Question

An aqueous solution of ethanol has density 1.025 g/ml and it is 2 M. What is the molality of this solution ?

Answer 1

Answer on Question #44101, Chemistry, Other

Question:

An aqueous solution of ethanol has density $1.025\ \mathrm{g/ml}$ and it is $2\ \mathrm{M}$. What is the molality of this solution?

Solution:

Molarity and molality are both measures of concentration of solutions. Molarity, symbolized M, is defined as the number of moles of solute per liter of solution:

$$M = \frac{\text{moles of solute}}{\text{liters of solution}}.$$

Molarity, symbolized m, is the number of moles of a solute per kilogram of solvent:

$$m = \frac{\text{moles of solute}}{\text{kilogram of solvent}}.$$

Step 1. Make an assumption

Assume you have $1\ \mathrm{L}$ of $2.0\ \mathrm{M}$ ethanol solution. $2.0\ \mathrm{M}$ ethanol solution means that there is 2 moles of ethanol per 1 liter of solution.

Step 2. Find the total mass of the solution

$$1.025\ \mathrm{g/ml} = 1.025\ \mathrm{kg/L}$$ $$\text{mass of solution} = \text{volume} \times \text{density} = 1\ \mathrm{L} \times 1.025\ \mathrm{kg/L} = 1.025\ \mathrm{kg} = 1025\ \mathrm{g}$$

Step 3. Calculate the mass of the solute

2.0 M ethanol solution means that there is 2 moles of ethanol per 1 liter of solution.

Convert 2 moles to grams:

$$\text{mass} = \frac{\text{moles} \times \text{molar mass}}{\text{moles of ethanol}}.$$

The molar mass of ethanol is $46\ \mathrm{g/mol}$ (from the periodic table: $C_2H_6O$, $12 \times 2 + 1 \times 6 + 16 \times 1 = 46$)

$$2\ \mathrm{moles} \times 46\ \mathrm{g/mol} = 92\ \text{grams of ethanol}$$

Step 4. Calculate the mass of the solvent

1025 grams of solution – 92 grams of solute = 933 grams of solvent = 0.933 kg of solvent

Step 5. Calculate the molality

2 moles of solute / 0.933 kg of solvent = 2.1 mol/kg = 2.1 m

Answer: Molality of the solution is 2.1.

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