Question

The density of water and ethanol at room temperature is $1.0$g $/$mL and $0.789$g$/$mL respectively. What volume of ethanol contains the same number of molecules as are present in $100$mL of water?

• A. $307.8$mL
• B. $168.7$mL
• C. $323.9$mL
• D. $253.3$mL

Answer 1

Answer: (C)

$323.9$mL

An equal number of moles contain equal number of molecules.

$\frac{wt.of{C}_2{H}_{5}OH}{mol.wt.of{C}_2{H}_{5}OH}=\frac{wt.of{H}_{2}O}{mol.wt.of{H}_{2}O}$

$\frac{0.789\times volumeof{C}_2{H}_{5}OH}{46}=\frac{1.0\times 100}{18}$

Volume of $C_2{H}_{5}OH=\frac{100}{18}\times \frac{46}{0.789}$

$=323.9$ mL.

Hence, option $C$ is correct.