Question

At room temperature, the density of water is 1.0 g/mL and the density of ethanol is 0.789 g/mL. What volume of ethanol contains the same number of molecules as are present in 175 mL of water?

• A. 670.85 mL
• B. 581.68 mL
• C. 356.25 mL
• D. 566.82 mL

Answer 1

The correct option is D 566.82 mL

Let the volume of ethanol containing the same number of molecules as are present in 175 mL of $H_{2}O$ be $v$ mL.
Thus,
$\text{moles of}{C}_2{H}_{5}OHinvmL=\text{moles of}{H}_{2}Oin175mL$
Therefore,

$\frac{\text{weight of}{C}_2{H}_{5}OH}{\text{molar mass of}{C}_2{H}_{5}OH}=\frac{\text{weight of}{H}_{2}O}{\text{molar mass of}{H}_{2}O}$

$\Rightarrow \frac{0.789\times v}{46}=\frac{1.0\times 175}{18}$

$\Rightarrow v=566.82mL$