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 \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(l) ?\) (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 cooling effect observed when liquid ethyl chloride is sprayed on a room-temperature surface indicates that the specific heat of ethyl chloride in the gaseous state is higher than in the liquid state since the evaporation requires heat energy. To calculate the final temperature of the surface, we need to consider the following enthalpies: 1) the heat transfer from the surface to the ethyl chloride due to the change in temperature, and 2) the enthalpy of vaporization of liquid ethyl chloride as it absorbs heat to go from the liquid state to the gaseous state.

Step-by-step solution

(a) Comparing specific heats of ethyl chloride in gas and liquid states

When liquid ethyl chloride evaporates and goes into the gaseous state, it absorbs heat from the surface. This heat absorption is a strong indicator that the specific heat of ethyl chloride in the gaseous state is higher than in the liquid state. This is because the evaporation requires heat energy to break the bonds between the molecules; hence ethyl chloride has higher specific heat in the gas state. Now, let's move to part (b) of the problem:

(b) Considering enthalpies involved

Since we are assuming that the heat lost by the surface is gained by the ethyl chloride, we have to consider the enthalpies involved in this process. The following enthalpies should be considered: 1. The heat transfer (\(q\)) from the surface to the ethyl chloride due to the change in temperature of the surface. 2. The enthalpy of vaporization (\(∆H_{vap}\)) of liquid ethyl chloride as it absorbs heat to go from the liquid state to the gaseous state. By considering these enthalpies, we can calculate the final temperature of the surface using the energy conservation concept and knowing the specific heats and masses of the surface and ethyl chloride involved in the process.

Key concepts

Specific Heat

The specific heat of a substance is a measure of how much energy is needed to change its temperature. When comparing the specific heats of ethyl chloride in the gaseous and liquid states, the difference reveals a lot about its behavior during a transition. In the problem, liquid ethyl chloride is sprayed onto a warm surface. As it evaporates, it absorbs heat, cooling the surface. This absorption of heat indicates that the specific heat of ethyl chloride in its gaseous state is higher than in its liquid state.

This happens because the process of vaporization requires energy to break the intermolecular forces present in the liquid state. Here, heat from the room-temperature surface is consumed, making the transition to gas possible. The specific heat concept helps us understand how substances like ethyl chloride store and use energy differently in various states. This can be essential for designing processes where energy exchange and temperature control are crucial.

Vaporization

Vaporization is the process of turning from liquid to gas, and it plays a critical role in the scenario given with ethyl chloride. When a liquid evaporates, it absorbs energy from its environment. In the case of ethyl chloride, upon vaporization, the energy required is used to break the bonds that hold the molecules in a liquid state, such as Van der Waals forces.

The enthalpy of vaporization (\(∆H_{vap} \)) is a key term here. It represents the amount of energy needed to vaporize one mole of a liquid at constant pressure. For ethyl chloride, this means it requires a significant amount of heat drawn from its surroundings, explaining why the surface cools down. Understanding vaporization and the energy involved is crucial in contexts like chemical manufacturing and air conditioning where phase changes are part of the core processes.

Energy Conservation

Energy conservation is a fundamental principle in physics stating that energy cannot be created or destroyed, only transformed from one form to another. In the context of ethyl chloride vaporization, energy conservation helps us comprehend the heat exchange between the surface and the ethyl chloride.

When ethyl chloride absorbs heat from the surface, the energy is not lost; it is transferred into the gaseous state of ethyl chloride. The heat lost by the surface is exactly the amount gained by the ethyl chloride assuming no other losses like radiation or conduction to the environment. Therefore, monitoring these energy changes can determine the surface's final temperature.

• The heat transfer (\(q\)) is calculated evaluating the specific heat values.
• Enthalpy changes also involve \(\Delta H_{vap}\), which involves phase transitions.

Using these factors, energy conservation serves as the backbone for understanding how energy flows in physical and chemical systems.