$20.4 g o f K H P (K C_{8} H_{5} O_{4})$ is dissolved in water, giving a solution with a mass of $118.4 g .$ A solution of sodium hydroxide is also prepared. $4.4 g$ of this sodium hydroxide solution reacts completely with 5.8 of the KHP solution above. Sodium hydroxide reacts in a 1:1 mole ratio with KHP. In a similar reaction, $4.4 g$ of the sodium hydroxide solution reacts completely with a $5.9 g$ sample of vinegar (containing acetic acid, $C H_{3} C O O H$ ). Sodium hydroxide reacts in a 1:1 mole ratio with acetic acid. Calculate the percentage by mass of acetic acid present in the vinegar sample.
$[M o l a r m a s s o f K H P = 204, N a O H = 40 a n d C H_{3} C O O H = 60]$

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answer is 5.

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Detailed Solution

$w_{K H P} in 5.8 g soln = \frac{20.4}{118.4} \times 5.8 \Rightarrow n_{K H P} = \frac{20.4}{118.4} \times \frac{5.8}{204} = n_{N a O H} = n_{A c O H} \Rightarrow w_{A c O H} = \frac{20.4}{118.4} \times \frac{5.8}{204} \times 60 \Rightarrow % A c O H = \frac{20.4}{118.4} \times \frac{5.8}{204} \times \frac{60}{5.8} \times 100 = 5$