Question

What is the molality of a solution in which 25 g of NaCl is dissolved in 20 Kg of water?

Answer 1

`"0.02 mol kg"^(-1)`

Explanation:

The molality of a solution essentially relates the number of moles of solute and the mass of the solvent.

More specifically, molality is defined as the number of moles of solute, which in your case is sodium chloride, `"NaCl"`, present in one kilogram of solvent, which is water.

To find the number of moles of sodium chloride present in your sample, sue the compound's molar mass

`25 color(red)(cancel(color(black)("g"))) * "1 mole NaCl"/(58.44color(red)(cancel(color(black)("g")))) = "0.428 moles NaCl"`

Now, you know that you're dissolving this many moles of sodium chloride in `"20 kg"` of water. You can thus use the composition of this solution to find the number of moles of solute present in `"1 kg"` of water

`1 color(red)(cancel(color(black)("kg water"))) * "0.428 moles NaCl"/(20color(red)(cancel(color(black)("kg water")))) = "0.0214 moles NaCl"`

Rounded to one significant figure, the number of sig figs you have for the mass of water, the molality of the solution will be

`color(green)(bar(ul(|color(white)(a/a)color(black)("molality" = "0.02 mol kg"^(-1))color(white)(a/a)|)))`