# Find the volume of sea water

The concentration of all salts present in sea-water is 3.52 % (m/v). Calculate the volume of sea-water, which on evaporation will produce 5 kg of salt.

My attempt: \begin{align} 5~\mathrm{kg} &= 5000~\mathrm{g}\\ \text{Volume} &= \frac{\text{Mass}}{\text{Density}}\\ \text{Volume of salt} &= 5000~\mathrm{mL}\\ \text{Total Volume of Solution} &= \text{Volume of Salt} + \text{Volume of water}\\ \therefore \text{Total Volume of Solution} &= 5000 + x\\ \text{Concentration} &= \left(\frac{\text{Mass of Solute}}{\text{Volume of Solution}}\right) \cdot 100\\ 3.52 &= \left(\frac{5000}{5000 + x}\right) \cdot 100\\ x &= 137045.45 \end{align}

• Percent proportions are dimensionless. 3.52% means that there are 0.0352 kg salt in 1.000 kg sea water. To calculate the volume you need to know the density of 3.52% sea water which is 1.025 kg/l at 25°C. – aventurin Jun 30 '16 at 19:04
• @aventurin Please note the incorrect, but common usage of the percent concentration, as stated in Wikipedia. – Martin - マーチン Jul 4 '16 at 4:02
• I have updated your post with chemistry markup. If you want to know more, please have a look here and here. We prefer to not use MathJax in the title field, see here for details. What is actually your question? Do you want to know if your approach is correct? – Martin - マーチン Jul 4 '16 at 4:10

3.52% m/v means 3.52g/100ml.

So, 5/0.0352 = 142.045.

5 g per 142.045 ml = 5kg/142.045L.

• It would be preferable, if you could add some explanations instead of just equations. Especially when such a weird unit is used. – Martin - マーチン Jul 4 '16 at 4:21
• @Martin-マーチン The expression of mass per volume (% m/v) is very common, (probably) because it is convenient; but it's not great for accuracy (depends on temperature). There is a supposition in the question that the volume of salt is 5000 ml. This is far from accurate. The volume of salt is not 5000ml. From the question, x is approximately the volume of H2O. The volume of sea water = 137045.45 + (5000, not) = 142045.45ml. Actually the volume of salt is variable depending on whether it is solid or dissolved; but either way, it's irrelevant. 3.52 = (5kg/(1ml + x))*100. x +1ml = 14202545.45 ml – Ben Welborn Jul 5 '16 at 13:41
• With a strange unit I mean that it does not fit in the SI system. It omits the unit completely. You can edit your answer to add further explanations. The volume of the salt is neither given, implied, nor relevant to the question. You are simply looking for the volume of a solution, given its concentration and mad of solute. Your comment does not make any sense. – Martin - マーチン Jul 5 '16 at 15:26
• @Martin-マーチン I think that you might not have been able to see the question. You reiterated my comment, that the volume of salt is irrelevant. The volume of salt was figured to be 5000ml (in the question that perhaps you can't see?). The volume of salt could be 123ml... you still get 142.045L of salt water (from these equations). – Ben Welborn Jul 5 '16 at 17:09
• I am perfectly well capable of seeing the question, including the attempt of the OP. I was the one reformating it. I was simply trying to tell you, that presenting some equations without the use of proper units and without any explanation is not helpful for anyone. This is why I downvoted your post. The screenshot you have posted still does not help much, as it does not explain, it rather hints with a few words that something is wrong. The biggest issue with the question itself (not the attempt included in the post) is the problem with the highly ambiguous % m/v unit. – Martin - マーチン Jul 5 '16 at 17:33