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Looking at a system in which phosphoric acid is concentrated in an evaporator which uses a constant recycle stream with a heat exchanger in this stream to heat the acid so that water evaporates out of the acid when it re-enters the main stream, How can I find the Q needed to remove a certain amount of water from the stream in order to concentrate the acid to a specific level?

I am given the amount of water evaporated, both concentrations, and the flow rate of both the entering acid stream and the exiting acid stream. I have also been told that you cannot simply use $Q=mC_p\Delta T$, because this is inacurate for phosphoric acid.

Any help or sources you could link me to would be greatly appreciated.

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You need to know the latent heat of vaporization of the solution, which would be the same as that of water when phosphoric acid concentration is low.

See Fig. 10 of this bulletin for latent heat of vaporization as a function of phosphoric acid concentration, but keep in mind this is only strictly valid at the stated temperature.

If you are varying phosphoric acid concentration (concentrating phosphoric acid) you would need to integrate heat of vaporization as a function of phosphoric acid concentration over the appropriate concentration range.

Also, as phosphoric acid concentration gets very high, it is no longer valid to consider the evaporating solution to be only water, it will increasingly contain phosphoric acid as well.

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  • $\begingroup$ Hello, I am given latent heat and it is assumed that the concentration within the evaporator as well as the concentration in the recycle stream are the same concentration as the exit stream. Can you help with what I should do in this case? $\endgroup$ – Samantha Jan 29 '15 at 14:28
  • $\begingroup$ If this is a homework problem, add the exact problem to your question and explain what you need help with $\endgroup$ – DavePhD Jan 29 '15 at 14:52
  • $\begingroup$ I'm sorry, this is not a homework problem. It's independent study from a professor who posed the question verbally. $\endgroup$ – Samantha Feb 2 '15 at 12:22
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As it turns out, I was just confused on the question being asked. You actually can use Q=mC p ΔT to answer the question. However, instead of using it for Phosphoric acid, you use it based on the water, as you know the mass of water being evaporated out, the specific heat capacity of water at this temperature, and the change in temperature of the water. This Q required by the water will be equal to that added to the phosphoric acid by the heat exchanger.

As a side note, I was incorrect in stating that Q=mC p ΔT is not applicable to phosphoric acid. It is applicable, however not reccomended for this problem as you do not know the mass flow rate of the phosphoric acid through the recycle stream, nor is it easy to find the heat capacity of dilute phosphoric acid at the very high temperatures at which this evaporation would take place.

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