The mole fraction of iodine, \({{\bf{I}}_{\bf{2}}}\), dissolved in dichloromethane,\({\bf{C}}{{\bf{H}}_{\bf{2}}}{\bf{C}}{{\bf{l}}_{\bf{2}}}\), is 0.115. What is the molal concentration, m, of iodine in this solution?

Molality may be defined as the ratio of the number of moles of the solute and the mass of the solvent (kg).

\(\begin{aligned}{l}{\bf{Molality = }}\frac{{{\bf{Number of moles}}}}{{{\bf{Mass of solvent(Kg)}}}}\\{\bf{Number of Moles = }}\frac{{{\bf{Mass of solute}}}}{{{\bf{Molarmass}}}}\end{aligned}\)

Mole Fraction of\({{\rm{I}}_{\rm{2}}}\)dissolved in dichloromethane,\({\rm{C}}{{\rm{H}}_{\rm{2}}}{\rm{C}}{{\rm{l}}_{\rm{2}}}\), is 0.115.

\({\rm{Mole Fraction of I2}} = \frac{{{\rm{Mole of I2}}}}{{{\rm{ Moles of I2 + Moles of CH2Cl2}}}}{\rm{ }}\)

Mole Fraction of\({{\rm{I}}_{\rm{2}}}\):

\({\rm{0}}{\rm{.115 = }}\frac{{{\rm{0}}{\rm{.115mole}}}}{{{\rm{0}}{\rm{.115 mole of I2 + 0}}{\rm{.885 mole of CH2Cl2}}}}\)

Mole Fraction of\({\rm{C}}{{\rm{H}}_{\rm{2}}}{\rm{C}}{{\rm{l}}_{\rm{2}}}\):

\({\rm{0}}{\rm{.885 = }}\frac{{{\rm{0}}{\rm{.885 mole of CH2Cl2}}}}{{{\rm{(0}}{\rm{.115 mole of I2\; + 0}}{\rm{.885mole ofCH2Cl2)}}}}\)

Mass of solvent,\({\rm{C}}{{\rm{H}}_{\rm{2}}}{\rm{C}}{{\rm{l}}_{\rm{2}}}\):

\({\rm{0}}{\rm{.885 mole\; \times 85 gmol}}{{\rm{e}}^{{\rm{ - 1}}}}{\rm{ = 75g}}\)

Mass of solvent,\({\rm{C}}{{\rm{H}}_{\rm{2}}}{\rm{C}}{{\rm{l}}_{\rm{2}}}\)= 0.075kg

\({\rm{Molality = }}\frac{{{\rm{0}}{\rm{.115g}}}}{{{\rm{0}}{\rm{.075}}}}{\rm{ = 1}}{\rm{.50m}}\)