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

(i) Mass of sugar = 34.2 g

No. of moles of sugar $= \frac{34.2}{M o l . m a s s} = \frac{34.2}{342} = 0.1$

Mass of water = (214.2-34.2) $= 180 g = \frac{180}{1000} k g$

No. of moles of water $= \frac{180}{18} = 10$ mole

Molarity $= \frac{N o . o f m o l e s o f s u g a r}{M a s s o f w a t e r i n k g} = \frac{0.1}{180} \times 1000$

$= 0.555 M$

Thus, the molarity of sugar is 0.555 M

(ii) Total number of moles $= 10.0 + 0.1 = 10.1$

Mole fraction of sugar $= \frac{N o . o f m o l e s o f s u g a r}{T o t a l n u m b e r o f m o l e s}$

$= \frac{0.1}{10.1} = 0.0099$

Thus mole fraction of sugar syrup is 0.0099

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