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 \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(l) ?\) 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?

The cooling effect is observed when liquid ethyl chloride under pressure is sprayed on a room-temperature surface. This means that the evaporation of the liquid ethyl chloride cools down the surface. Since the heat lost by the surface is gained by the ethyl chloride, we can conclude that the specific heat of gaseous ethyl chloride must be greater than that of liquid ethyl chloride.

When considering the enthalpies for this process, we should take into account the following: 1. The enthalpy of vaporization for ethyl chloride (\(\Delta H_{vap}\)): This refers to the amount of heat required to convert a given amount of liquid ethyl chloride into its gaseous form. 2. The enthalpy of heating/cooling for ethyl chloride, both for the liquid and gaseous state: These quantities describe the amount of heat transferred to or from ethyl chloride as it gains or loses heat during the cooling process and will be given in terms of its specific heat and mass. By considering these enthalpies and the concept of heat transfer, we could derive an equation to calculate the final temperature of the surface after spraying liquid ethyl chloride under pressure.