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According to Freezing Point Depression relation, $$ \boxed { \Delta { T }_{ f } = K_{ f } \times m } $$ Lets substitute the value to molality m, $$ \Delta { T }_{ f } = K_{ f } \times \frac { W_{ 2 } }{ W_{ 1 }M_{ 2 } } \times 1000 $$ $$ \therefore \boxed { M_{ 2 } = \frac { 1000W_{ 2 }K_{ f } }{ \Delta { T }_{ f }W_{ 1 } } } $$ Thus, by determining the depression in freezing point of the solution it is possible to calculate the molecular weight of the dissolved solute.
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