91Ó°ÊÓ

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.

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

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

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

Mole Fraction can be defined as the ratio of the number of moles of the solute to the number of moles of solvent and number of solute.

$\mathbf{Mole} \mathbf{Fraction}\mathbf{=}\frac{\mathbf{Number} \mathbf{of}\mathbf{} \mathbf{Moles}\mathbf{} \mathbf{of}\mathbf{} \mathbf{One}\mathbf{} \mathbf{Component}}{\mathbf{Number} \mathbf{of}\mathbf{Moles} \mathbf{of} \mathbf{the}\mathbf{} \mathbf{Solvent}\mathbf{+}\mathbf{Number}\mathbf{} \mathbf{of}\mathbf{} \mathbf{Moles} \mathbf{of}\mathbf{} \mathbf{Solute}}$

$\mathbf{Mass}\mathbf{\%}\mathbf{=}\frac{\mathbf{Mass}\mathbf{} \mathbf{of} \mathbf{solute}}{\mathbf{Mass} \mathbf{of} \mathbf{solution}}\mathbf{×}\mathbf{100}$

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

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

Volume of Water$\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{500}\mathbf{L}\mathbf{=}\mathbf{500}\mathbf{mL}$

Density of the Water $\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{g}\mathbf{/}\mathbf{mL}$

$$\begin{gathered} \mathbf{Density}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Benzene}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Volume}} \\ \mathbf{1}\mathbf{.}\mathbf{0}\mathbf{g}\mathbf{/}\mathbf{mL}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{2}\mathbf{.}\mathbf{66}\mathbf{mL}} \\ \mathbf{Mass}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{g}\mathbf{/}\mathbf{mL}\mathbf{×}\mathbf{500}\mathbf{mL} \\ \mathbf{Mass}\mathbf{=}\mathbf{500}\mathbf{g} \end{gathered}$$

Mass of Solvent, Water $\mathbf{=}\mathbf{500}\mathbf{g}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{500}\mathbf{kg}$

Molality of solute, CsBr $\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{4}\mathbf{m}$

$$\begin{gathered} \mathbf{Molality}\mathbf{=}\frac{\mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}}{\mathbf{Mass}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{Solvent}\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{in}\mathbf{ }\mathbf{kg}\mathbf{ }\mathbf{)}} \\ \mathbf{0}\mathbf{.}\mathbf{4}\mathbf{m}\mathbf{=}\frac{\mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}}{\mathbf{0}\mathbf{.}\mathbf{500}\mathbf{kg}} \\ \mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{2} \end{gathered}$$

Number of moles of water $\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{m}$

$$\begin{gathered} \mathbf{Number} \mathbf{of} \mathbf{Moles}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Molar} \mathbf{Mass}} \\ =\frac{\mathbf{500}\mathbf{g}}{\mathbf{18}\mathbf{g}\mathbf{/}\mathbf{mole}} \\ \mathbf{=}\mathbf{28}\mathbf{mole} \end{gathered}$$

Number of moles of CeBr $\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{moles}$

Number of moles of water $\mathbf{=}\mathbf{28}\mathbf{moles}$

role="math" localid="1659355972498" $$\begin{gathered} \mathbf{Mole}\mathbf{ }\mathbf{Fraction}\mathbf{=}\frac{\mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{One}\mathbf{ }\mathbf{Component}}{\mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{Solvent}\mathbf{+}\mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Solute}} \\ \mathbf{Mole}\mathbf{ }\mathbf{Fraction}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{CsBr}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{2}}{\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{+}\mathbf{28}} \\ \mathbf{Mole}\mathbf{ }\mathbf{Fraction}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{CsBr}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{2}}{\mathbf{28}\mathbf{.}\mathbf{2}} \\ \mathbf{Mole}\mathbf{ }\mathbf{Fraction}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{CsBr}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0071} \end{gathered}$$

$$\begin{gathered} \mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Molar}\mathbf{ }\mathbf{Mass}} \\ \mathbf{NumberofMoles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{CsBr}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{213}\mathbf{g}\mathbf{/}\mathbf{mol}} \\ \mathbf{0}\mathbf{.}\mathbf{2}\mathbf{mole}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{213}\mathbf{g}\mathbf{/}\mathbf{mol}} \\ \mathbf{Mass}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{CsBr}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{mol}\mathbf{×}\mathbf{213}\mathbf{g}\mathbf{/}\mathbf{mol} \\ \mathbf{Mass}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{CsBr}\mathbf{=}\mathbf{42}\mathbf{.}\mathbf{6}\mathbf{g} \end{gathered}$$

Mass of CsBr $\mathbf{=}\mathbf{42}\mathbf{.}\mathbf{6}\mathbf{g}$

Mass of water $\mathbf{=}\mathbf{500}\mathbf{g}$

$$\begin{gathered}  \mathbf{Mass}\%\mathbf{=}\frac{\mathbf{Mass} \mathbf{of} \mathbf{Solute}}{\mathbf{Mass} \mathbf{of} \mathbf{the} \mathbf{Solution}}\mathbf{×}\mathbf{100} \\ \mathbf{=}\frac{\mathbf{42}\mathbf{.}\mathbf{6}\mathbf{g}}{\mathbf{500}\mathbf{+}\mathbf{42}\mathbf{.}\mathbf{6}\mathbf{g}}\mathbf{×}\mathbf{100} \\ \mathbf{=}\frac{\mathbf{42}\mathbf{.}\mathbf{6}\mathbf{g}}{\mathbf{542}\mathbf{.}\mathbf{6}\mathbf{g}}\mathbf{×}\mathbf{100} \\ \mathbf{=}\mathbf{7}\mathbf{.}\mathbf{9}\mathbf{\%} \end{gathered}$$