If a very minute quantity spilled acid (e.g. $\ce{H2SO4}$, though the question would apply to other acids as well) is cleaned up with water (e.g. yielding a $0.0001~\mathrm{M}$ solution), and some of the water (dilute acid solution) is left behind, will the resulting solution become more concentrated as the water evaporates? Would there be any danger that a drop of an initially-harmless concentration might become a visually-unnoticeable quantity of acid that was strong enough to pose a contact hazard? Would wiping an area down with a moderately-dilute solution of a weak base such as sodium bicarbonate be an appropriate safety precaution, or would it be unnecessary if any acid droplets that might exist on a surface have been thoroughly diluted?
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Sulfuric acid (and other acids) can be concentrated through evaporation of water. It would be a good idea to wash the surface down with dilute, basic solution. That said, if I'm reading your post correctly, your droplets are already 0.1M. That is still a strong acid and care should be taken in its clean up. I was once working with a 0.01M solution of sulfuric acid and when cleaning the flask a few drops of the dilute solution splattered onto my foot, I didn't even notice it at the time. An hour or so later my foot started to burn. When I looked, my sock was gone in the affected area. If you're dealing with anything more than drop or two use a spill kit and let someone know what you are doing.
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$\begingroup$ Yeah, I probably meant something more like 0.001M or maybe 0.00001M [it's been ages since I've taken chemistry]. Basically, the question is not so much about a spilled quantity which is large enough to be visible, but rather the possibility that wiping down a surface where acid was handled, and were it would be possible that a drop might have fallen without being noticed, might end up leaving behind a highly-concentrated residue. $\endgroup$– supercatCommented Jul 29, 2014 at 23:04
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$\begingroup$ Yes, if anything is left behind it will re-concentrate. A mild base wash would make good sense. $\endgroup$– ronCommented Jul 29, 2014 at 23:08
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$\begingroup$ That's what I figured, but I would have expected that if re-concentration was a hazard the instructions that came with the battery and acid for my sump pump would have suggest that as a reason for why use of baking soda was a good idea. $\endgroup$– supercatCommented Jul 29, 2014 at 23:11
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$\begingroup$ "If you aren't in a hurry, you can concentrate sulfuric acid by allowing the water to evaporate naturally. This takes several days." chemistry.about.com/od/makechemicalsyourself/a/… $\endgroup$– ronCommented Jul 29, 2014 at 23:13
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$\begingroup$ Is there any minimum quantity or concentration below which one wouldn't have to worry? If a drop were placed in a bathtub full of distilled water and left alone long enough for the water to evaporate, could that drop still pose a hazard? $\endgroup$– supercatCommented Jul 30, 2014 at 3:03