Question

Question #fa222

Answer 1

Here's what I got.

Explanation:

In order to find the molality of a solution, you need to divide the total number of moles of solute by the total mass of the solvent expressed in kilograms--this will get you the number of moles of solute present in `"1 kg"` of solvent.

Use the molar mass of sodium carbonate to convert the number of grams to moles

`5.3 color(red)(cancel(color(black)("g"))) * ("1 mole Na"_2"CO"_3)/(106color(red)(cancel(color(black)("g")))) = "0.050 moles Na"_2"CO"_3`

Convert the mass of water from grams to kilograms

`90 color(red)(cancel(color(black)("g"))) * "1 kg"/(10^3color(red)(cancel(color(black)("g")))) = 9 * 10^(-2)` `"kg"`

Now divide the number of moles by the total mass of the solvent

`"molality" = "0.050 moles"/(9 * 10^(-2)color(white)(.)"kg")`

`= "0.050 moles"/(9 * 10^(-2)) * 1/"1 kg"`

`= color(darkgreen)(ul(color(black)("0.56 mol kg"^(-1))))`

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one significant figure for the mass of water.