Textbook 4F.17

[Lucy Wang 2J]

Calculate the standard entropy of vaporization of water at 85 C, given that its standard entropy of vaporization at 100 C is 109.0 J/K*mol and the molar heat capacities at constant pressure of liquid water and water vapor are 75.3 J/K*mol and 33.6 J/K*mol, respectively, in this range.

Why is that when you calculate the standard entropy, you must also calculate the change in entropy for the water to cool back down to 85 C?

[Charlotte Adams 1A]

I thought the same thing but I think the book wants us to calculate the standard entropy as the water temp rises, calculate the entropy for the vaporization of water, then calculate the entropy for it to cool back down to 85 degrees. Basically, the book is just unclear in their directions

[Sunny Wu 3A]

Since entropy is a state function, this problem is asking you to find delta S taking another path instead of 85 C liquid straight to 85 C gas. The problem doesn't give you standard entropy of vaporization at 85 C, otherwise you could find delta S immediately. Instead, since it only gives you standard entropy of vaporization at 100 C. Then, your new path would be 85 C liquid to 100 C liquid, 100 C liquid to 100 C gas, 100 C gas to 85 C gas. This new path would give the same delta S value as 85 C liquid directly to 85 C gas.

[Kayko Lee 1C]

In this question the book asks for the entropy of the whole process of water heating up, turning into vapor, and the water vapor cooling down to the 85 degrees. Realistically the process of the problem doesn't make sense since going below 100 degrees C would be liquid water instead of water vapor but that's the way I solve these problems. You also want to make sure that the entropy of water vapor is negative in your calculations as the entropy is decreasing but plugging in the temperatures in the equation should account for it when you take the natural log of a lower temperature over a higher temperature.

[Brian Nguyen 2I]

Entropy is a state function, thus meaning that it doesn't matter which path is taken. You're asked to calculate the entropy of vaporization at 85 degrees, but you only are given the entropy values at 100 degrees, so you must create a path where 85 degrees is the start and end point. This is why you have to calculate the change in entropy when the water cools back down to 85 degrees.