# If a liter of solution is needed, how many grams of ethanol, C2H6O will be added when a scientist creates a 0.25 molal solution?

May 31, 2018

The scientist must add 11.3 g ethanol.

#### Explanation:

Step 1. Calculate the mass of 1 L solution

To convert mass to volume, we need the density of the solution. It should be slightly less than that of water.

I shall assume that the density is 0.996 g/mL.

Then,

$\text{Mass of solution" = 1000 color(red)(cancel(color(black)("mL solution"))) × "0.996 g solution"/(1 color(red)(cancel(color(black)("mL solution")))) = "996 mL solution}$

Step 2. Calculate the mass of ethanol in 1000 g water

The molal concentration $b$ is the moles of solute per kilogram of solvent.

color(blue)(bar(ul(|color(white)(a/a)b = n_text(solute)/"kilograms solvent"color(white)(a/a)|)))" "

Thus, a 0.25 mol/kg solution will contain 0.25 mol ethanol and 1000 g water.

m_text(ethanol) = 0.25 color(red)(cancel(color(black)("mol ethanol"))) × "46.07 g ethanol"/(1 color(red)(cancel(color(black)("mol ethanol")))) = "11.5 g ethanol"

Thus, the solution contains 11.5 g ethanol in 1011.5 g solution
($\text{11.5 g NaCl + 1000 g water}$).

Step 3. Calculate the mass of ethanol in 1 L solution

Mass of 1 L solution = 996 g

$\text{Mass of ethanol" = 996 color(red)(cancel(color(black)("g solution"))) × "11.5 g ethanol"/(1011.5 color(red)(cancel(color(black)("g solution"))))= "11.3 g ethanol}$