Question

The density of an aqueous solution containing 10.0 percent of ethanol (C2H5OH) by mass is 0.984 g/mL. (a) Calculate the molality of this solution. (b) Calculate its molarity. (c) What volume of the solution would contain 0.125 mole of ethanol

Answer 1

Answer:

a. 2.41 molal

b. 0.21 M

c. 58.5 mL

Explanation:

First of all let's think the data 10 % by mass, which means, that 10 grams from the solute is contained in 100 g of this solution.

So If we know solution density, we can get its volume.

Solution density = Solution mass / Solution volume

0.984 g/ml = 100 g / Solution volume

Solution volume = 100 g/ 0.984g/ml

Volume = 101.6 mL

As we have 10 g of solute, 100 g of solution, we have 90 g of solvent.

Solute mass + Solvent mass = Solution mass

How many moles do we have in 10 g of ethanol?

Molar mass of ethanol: 46.07 g/m

Mass / molar mass = Moles

10 g/ 46.07 g/m = 0.217 mol

This quantity is in 90 g of solvent and 101.6 mL of solution. For molality and molarity, we should use a rule of three to find out the moles in 1 kg of solvent and 1 L of solution.

1 L = 1000 mL

1kg = 1000 g

Molality

90 g _____ 0.217 moles

1000 g _____ (1000 . 0.217)/ 10 = 2.41 molal

Molarity

101.6 mL ___ 0.217 moles

1000 mL ____  (1000 . 0.217) / 101.6 = 0.21 M

What volume of the solution would contain 0.125 mole of ethanol?. Let's think a new rule of three.

0.217 moles of solute ___ are in __ 101.6 mL of solution

0.125 moles of solute___ are in (0.125 . 101.6)/0.217 = 58.5 mL