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Relative Lowering of Vapour Pressure

Cane sugar un...

Question

Cane sugar underoges the inversion as follow:
$C_{12} H_{22} O_{11} + H_{2} O \to C_{6} H_{12} O_{6} + C_{6} H_{12} O_{6}$
If solution of 0.025 moles of sugar in 200 gm of water show depression in freezing point 0.372 $^{o}$ C, then what % sucrose has inverted. $(K_{f} (H_{2} O) = 1.86 K k g m o l^{1})$

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Solution

The expression for the depression in the freezing point is
$Δ_{i f} = i K_{f}$ .m
$0.372 = (1 + α) \times 1.86 \times \frac{0.025}{200} \times 1000$
$1 + α = 1.6$
$α = 0.6$ or 6 %
Hence, the percentage sucrose that has inverted is 6%.

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