Calculate the molarity, molality and mole fraction of ethyl alcohol in a solution of total volume 95 mL prepared by adding 50 mL of ethyl alcohol (density $= 0.789 m L^{- 1}$ ) to 50 mL water (density $= 1.00 g m L^{- 1}$ ).

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Solution

No. of moles of ethyl alcohol $= \frac{V o l u m e \times d e n s i t y}{M o l a r m a s s}$

$= \frac{50 \times 0.789}{46}$

$= 0.8576$

No. of moles of water $= \frac{V o l u m e \times d e n s i t y}{M o l a r m a s s}$

$= \frac{50 \times 1}{18}$

$= 2.7777$

Molarity $= \frac{N o . o f m o l e s}{V o l . o f s o l . i n m L} \times 1000$

$= \frac{0.8576}{95} \times 1000 = 9.027 M$

Molality $= \frac{N o . o f m o l e s o f s o l u t e}{M a s s o f s o l v e n t i n g r a m s} \times 1000$

$= \frac{0.8576}{50} \times 1000 = 17.152 m$

Mole fraction $= \frac{0.8576}{0.8576 + 2.7777} = \frac{0.8576}{3.6353} = 0.236$

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