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I have a question asked in jee main 2020. 10.30 mg of o2 is dissolved into a litre of sea water of density 1.03 g/ml. The concentration of o2 in ppm is?

Well I know that ppm is generally possibly mostly done as mg/L. Now in this question doing this we get 10.30 as the answer but the answer is 10 which suggests that it's done in some other mass related unit. How to understand when to use mass or volume? Please help me out.

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    $\begingroup$ The title and the body do not match. ( hardness versus oxygen ) $\endgroup$ – Poutnik Mar 24 '20 at 15:25
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    $\begingroup$ @Zenix Have you got a source for that? Sounds like hairsplitting to me. ;) $\endgroup$ – Karl Mar 24 '20 at 17:06
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    $\begingroup$ @Karl check this page. But it's controversial :) $\endgroup$ – Zenix Mar 24 '20 at 17:36
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    $\begingroup$ @Zenix Tnx! As suspected, a lot of hairsplitting. ;) In my opinion, sth. that is produced from a unitless quantity (i.e. a ratio of distances) via the application of a purely mathematical (i.e. trigonometric) operator cannot have a unit. Agreed, the case against ppm and % is not the same as for "rad". $\endgroup$ – Karl Mar 24 '20 at 19:17
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    $\begingroup$ @Zenix In terms of dimensional analysis, the most toenail-curling equation ever imo is the one transforming radians into degrees. ;) $\endgroup$ – Karl Mar 25 '20 at 19:59
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$1$ liter water weighs $1030$ g, and contains $10.3$ mg $O_2$. The mass concentration of $O_2$ in ppm is the ratio $0.0103 g/1030$ g = $10.0$ ppm.

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    $\begingroup$ Using significant figures, both the concentration of oxygen and the density have three. So the answer should be 10.0 ppm, not 10 ppm. $\endgroup$ – MaxW Mar 24 '20 at 16:20
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ppm is not necessarily defined for 2 quantities of the same unit.

There is ppm (w/w), ppm (V/V), ppm (w/V), ppm(n/n).

Sometimes these variants use an explicit affix, like ppm (V/V)=ppmv.

Due to the ambiguity of the default interpretation, it is highly recommended not to use ppm / ppb / ppt anymore. If one has to use them and no explicit interpretation is provided, one has to stick to the most probable or common variant used in the given context.

I suppose in your case it can be both ppm (w/V) and ppm (w/w), probably the latter, but no guarantee for that.

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  • $\begingroup$ Exactly that's why I got it wrong in jee main 2020 $\endgroup$ – Alex Mar 24 '20 at 16:14
  • $\begingroup$ Next time, if I were you, I would comment the ambiguity and provided both possible answers, if applicable. $\endgroup$ – Poutnik Mar 24 '20 at 16:17
  • $\begingroup$ @Karl Thanks, partly because of not being native, partly "Android mistyping", partly my strange typos I am always shocked seeing. :-) $\endgroup$ – Poutnik Mar 25 '20 at 11:17
  • $\begingroup$ @Karl ... but "not to verb" versus "to not verb" is a moot point. learnersdictionary.com/qa/Split-Infinitives "Be aware that putting "not" or another adverb between "to" and its verb adds some emphasis to that adverb. For example, in the sentence "They decided not to stay another night" the phrase "they decided" is the most important information, but the sentence "They decided to not stay another night" tells us that maybe they decided to stay another night before, but now it is important that they will not stay." $\endgroup$ – Poutnik Mar 25 '20 at 11:23
  • $\begingroup$ @Poutnik I though you were not quite up to your usual standard! :)) And yea, the "to not" / "not to" can give a different emphasis, although here on second thought I guess it makes no real difference. $\endgroup$ – Karl Mar 25 '20 at 19:14

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