equals the heat gained by the ethyl chloride. This implies that all energy changes when ethyl chloride evaporates stem from the surface. As ethyl chloride absorbs heat to raise its temperature and vaporize, it utilizes the heat from the surface, demonstrating the conservation of energy across the process. Understanding this principle helps us calculate how much the temperature of the surface would change given a specific amount of ethyl chloride and its known enthalpy values.