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Explanation:

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Given info : The solubility of substance X in pure ethanol is 0.1 g/l and in water is 0.01 g/l .to dissolve 11 gm of dry X we are adding 20ml of fresh 50%.(v/v) ethanol solution in each time on X.

To find : How many times do we add this ethanol solution to dissolve X ?

solution : each time, 20 ml of fresh 50% (v/V) ethanol solution is added.

so in 20 ml ethanol solution contains 10 ml ethanol and 10 ml water.

as solubility of substance X in ethanol is 0.1 g/L

and in water is 0.01g/L

so each time, substance X = 10ml/1000ml × 0.1 g (from ethanol) + 10ml/1000ml × 0.01 g (from water)

= 10¯³ g + 10¯⁴ g

= 1.1 × 10¯³ g

let n times we add ethanol solution.

so, n = mass of substance X/each time substance X

= 11g/(1.1 × 10¯³g)

= 10⁴

Therefore 10⁴ times, ethanol solution is added.