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Suppose I would like to create a one molar solution of NaCl in water. The molar concentration is defined as

$c_i=\frac{n_i}{V} $

$n_i=1$ in this case. I need to take 58.5 grams of NaCl (atomic weight of Na=23 & Cl=35.5) and dissolve it in water until the total solvent volume is 1 litre. The total volume of the water added is less than 1 litre. But what exactly is that amount of water and how can I determine it apriori from thermodynamics?

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You can calculate it using partial molar volumes.

The partial molar volume is defined as the differential change in volume with respect to change in mole fraction, and is determined experimentally. From the definition of partial molar properties, you can calculate the amount of one component needed to achieve a certain volume, if you know all of the partial molar volumes and pure component molar volumes.

There may be some complications to that for this system because you are talking about mixing a solid-phase ionic compound with water, instead of two liquids directly.

In practice, it is much easier to just use a volumetric flask so that you know the total volume is 1 L. If you measure the amount of water you actually used you will find that it is very close to 1 L.

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  • $\begingroup$ Thank you. I was just curious and maybe it will be useful to automate for industrial level production. $\endgroup$ – WanderingMind Oct 22 '14 at 18:51
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    $\begingroup$ Your best bet for automation would be to use a batch process that had a tank water-level sensor to shut off water flow when it reaches the correct volume. You could then measure out the right amount of salt by mass (also automated), dump it into the mixing vessel, and add water until it reaches the shutoff sensor. It might be possible to set up a continuous process instead of batch, but I don't think it would be worth the effort unless you needed very large amounts of continuously supplied solution. $\endgroup$ – thomij Oct 22 '14 at 20:46

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