Question #608c2

1 Answer
Jan 14, 2018

Answer:

#"0.391 mol kg"^(-1)#

Explanation:

As you know, a solution's percent concentration by mass tells you the number of grams of solute present for every #"100 g"# of the solution.

In your case, the solution is said to be #3.22%# sodium nitrate by mass, which means that if you take #"100 g"# of this solution, the sample will contain #"3.22 g"# of sodium nitrate, the solute.

Consequently, this #"100-g"# sample of the solution will contain

#"mass of solvent" = overbrace("100 g")^(color(blue)("mass of solution")) - overbrace("3.22 g")^(color(blue)("mass of solute"))#

#"mass of solvent = 96.78 g"#

of water, the solvent. Now, in order to find the molality of the solution, you need to figure out how many moles of sodium nitrate are present for every #"1 kg"# of solvent.

Since you know how many grams of sodium nitrate are present for every #"96.78 g"# of water, you can calculate the mass of sodium nitrate present for every #"1 kg" = 10^3 quad"g"# of water first

#10^3 color(red)(cancel(color(black)("g water"))) * "3.22 g NaNO"_3/(96.78color(red)(cancel(color(black)("g water")))) = "33.27 g"#

then use the molar mass of sodium nitrate to convert the number of grams to moles.

#33.27 color(red)(cancel(color(black)("g"))) * "1 mole NaNO"_3/(84.9947color(red)(cancel(color(black)("g")))) = "0.391 moles NaNO"_3#

You can thus say that the molality of the solution, i.e. the number of moles of sodium nitrate present for every #10^3 quad "g" = "1 kg"# of water, is equal to

#color(darkgreen)(ul(color(black)("molality = 0.391 mol kg"^(-1))))#

The answer is rounded to three sig figs, the number of sig figs you have for the percent concentration of the solution.