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Q)

A sugar syrup of weight 214.2g contains 34.2g of sugar ($C_{12}H_{22}O_{11})$. Calculate (i) Molal concentration and (ii) Mole fraction of sugar in the syrup.

$\begin{array}{1 1}(a)\;0.56,0.0099& (b)\;0.60,0.0999 \\(c)\;0.0099,0.56&(d)\;0.54,0.1999\end{array} $

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A)
(i) Weight of sugar syrup =214.2g
Weight of sugar in syrup=34.2g
$\therefore$ Weight of water in sugar syrup=(214.2-34.2)g
$\Rightarrow 180.0g$
Molecular weight of sugar=$(C_{12}H_{22}O_{11})$=342
$\therefore$ Molal concentration =$\large\frac{34.2\times 1000}{342\times 180}$$=0.56$
(ii) Mole fraction of sugar
$\large\frac{34.2/342}{(180/18)+(34.2/342)}$
(Mol.wt of water=18)
$\Rightarrow \large\frac{0.1}{10+0.1}=\frac{0.1}{10.1}$$=0.0099$
Hence (a) 0.56,0.0099 is the correct option.
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