Question

For \[1.5g\] of a substance when dissolved in $60g$ water lowered the freezing point by ${0.136^ \circ }C$. Calculate the molecular mass of the substance when depression constant of water is $1.86$
$
  A)329.1 \\
  B)439.5 \\
  C)341.9 \\
  D)335.9 \\
$

Answer 1

Hint: Freezing point depression is a colligative property observed in solutions that results from the introduction of solute molecules to a solvent. The freezing points of solutions are all lower than that of the pure solvent and is directly proportional to the molality of the solute.

Complete answer: Freezing point depression refers to the lowering of the freezing point of solvents substance freezes, caused when a smaller amount of another, non-volatile substance is added
$\Delta {T_f} = {K_f}.b.i$
Where,
$\Delta {T_f}$ is the freezing point depression,
$i$ is the Van’t Hoff factor,
${K_f}$ is the cryoscopic constant, and
$b$is the molality.
We know ,
$molality = \dfrac{{moles\;of\;solute}}{{kilogram\;of\;volume}}$
And, it is given in the question that, ${W_B} = 1.5g,{W_A} = 60g,{K_f} = 18.6,\Delta {T_f} = 0.136$
Here, ${W_B} = $Mass of solute
${W_A} = $Mass of solvent
${M_B} = $Molar mass of solute
Let’s put the values in the formula
\[ \Rightarrow \]
$\Delta {T_f} = \dfrac{{{K_f} \times {W_B} \times 1000}}{{{M_B} \times {W_A}}}$
${M_B} = \dfrac{{{K_f} \times {W_B} \times 1000}}{{\Delta {T_f} \times {W_A}}}$
${M_B} = \dfrac{{18.6 \times 1.5 \times 1000}}{{0.136 \times 60}}$
\[ \Rightarrow \]
${M_B} = 341.9gmo{l^{ - 1}}$
Hence option C is correct.

Additional information:
The Van't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as calculated from its mass. For most non-electrolytes dissolved in water, the Van't Hoff factor is essentially $1$. For most ionic compounds dissolved in water, the Van't Hoff factor is equal to the number of discrete ions in a formula unit of the substance.

Note:
The phenomenon of freezing point has numerous practical occupations. The radiator liquid in a vehicle is a combination of water and ethylene glycol. The freezing point depression keeps radiators from freezing in winter. Street salting exploits this impact to bring down the freezing point of the ice it is set on.