Vinegar is an acid with its key ingredient, acetic acid. It is widely used for food preservation and cooking. The acetic concentration for table vinegar is typically $5 %$ whereas higher concentration upto $18 %$ is used as preservative. The word "vinegar" is derived from vin aigre, meaning "sour wine".

A table vinegar sample contains $5 %$ (mass/mass) of acetic acid.

To what volume $10 m L$ of the above sample should be diluted to prepare $0.10 M$ acetic acid solution. (density $1.05 g m L^{- 1}$ , Molar mass of $C H_{3} C O O H - 60.0 g m o l^{- 1}$ )

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Solution

Let, mass of solution = $100 g$
Mass of vinegar = $5 g$

Molarity = $\frac{m o l e s}{v o l u m e}$ = $\frac{m a s s \times d e n s i t y}{m o l a r m a s s \times m a s s o f s o l u t i o n} \times 1000$

Molarity = $\frac{5 \times 1.05}{60 \times 100} \times 1000 = 0.875$ M

Again,
$M_{1} V_{1} = M_{2} V_{2}$

$0.875 \times 10 = 0.10 \times V_{2}$

Thus,
$V_{2} = 87.5 m l$

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