What is the molality of a solution consisting of 2.66 mL of carbon tetrachloride (${\mathbf{CCl}}_{\mathbf{4}}$ ; d = 1.59 g/mL) in 76.5 mL of methylene chloride $\left({\mathrm{CH}}_2{\mathrm{Cl}}_2;d=1.33g/\mathrm{mL}\right)$?

Solution can be formed from the dissolution of the solute in the solvent.The solute decides the nature of the solution.

Molality can be defined as the ratio of the mass of the solute to the mass of the solution present in kilogram measure.

$\mathbf{Molality}\mathbf{=}\frac{\mathbf{Number} \mathbf{of}\mathbf{} \mathbf{Moles} \mathbf{of}\mathbf{} \mathbf{solute}}{\mathbf{Mass}\mathbf{} \mathbf{of} \mathbf{the} \mathbf{Solvent} \mathbf{(} \mathbf{in} \mathbf{kilogram} \mathbf{)}}$

Number of moles can be defined as the ratio of the mass of the atom/molecule and molar mass of the atom/molecule.

$\mathbf{Number} \mathbf{of} \mathbf{Moles}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Molar}\mathbf{} \mathbf{Mass}}$

Density can be defined as the ratio of the mass of the matter to the volume of the matter.

$\mathbf{Density}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Volume}}$

Density of the Carbon Tetrachloride, ${\mathbf{CCl}}_{\mathbf{4}}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{59}\mathbf{g}\mathbf{/}\mathbf{mL}$

$$\begin{gathered} \mathbf{Density} \mathbf{of} \mathbf{Benzene}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Volume}} \\ \mathbf{1}\mathbf{.}\mathbf{59}\mathbf{g}\mathbf{/}\mathbf{mL}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{2}\mathbf{.}\mathbf{66}\mathbf{mL}} \\ \mathbf{Mass}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{59}\mathbf{g}\mathbf{/}\mathbf{mL}\mathbf{\times }\mathbf{2}\mathbf{.}\mathbf{66}\mathbf{mL} \\ \mathbf{Mass}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{23}\mathbf{g} \end{gathered}$$

Mass of carbon tetrachloride, ${\mathbf{CCl}}_{\mathbf{4}}\mathbf{}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{23}\mathbf{g}$

$$\begin{gathered} \mathbf{Number} \mathbf{of}\mathbf{} \mathbf{Moles}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Molar} \mathbf{Mass}} \\ \mathbf{Number}\mathbf{}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Moles} \mathbf{of} {\mathbf{CCl}}_{\mathbf{4}}\mathbf{=}\frac{\mathbf{4}\mathbf{.}\mathbf{23}\mathbf{g}}{\mathbf{154}\mathbf{g}\mathbf{/}\mathbf{mol}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{027}\mathbf{mol} \end{gathered}$$

Volume of methylene chloride, ${\mathbf{CH}}_{\mathbf{2}}{\mathbf{Cl}}_{\mathbf{2}}\mathbf{=}\mathbf{76}\mathbf{.}\mathbf{5}\mathbf{mL}$

Density of the methylene chloride, ${\mathbf{CH}}_{\mathbf{2}}{\mathbf{Cl}}_{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{33}\mathbf{g}\mathbf{/}\mathbf{mL}$

$$\begin{gathered} \mathbf{Density} \mathbf{of} \mathbf{Methylene} \mathbf{Chloride}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Volume}} \\ \mathbf{1}\mathbf{.}\mathbf{33}\mathbf{g}\mathbf{/}\mathbf{mL}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{76}\mathbf{.}\mathbf{5}\mathbf{mL}} \\ \mathbf{Mass}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{33}\mathbf{g}\mathbf{/}\mathbf{mL}\mathbf{\times }\mathbf{76}\mathbf{.}\mathbf{5}\mathbf{mL} \\ \mathbf{Mass}\mathbf{=}\mathbf{101}\mathbf{.}\mathbf{7}\mathbf{g} \end{gathered}$$

Mass of Solvent methylene chloride, ${\mathbf{CH}}_{\mathbf{2}}{\mathbf{Cl}}_{\mathbf{2}}\mathbf{=}\mathbf{101}\mathbf{.}\mathbf{7}\mathbf{g}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1017}\mathbf{kg}$

$$\begin{gathered} \mathbf{Molality}\mathbf{=}\frac{\mathbf{Number} \mathbf{of} \mathbf{Moles}}{\mathbf{Mass} \mathbf{of} \mathbf{the} \mathbf{Solvent} \mathbf{(} \mathbf{in} \mathbf{Litre} \mathbf{)}} \\ \mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{027}\mathbf{mol}}{\mathbf{0}\mathbf{.}\mathbf{1017}\mathbf{kg}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{265}\mathbf{m} \end{gathered}$$