Question

The solubility of substance $X$ in pure ethanol is $0.1\, g \,/ L$ and in water is $0.01\, g /\, L$. To dissolve $11\,g$ of dry $X$ we are adding $20\, ml$ of fresh $50 \%( V / V )$ ethanol solution in each time on $X$. How many times we are to add this ethanol solution to dissolve $X$?

• A. $100$
• B. $10^{6}$
• C. $10^{3}$
• D. $10^{4}$

Answer 1

Answer: (D)

Each time we are adding $20\, ml$ ethanol solution. In $20\, ml$ ethanol solution vol. $C _{2} H _{5} OH =10 \,ml$ and vol. of water $=10 \,ml$

In $10 \,ml$ ethanol mass of " $X$'' dissolved $=\frac{0.1}{1000} \times 10\, g$

In $10 \,ml$ water mass of ''$ X$'' dissolved $=\frac{0.01}{1000} \times 10\, g$

In each time, total mass of " $X$ ''dissolved $=\frac{1.1}{1000} \,g$

$\therefore $ No. of times of addition of ethanol solution

$=\frac{11}{1.1} \times 1000=10^{4}$