# Question fa222

Jun 22, 2017

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 $\text{1 kg}$ 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) $\text{kg}$

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

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

$= \text{0.050 moles"/(9 * 10^(-2)) * 1/"1 kg}$

$= \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{0.56 mol kg}}^{- 1}}}}$

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.