The formula of molarity is:
[tex]molarity = \frac{number of moles of solute}{volume of solution in Liter}[/tex]
Number of moles is given as:
[tex]number of moles of solute= \frac{mass of solute}{Molar mass of solute}[/tex]
So, the formula of molarity can be written as:
[tex]molarity = \frac{\frac{mass of solute}{Molar mass of solute}}{volume of solution in Liter}[/tex] -(1)
Molar mass of ethyl alcohol, [tex]C_2H_5OH[/tex] = [tex]2\times 12+6\times 1+16 = 46 g/mol[/tex]
Molarity of ethyl alcohol, [tex]C_2H_5OH[/tex] = 1 molar (given)
Let the volume of solvent that is water be 1 L.
Substituting the values in formula (1):
[tex]1 M = \frac{\frac{mass of solute}{46 g/mol}}{1 L}[/tex]
[tex]mass of solute = 46 g/mol\times 1 mol/L\times 1 L[/tex]
[tex]mass of solute = 46 g[/tex]
Since, ethyl alcohol is liquid in room temperature:
Density of ethyl alcohol is [tex]0.7892 g/mL[/tex]
Density = [tex]\frac{mass}{volume}[/tex]
So, volume of ethyl alcohol = [tex]\frac{mass of ethyl alcohol}{density of ethyl alcohol}[/tex]
Volume of ethyl alcohol = [tex]\frac{46 g}{0.7892 g/mL}[/tex]
Volume of ethyl alcohol = [tex]58.29 mL[/tex]
Hence, by dissolving 58.29 mL of ethyl alcohol in 1 L of water, 1 M solution of ethyl alcohol can be prepared.