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How can we determine the concentration of sulfuric acid in a very small sample?

We are working on a “mechanical” process that transports a very small amount of sulfuric acid to an instrument and we need to provide the concentration of the acid on the output from our system tests (this does not need to be built into the system for operation, just bench testing validations). Our process involves levels of medium and high vacuum, I am considering the materials inside non-reactive (almost completely stainless steel), and the flow in the system is quick. I am assuming the only change to the acid is some amount of the water in the solution potentially boiling off from the vacuum, increasing the acid concentration. We know the acid solution at the input, and for safety and ease of testing at this point using a lower concentration, 0.12N solution. The output volumes are much lower than a drop of water, and I am guessing are in the 10s of microliters. We have access high quality balance and basic lab tools / glassware.

I had considered adding a drop of water to the test sample and then placing that in a refractometer to measure the diluted acid % w/w, specific gravity, and density. Then run the dilution calculations (how much water to add to concentrated acid to make low concentration acid) backwards to find the sample concentration before I added the drop of water. It seems too many things about the “concentrated acid” (the test sample) are unknowns to perform that calculation. I am also concerned that the concentration of the mixture would be too diluted to accurately measure with a refractometer.

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Spike the acid with some [Fe(CN)2(2,2'-bipy)] and rig up a mini UV/vis machine to record the colour of the droplet.

If you take a iron(II) salt and then add 2,2'bipyridine to it you will get a blood red solution. In a fumehood add sodium cyanide to this and you will get a a dark solid. Collect the solid by filtration and then wash it with water to remove any excess sodium cyanide and 2,2'bipy. Next dissolve the solid in concentrated sulfuric acid to give you a bright yellow solution. Filter this through glass wool (do not use paper or cotton wool as the sulfuric acid will char the cellulose). Now add the yellow solution to distillated water, you will now get a slurry of a deep red solid in a pale red solution.

The compound I have told you how to make is solvatochromic the more able a solvent is to accept lone pairs (act as a a Lewis acid) the more yellow the solution will be. Make a dilute solution of this iron compound in the dilute sulfuric acid and then do your experiment.

See

METAL-COMPLEXES AS COLOR INDICATORS FOR SOLVENT PARAMETERS R.W. SOUKUP and R. SCHMID, Journal of Chemical Education Volume62 Issue6 Page459-462 DOI10.1021/ed062p459 Published1985

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Determining the concentration of a very small sample of sulfuric acid

From Details of what actually happens in cold sulfuric acid between 80 and 90%; what molecular changes cause the viscosity to skyrocket? we can see that up to about 80% concentration the viscosity of sulfuric acid increases monotonically.

Since you (seem to be) working with pressure differentials and capillary forces, you are likely already very sensitive to viscosity and should be able to start measuring it if you have apertures or microfluidic/capillary passages of dimensions that are constant (don't vary with time).

Make a little gizmo that's sensitive to viscosity, e.g. flow rate or movement speed with a known pressure differential, and calibrate it with known dilutions. Then you've got your "concentratometer" suitable for your in-lab measurements.

Be very careful to control for the temperature - better calibrate at many closely-spaced temperatures and be sure to include a temperature reading as part of your concentration determinations.

From Details of what actually happens in cold sulfuric acid between 80 and 90%; what molecular changes cause the viscosity to skyrocket?

AChem's answer to Why does the graph of the electrical conductivity of sulfuric acid/water solutions have this knee in the ~85%-~92% range? includes this plot from Horace E. Darling in "Conductivity of sulfuric acid solutions" (Journal of Chemical & Engineering Data 9.3 (1964): 421-426.) and mentions:

There is a sharp increase in viscosity at 85%, which indicates there is a major structural change in sulfuric acid solution in the range 85-92%. Sulfuric acid forms a hydrate in this range. When the viscosity is high, the conductance goes down, there is a depression in the curve. This viscosity jump is causing the double hump. Once we are past the high viscosity range, conductance goes up again.

It is amazing how simple molecules do not stop from surprising us!

Das et al. (1997) Electrical Conductance and Viscosity of Concentrated H2SO4/H2O Binary Systems at Low Temperatures: Correlation with Phase Transitions (J. Phys. Chem. B 1997, 101, 4166-4170) do a thorough analysis and mention phase transitions and hydrate formation, but 25 years later are there more detailed molecular models of what is happening that might address the exact form of the hydrate(s) formed or any long-range correlations or ordering behind the peak in viscosity at a certain high concentration?


from Horace E. Darling in "Conductivity of sulfuric acid solutions" (Journal of Chemical & Engineering Data 9.3 (1964): 421-426.)

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Micro pH meters are available for samples as small as 0.1 drop. The smaller they get, the more they cost ($1132, Ref 1, Ref 2). The OP mentions a fairly low concentration of acid: "We know the acid solution at the input, and for safety and ease of testing at this point using a lower concentration, 0.12N solution."

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Ref 1. https://www.thomassci.com/Instruments/Electrodes-pH/_/MICRO-COMBINATION-pH-ELECTRODES?q=Micro%20Ph%20Meter

Ref 2. https://www.horiba.com/int/water-quality/support/electrochemistry/measurement-of-ph/measurement-method-for-single-micro-liter-sample-using-compact-ph-meter/

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    $\begingroup$ For strong sulfuric acid solutions it is not reasonable to use the pH scale $\endgroup$ Oct 14, 2022 at 20:22
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I think that the easiest analyses might be turbidity with BaCl2 solution or conductivity. The limiting factor would be precise measurement of the sample size. Of course 18 Meg water for the conductivity. It might be possible to make the sample size a constant systematic error

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