Question

at room temperature the density of water is 1 gram per ml and density of Ethanol is 0.78 9 gram per ml what volume of Ethanol contains the same number of molecules are present in 75 ml of water

Answer 1

Final Answer : 242.92mL

Formulas Used :(Here)
1) Mass, M = Density (d) * Volume (V)
2) No. of moles = Given Mass / Molar Mass
3) No. of molecules = No. of moles * Avogadro Number.

Steps:
1) D(water ) = 1 g/mL
Volume of water, (V) = 75 mL
Mass of water, M = 75 *1 = 75 g

D(Ethanol ) = 0.789 g/mL
Volume of water, V(Ethanol) = x (say)

We need to find volume of ethanol such that no. of molecules are same as that of water.

That is,
no. of moles (water) = no. of moles (Ethanol)
$= > \frac{75}{18} = \frac{x \times 0.789}{46} \\ = > x = 242.92 \:$
Hence, Required Volume of Ethanol is
242.92 mL

Answer 2

Density of the water = 1 g/ml.
Volume of the water = 75 ml.

∵ density = Mass/Volume.
∴ Mass = 1 × 75
    = 75 g. 

∴ No. of molecules = 75/ 18 × 6.022 × 10²³
  = 25.09 × 10²³ molecules. 


Now, 
 Mass of the Ethanol = (25.09 × 10²³ × 10⁻²³ × 46)/6.022 
   = 191.67 grams. 

∴ Volume of the Ethanol = Mass/Density
   = 191.67/0.789 
   = 242.93 mL.


Hope it helps.