Question

When $10$ mL of ethyl alcohol (density $=0.7893gm{L}^{-1})$ is mixed with $20$ mL of water (density $0.9971gm{L}^{-1})$ at ${25}^{o}C$, the final solution has a density of $0.9571gm{L}^{-1}$. The percentage change in total volume on mixing is :

• A. $3.1\%$
• B. $2.4\%$
• C. $1\%$
• D. none of these

Answer 1

The correct option is A $3.1\%$

Mass $=$ density $\times$ volume

Mass of ethyl aclohol $=0.7893\times 10=7.893$g

Mass of water $=0.9971\times 20=19.942$g

Total mass of solution $=7.893+19.942=27.835$ g

Volume of solution after mixing $=\frac{Mass}{Density}=\frac{27.835}{0.9571}=29.083mL$

Total volume of ethanol and water before mixing $=10+20=30mL$

The percentage change in total volume on mixing is $=\frac{30-29.083}{30}\times 100=3.1$ %.