# Calculate the molality of a solution made by dissolving "115 g" of "NaNO"_3 in "500. mL" of water? The molar mass of "NaNO"_3 is "85.0 g/mol" and the density of water is "1.00 g/mL".

Dec 20, 2017

${\text{2.71 mol kg}}^{- 1}$

#### Explanation:

As you know, the molality of a solution tells you the number of moles of solute present for every $\text{1 kg}$ of the solvent.

This means that the first thing that you need to do here is to figure out how many grams of water are present in your sample. To do that, use the density of water.

500. color(red)(cancel(color(black)("mL"))) * "1.00 g"/(1color(red)(cancel(color(black)("mL")))) = "500. g"

Next, use the molar mass of the solute to determine how many moles are present in the sample.

115 color(red)(cancel(color(black)("g"))) * "1 mole NanO"_3/(85.0color(red)(cancel(color(black)("g")))) = "1.353 moles NaNO"_3

So, you know that this solution will contain $1.353$ moles of sodium nitrate, the solute, for $\text{500. g}$ of water, the solvent.

In order to find the molality of the solution, you must figure out how many moles of solute would be present for $\text{1 kg} = {10}^{3}$ $\text{g}$ of water.

10^3 color(red)(cancel(color(black)("g water"))) * "1.353 moles NaNO"_3/(500. color(red)(cancel(color(black)("g water")))) = "2.706 moles NaNO"_3

You can thus say that the molality of the solution is equal to

color(darkgreen)(ul(color(black)("molality"))) = "2.706 mol kg"^(-1) ~~ color(darkgreen)(ul(color(black)("2.71 mol kg"^(-1)))

The answer is rounded to three sig figs.

So, you know that this solution will contain $2.71$ moles of solute for every $\text{1 kg}$ of solvent.