Question fb5ec

Feb 16, 2016

${\text{0.670 mol kg}}^{- 1}$

Explanation:

Start by making sure that you know what it is you're looking for here.

A solution's molality tells you how many moles of solute you get per kilogram of solvent.

$\textcolor{b l u e}{b = {n}_{\text{solute"/m_"solvent}}}$

This means that in order to find any solution's molality, you need to know two things

• how many moles of solute you have present
• the mass of solvent expressed in kilograms

Notice that the problem provides you with the mass of solute, which will get you the number of moles of solute, and the mass of the solvent, which means that you don't need to use the solution's density to find its molarity.

So, use naphthalene's molar mass to determine how many moles you get in that $\text{36.5-g}$ sample

36.5 color(red)(cancel(color(black)("g"))) * ("1 mole C"_10"H"_8)/(128.17color(red)(cancel(color(black)("g")))) = "0.2848 moles C"_10"H"_8

To convert the mass of the solvent from grams to kilograms, use the conversion factor

$\text{1 kg" = 10^3"g}$

The molality of the solution will thus be

b = "0.2848 moles"/(425 * 10^(-3)"kg") = color(green)("0.670 mol kg"^(-1))#

The answer is rounded to three sig figs.