Molality

Introduction

Molality uses a mass denominator instead of volume: moles of solute per kilogram of solvent . It is useful when temperature changes liquid volume or when a calculation naturally begins with weighed solvent. The symbol often used is lowercase m, which should not be confused with mass m in other equations.

Core explanation

Molality b = n(solute)/m(solvent in kg). If 0.200 mol solute dissolves in 0.500 kg water, b = 0.200/0.500 = 0.400 mol kg⁻¹, often described as 0.400 molal. The denominator is 0.500 kg water even though the finished solution weighs more than 0.500 kg. Dividing by solution mass would calculate a different ratio.

When solute mass is given, find moles with its molar mass. Suppose 18.0 g glucose of molar mass 180 g mol⁻¹ dissolves in 250 g water. Glucose amount is 0.100 mol and water mass is 0.250 kg, so molality is 0.400 mol kg⁻¹. If a student accidentally uses 250 as kilograms, the answer becomes a thousand times too small. If the student includes the 18.0 g solute in the denominator, the result is also wrong because the definition calls for solvent only.

Molality is not molarity. Molarity uses litres of final solution; molality uses kilograms of solvent. They can have numerically similar values for some dilute aqueous samples, but equality is not guaranteed. To convert exactly, one may need solution density and the composition to connect solution volume with solvent mass. A closed solution can change volume with temperature while component masses remain the same, so molality avoids a direct volume dependence.

Molality can describe a particular named solute in a mixture containing several dissolved compounds. The denominator remains mass of solvent, while the numerator counts only that solute's amount. If the solvent itself is a mixture, the problem must specify how solvent mass is defined. Some advanced colligative-property calculations count dissolved particle amounts, which may differ from formula amount when an electrolyte dissociates.

The term “molal” is a ratio unit, not a description of how much can dissolve. A 1 molal solution may be unsaturated or saturated depending on the substance and conditions. Always separate concentration from equilibrium solubility.

Step-by-step reasoning

1. Identify the named solute and the solvent component. 2. Convert solute mass to moles if necessary. 3. Convert solvent mass from grams to kilograms. 4. Divide moles by solvent kilograms. 5. Check that solution mass was not used as the denominator.

Visual explanation

Draw a container labeled 250 g water plus 18 g glucose. Circle 250 g as the denominator and an arrow from 18 g through 180 g mol⁻¹ to 0.100 mol. The final fraction is 0.100 mol/0.250 kg.

Real-world analogy

A fertilizer recipe may state grams of additive per kilogram of soil before the additive is mixed in. The denominator refers to the carrier material, not the weight of the final combined mixture.

Real-world example

Molality is often used when studying boiling or freezing changes because the solvent mass basis does not directly expand with temperature. A calculation still requires the correct chemical particle model and measured property constants.

Why?

Why is molality less directly temperature-sensitive than molarity? It uses component masses, which stay constant in a closed sample, rather than solution volume, which can expand or contract.

Common misconception

“Molality is moles per kilogram of solution.” That is wrong. Its denominator is kilograms of solvent alone, excluding all dissolved solutes from that denominator.

Worked example

Dissolve 5.85 g NaCl, molar mass 58.5 g mol⁻¹, in 200 g water. NaCl formula amount is 5.85/58.5 = 0.100 mol and water mass is 0.200 kg. Formal NaCl molality is 0.100/0.200 = 0.500 mol kg⁻¹. The total solution mass is 205.85 g, but it is not used in the denominator.

Quick check

1. What is molality for 0.050 mol solute in 100 g solvent? Answer: Convert 100 g to 0.100 kg; b = 0.050/0.100 = 0.50 mol kg⁻¹.

Exam focus

Underline “solvent” in the definition and convert grams to kilograms. Do not equate a molal number with molarity without additional information.

Advanced insight

Colligative effects depend on the effective number of dissolved particles. Formal salt molality based on formula units may need a van ’t Hoff factor or more refined activity treatment to model real electrolyte solutions.

Summary

Molality is solute moles per kilogram of solvent. It avoids a final-volume denominator and remains tied to weighed components. Keep it distinct from molarity and from mass per kilogram of total solution.

Practice questions

1. Find molality for 0.30 mol solute in 0.60 kg water. Answer: b = 0.30/0.60 = 0.50 mol kg⁻¹. 2. A solution contains 0.10 mol solute and 500 g water. What denominator enters molality? Answer: 500 g water equals 0.500 kg solvent, giving b = 0.10/0.500 = 0.20 mol kg⁻¹. 3. Why might molarity change with warming while molality does not directly change? Answer: Warming may alter solution volume, which is molarity's denominator, while solvent mass remains fixed in a closed sample.