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A solution of sucrose (molar mass = 342 g $mol^{-1}$) has been prepared by dissolving 68.5 g of sucrose in 1000 g of water. The freezing point of the solution obtained will be ($K_f$ for water = 1.86 K kg $mol^{-1}$)
A
$-0.570^\circ C$
B
$-0.372^\circ C$
C
$-0.520^\circ C$
D
$+0.372^\circ C$
Detailed Solution
Moles of sucrose = $\frac{68.5}{342} = 0.2003$ mol
Molality: $m = \frac{0.2003\ mol}{1\ kg} = 0.2003$ mol $kg^{-1}$
Sucrose is a non-electrolyte (i = 1): $\Delta T_f = K_f\times m = 1.86\times0.2003$
$\Delta T_f = 0.372$ K
Freezing point of solution = $0 - 0.372$
$= -0.372^\circ C$
Molality: $m = \frac{0.2003\ mol}{1\ kg} = 0.2003$ mol $kg^{-1}$
Sucrose is a non-electrolyte (i = 1): $\Delta T_f = K_f\times m = 1.86\times0.2003$
$\Delta T_f = 0.372$ K
Freezing point of solution = $0 - 0.372$
$= -0.372^\circ C$