Thermodynamics Question

[RichardMNixon]

Anyone good with thermo of solutions and vapor-liquid equilibrium? I have to put together an exam for the new kids in the department. I have what I think is a fairly elegant question tying together basically everything they've learned so far, but I don't know that I can solve it or that it really makes sense.

You have a mixture of water and acetic acid. I'd give the pressure, the vapor phase mol fraction of water, and Ka for acetic acid, which should balance Gibbs' phase rule. I could also give van Laar constants to calculate activity coefficients. They'd need to give the temperature and liquid phase mole fractions.

Is this doable? I'm having trouble at the interface of electrolyte activity/equilibrium and phase equilibrium. Any insight would be fantastic.

I'm also slightly concerned that I'm misunderstanding the water-acetic acid mixture. Just because it's an acid doesn't change anything, does it? The non-dissociated acetic acid would still have a vapor pressure, yes?

 

[UNFFwildcard]

If you're having trouble solving the question, then the kids are going to have incredible difficulty.

Perhaps put this as a bonus question, or put it in the form of asking the students what they would do to solve the problem.

 

[RichardMNixon]

Sorry, I should clarify that I'm a 2nd-year TA and the exam is for 1st-years. At this point they've technically taken the same course I have.

The class has a new style this year where the students have been teaching their own lectures. We were asked to make an exam comparable to ours from last year so we could compare the two learning methods. Our exam last year was impossible, so one of my concerns is actually that ours will be too easy since it's based on a pair of second-years being able to solve it instead of a renowned Thermodynamics professor.

 

[Master_Ghost_Knight]

How the hell did you get in that mess?
By the way what is a TA, Technical Albatroz?
Anyways.

Well if you have sucessfully taken the course then you should be able to check back your notes and solve the problem, if you can't then you shouldn't be where you are, but that is just me.
You should start by writing the model of the problem in terms of something you know or can calculate. If you are sure that you have the complete model, that you have parameters that are missing and that you can consistently change the value of those parameters and consequentialy change the final result, then that is a good indication that your problem is probably under defined. The basic method to engineer a academic problem is to know the degrees of freedom of the problem, indentify the propreties that are important the student know how to manipulate (within the paradigm of the curriculum) and add the constraints acordingly (preferably the constraits that candirectly come from measurable data, and vary the set of constraints in different problems to make sure tha they can tackle the problem from different angles) in order to remove the degrees of freedom (and visit particular cases to).

In regards to the particular problem you are proposing, I am not a chemist, but it hapears to me that you have several factors to consider. First that the concentration of dissolved acid will increase as the elements separate, this in turn will make the evaporation temperature increasingly higher (which I believe will transform your problem into a non-linear one, and probably also discontinuous).
With this you need to know the initial conditions, temperature, pressure, mixture ratio (or interchange one of the propreties with liquid/gas ratio or phase). If the process is taken in constant volume, then you don't need to give that (altough specifying that is requiered), if it isn't you can either give initial and final volume or a volume ratio (to say that the process takes place at constant volume is to say that volume ratio is 1; not specifying this makes your problem undefined when aiming for unknown temperature and you missed that).
The constants like heat coeficient and volume coeficient (or ds/dT du/dT, for both the acid and water) can be taken out of a experimental table (student's can do that) (or you can also interchange this with information that allows the calculation of this properties), you will also requier an aditional information that will categorize the increment of heat (or something else that replaces that) due the difference in concentration of the acid. You requier the diferential proprety, heat? work? (0 if there is no exange). Is it a closed system? (if not what is the propreties of the flow of matter? is it instantaneous or continuous? What is the initial, temperture, pressure mix ratio if they are going in. Or how much it goes out and how it goes out during the process).
Finaly you will requier some of the limiting final conditions (pressure, volume already explained) (you can interchange heat, pressure or volume with liquid/gas ratio or phase if there is such). I believe that the problem is then defined with 1 solution and only 1 solution (not sure).

good luck.