Question #5a849

1 Answer
Mar 3, 2017

Answer:

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

Explanation:

We use molality as a measure of the number of moles of solute present in a solution for every #"1 kg"# of solvent.

In your case, the molality of the solution will tell you how many moles of sodium hydroxide, your solute, you'd get for every #"1 kg"# of water, your solvent.

You already know that a sample of this solution contains #"2 g"# of sodium hydroxide in #"500 g"# of water, so the first thing to do here is to figure out how much sodium hydroxide you'd get for #"1 kg"# of water.

#1 color(red)(cancel(color(black)("kg water"))) * (10^3color(red)(cancel(color(black)("g"))))/(1color(red)(cancel(color(black)("kg")))) * "2 g NaOH"/(500color(red)(cancel(color(black)("g water")))) = "4 g NaOH"#

Now all you have to do is convert the mass of sodium hydroxide to moles by using the compound's molar mass

#4 color(red)(cancel(color(black)("g"))) * "1 mole NaOH"/(40.0color(red)(cancel(color(black)("g")))) = "0.1 moles NaOH"#

Since this represents the number of moles of solute present in #"1 kg"# of water, the molality of the solution will be

#color(darkgreen)(ul(color(black)("molality = 0.1 mol kg"^(-1))))#

The answer is rounded to one significant figure.