A solution of glucose (C6H12O6 ) is 18% by mass. The mole fraction of glucose will be

# A solution of glucose (C6H12O6 ) is 18% by mass. The mole fraction of glucose will be

1. A

0.18

2. B

0.25

3. C

0.0214

4. D

0.015

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### Solution:

Molar mass of ${\mathrm{C}}_{6}{\mathrm{H}}_{12}{\mathrm{O}}_{6}$  , ${M}_{2}=180\mathrm{g}{\mathrm{mol}}^{-1}$

Mass of glucose in the 100 g solution  m2 = 18 g

Amount of glucose in 100 g solution ${n}_{2}=\frac{{m}_{2}}{{M}_{1}}=\frac{10\mathrm{g}}{180\mathrm{g}{\mathrm{mol}}^{-1}}=0.1\mathrm{mol}$

Mass of water in 100 g solution, ${m}_{1}=82\mathrm{g}$

Amount of water in 100 g solution ${n}_{1}=\frac{{m}_{1}}{{M}_{1}}=\frac{8\mathrm{\angle }\mathrm{g}}{18\mathrm{g}{\mathrm{mol}}^{-1}}=4.56\mathrm{mol}$

Mole fraction of glucose, ${x}_{2}=\frac{{n}_{2}}{{n}_{1}+{n}_{2}}=\frac{0.1\mathrm{mol}}{\left(4.56+0.1\right)\mathrm{mol}}=0.0214$