Question

# 214.2 g of sugar syrup contains 34.2 g of sugar.Calculate (i) molarity of the solution(ii) mole fraction of sugar in the syrup.

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Solution

## Analyzing the given data:Given Mass of sugar $=34.2\mathrm{g}$Molar Mass of sugar $=342\mathrm{g}{\mathrm{mol}}^{-1}$No. of moles of sugar = $\frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molecular}\mathrm{mass}}=\frac{34.2}{342}=0.1\mathrm{mole}$Sugar syrup contains sugar in water.So, $\mathrm{mass}\mathrm{of}\mathrm{water}=\left(214.2-34.2\right)\mathrm{g}=180\mathrm{g}$Molar Mass of Water $=18\mathrm{g}{\mathrm{mol}}^{-1}$No. of moles of water = $\frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molecular}\mathrm{mass}}=\frac{180}{18}=10\mathrm{mole}$Part (i): Molarity of solutionMolarity(M): The number of moles of a solute dissolved in 1 L (1000 ml) of the solution is known as the molarity of the solution.$\mathrm{Molarity}\left(\mathrm{M}\right)=\frac{\mathrm{Mole}\mathrm{of}\mathrm{solute}}{\mathrm{Volume}\mathrm{of}\mathrm{solution}\left(\mathrm{in}\mathrm{litre}\right)}$$\mathrm{M}=\frac{0.1}{180}×1000=0.555\mathrm{M}$Thus, the molarity of sugar is 0.555 MPart (ii): Mole fraction of sugar Total number of moles of solution = mole of solute + mole of solvent $=0.1+10=10.1$$\mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{sugar}=\frac{\mathrm{Mole}\mathrm{of}\mathrm{sugar}}{\mathrm{Total}\mathrm{mole}\mathrm{of}\mathrm{solution}}=\frac{0.1}{10.1}=0.0099$Thus, mole fraction of sugar in the syrup is 0.0099.

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