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Question

# An aqueous solution containing 35.9 g of an unknown molecular (no nelectrolyte) compound in 150.0 g of water has a freezing point of - 1.3$^{\circ} \mathrm{C}$. Calculate the molar mass of the unknown compound.

Solution

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The freezing-point depression ($\mathcal 4 T_f$) is defined as the freezing point of the pure solvent ($T_f$) minus the freezing point of the solution ($T^o_f$):

$\mathcal 4 T_f = T_f^o -T_f$

$\mathcal 4 T_f = K_fm$

$\mathrm{1.3 ^oC }= \mathrm{ 1.86\text{ } \dfrac{^oC}{m} \times } x_{molal}$

$x_{molal}= \mathrm{0.6989 \text{ } \dfrac{mol}{kg} }$

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