Calorimetric Theory Discrepancy

[DT21]

TL;DR

When calculating the heat of solution, you should include the solute mass with your solution mass. I would appreciate some clarification regarding some discrepancies in my understanding of this.

When solving "coffee cup calorimeter" problems, you're supposed to include the solute mass with the mass of your solution.

However, you're also supposed to assume that dilute solutions have the same density and heat capacity as water.

So if I add 5g of NaOH to 500g of water, the solution volume likely remains 500 mL (due to negligible volume change).

When solving for the heat of solution in this case (plugging into Q=mct), should I use 505g as the mass of the solution (solute+solvent) or 500g (density of dilute solution is assumed to be 1g/mL, same as water at room temp)?

Furthermore, when adding solute mass to solvent mass, wouldn't you end up over-estimating the heat capacity of the solution?

Water has a fairly high heat capacity of 4.18 J/g C. Meanwhile, I assume the heat capacity of NaOH is significantly lower.

Wouldn't including the extra 5g of solute, and assuming it's heat capacity is the same as water give you a higher value than it should be?

Thanks in advance for clarifying!

 

[mjc123]

A similar question came up in this thread: https://www.physicsforums.com/threads/molar-enthalpy-change-calorimetry.1002423/
Googling turned up an obscure old paper from which I estimated (mental arithmetic!) that the SHC of a NaOH solution of that concentration (about twice as concentrated as yours) was ca. 4.03 J/g/K. So total mass*true SHC was slightly lower than water mass*water SHC. But that won't be true for all solutes. My recommendation was to use water mass and water SHC. Unless you've a good idea of the true SHC, this is probably the most reasonable thing to do, at least for dilute solutions.
Here's the reference if you're interested: https://nvlpubs.nist.gov/nistpubs/jres/4/jresv4n2p313_A2b.pdf

 

[DT21]

Thanks mjc123!

I found another article related to this topic, wherein the author shows a slightly larger error when including solute mass, as opposed to ignoring solute mass (for a dilute solution).

https://uwaterloo.ca/chem13-news-ma...calorimeter-calculations-aqueous-electrolytes

I admit that I had never really given it much thought, and always followed the textbook when teaching my high school classes to always include solute mass.

But when a student questioned the purpose of doing so, I found myself wondering if it would be more accurate to ignore the solute mass in dilute solutions.

I was hoping to get another perspective on the matter, and greatly appreciate your contribution.

 

[Borek]

While not including the solute mass might produce slightly better results due to the changes in SHC I would prefer to stick to the standard approach (mass of the solvent+solute @ 4.18J/(gK)) for pedagogical reasons.

Students often have problems grasping what the "system" is, and what is "outside" of the system. Telling them to not include solute mass (when it is definitely something that IS part of the system) will IMHO only confuse them further. Especially for beginners I would prefer to have them understanding what is going on and making an error by assuming wrong SHC, than to dig into confusing minutiae (interesting and obvious in the meaning for us).

 

[mjc123]

Good point Borek. I suppose it's a simplification like treating the Earth as a perfect sphere, or ignoring air resistance, to focus on the fundamental principles of a problem. But these other factors do exist, and in real-world problems one has to take account of them. The question discussed in the article referenced by DT21 was aimed at high school students (admittedly the top 10% of them), and your approach is no doubt appropriate. People studying the subject at university level ought to be aware of the inaccuracies involved (in fact, another recent thread asked about sources of error in a calorimetry experiment).