1.2.7. Molality

Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent and is expressed as:

Moles of solute

Molality (m) =
Mass of solvent in kg

For example, 1.00 mol kg–1 (or 1.00 m) solution of KCl means that 1 mol (74.5 g) of KCl is dissolved in 1 kg of water.

Molality is a unit of concentration that indicates the amount of solute present in a specific amount of solvent. It measures how many moles of a solute are present per kilogram of solvent, differing from molarity, which measures solute concentration per liter of solution. This makes molality particularly useful when considering changes in temperature and pressure, as it remains unaffected by these factors.

Imagine you are making a concentrated lemonade. If you use 1 kg of water (which is large enough to fill a pitcher) and dissolve 1 mol of lemonade powder in it, the molality of your lemonade is 1 mol/kg. This tells you exactly how concentrated your drink is based on the amount of water in your pitcher.

Each method of expressing concentration of the solutions has its own merits and demerits. Mass %, ppm, mole fraction and molality are independent of temperature, whereas molarity is a function of temperature. This is because volume depends on temperature and the mass does not.

Different methods of expressing the concentration of solutions are useful in various contexts:

• Mass percentage is often used in food labeling.
• Parts per million (ppm) is typical in environmental science for tracking pollutants.
• Mole fraction is useful in understanding gas behaviors. Molality is particularly important in cases involving colligative properties because it does not change with temperature like molarity does, ensuring consistent measurements.

Think of cooking: when you bake cookies and measure by weight (grams) for ingredients, the concentration of your ingredients stays the same, regardless of the temperature of the kitchen. In contrast, if you were to measure liquids in cups, your measurements would change slightly if the room were hot or cold, due to the liquids expanding or contracting.

Calculate molality of 2.5 g of ethanoic acid (CH COOH) in 75 g of benzene.

Molar mass of C H O = 12 × 2 + 1 × 4 + 16 × 2 = 60 g mol–1.

2 4 2 2.5 g

Moles of C H O = = 0.0417 mol 60 g mol–1

Mass of benzene in kg = 75 g/1000 g kg–1 = 75 × 10–3 kg Moles of C H O 0.0417 mol×1000 g kg–1 Molality of C H O = 2 4 2 = 75 g kg of benzene = 0.556 mol kg–1.

To calculate molality, we first need to determine the number of moles of the solute (ethanoic acid). This involves dividing the mass of the solute by its molar mass. Next, convert the mass of the solvent (benzene) from grams to kilograms. Finally, molality is computed by taking the number of moles of the solute and dividing it by the mass of the solvent in kilograms.

Suppose you are preparing a chemical solution for an experiment. You have a 75 g can of benzene, which is your solvent, and you want to add just enough ethanoic acid to see how the properties of the benzene change. If you weigh out 2.5 g of ethanoic acid, dissolve it in your benzene, and measure the concentration, you now know exactly how much you've added in terms of molality!

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