Question

At $ 25^{\circ} C $ consider the density of water is $ 1 \,g/L $ and that of propanol to be $ 0.925\, g/L $ . What volume of propanol will have same number of molecules as present in $ 210\, mL $ of water?

• A. $ 757 \,mL $
• B. $ 825 \,mL $
• C. $ 646 \,mL $
• D. $ 437 \,mL $

Answer 1

Answer: (A)

${\text{Density}} =\frac{\text{Mass}}{\text{Volume}}$
For water: $1=\frac{18}{V_{H_2 O}}$
$[\because$ Molar mass of $H_{2}O=18\,g\,mol^{-1}]$
$V_{H_2 O}=18 L $
$\Rightarrow N_{A}$ molecules
For propanol: $0.925=\frac{60}{V_{\text{propanol}}}$
$[\because$ Molar mass of $CH_{3}CH_{2}CH_{2} OH=60\,g\,mol^{-1}]$
$V_{\text{propanol}}=64.86\,L$
$\Rightarrow N_{A}$ molecules
Ratio: $\frac{V_{\text{propanol}}}{V_{H_2 O}}$
$=\frac{64.86}{18}$
$V_{\text{propanol}}=3.603\times V_{H_2 O }$
$\Rightarrow V_{\text{propanol}}=3.603\times210$
$=756.63$
$=757\, mL$