Respuesta :

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.