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# A solution of glucose in water is labelled as 10% w/w, what would be the molality and mole fraction of each component in the solution? If the density of solution is $1.2 g mL^{–1}$, then what shall be the molarity of the solution?

$\begin{array}{1 1}0.617m,0.01,0.99,0.67M\\1.617m,0.02,0.98,0.57M\\2.617m,0.05,0.95,0.47M\\4.617m,0.08,0.92,0.87M\end{array}$

10g glucose is present in 100g solution (ie) 90g of water =0.090 kg of water
10g glucose =$\large\frac{10}{180}$ mol
$\qquad\qquad\;=0.0555$ mol
90g $H_2O=\large\frac{90}{18}$$=5 moles Molarity =\large\frac{0.0555}{0.090kg}$$=0.617m$
Mole fraction of glucose $x_B=\large\frac{0.0555}{5+0.0555}$
$\Rightarrow 0.01$
Mole fraction of water $(x_A)=1-0.01$
$\Rightarrow 0.99$
100g of solution =$\large\frac{100}{1.2}$mL
$\Rightarrow$ 83.33mL
$\Rightarrow 0.08333$L
Molarity =$\large\frac{0.0555}{0.08333L}$$=0.67$M