Molality and Solvent Mass

Introduction

Molality uses solvent mass rather than final solution volume. This makes it a useful concentration scale when temperature changes volume but does not change the sample's component masses. The key challenge is choosing the correct denominator: kilograms of solvent only, not kilograms of the entire solution.

Core explanation

Molality b = n(solute)/m(solvent in kg), with unit mol kg⁻¹. If 0.500 mol glucose is dissolved in 1.00 kg water, molality is 0.500 mol kg⁻¹. If the same solute amount is dissolved in 0.500 kg water, molality doubles to 1.00 mol kg⁻¹. The definition counts moles of the named solute per mass of its solvent.

The word molality resembles molarity but the bases differ. Molarity is solute moles per litre of solution ; molality is solute moles per kilogram of solvent . A number cannot be converted from one to the other by a simple litre-to-kilogram unit conversion unless solution density and composition are known. For dilute aqueous solutions their numerical values may be close, but this is an approximation, not an identity.

If masses are supplied, convert solute mass to moles using its molar mass, then convert solvent grams to kilograms. For 18.0 g glucose with M ≈ 180.16 g mol⁻¹ dissolved in 200 g water, solute amount is about 0.100 mol and solvent mass is 0.200 kg, giving about 0.500 mol kg⁻¹. Using total solution mass of 218 g in the denominator would answer a different question.

Temperature changes can alter solution volume enough to change molarity, whereas molality calculated from unchanged component masses remains the same. This is one reason molality appears in descriptions of colligative properties such as boiling-point elevation and freezing-point depression. Those properties also depend on the effective number of dissolved particles, so dissociation of salts needs care beyond the basic concentration definition.

When a solute reacts or evaporates, its amount changes and so may molality. Similarly, evaporation of solvent raises molality by shrinking the solvent mass. The temperature-stability statement presumes a closed sample with unchanged solute and solvent masses, not a permanently fixed concentration under every physical process.

Step-by-step reasoning

1. Name the solute and solvent and separate their masses. 2. Convert solute grams to moles with its molar mass. 3. Convert solvent mass to kilograms. 4. Divide solute moles by solvent kilograms and label mol kg⁻¹.

Visual explanation

Draw one container with a small solute pile and a separate solvent pile on balances. The equation arrow uses moles from the solute pile and kilograms from the solvent pile, not the combined mass.

Real-world analogy

A recipe might state spoonfuls of sugar per kilogram of flour rather than per litre of finished dough. The specified base ingredient remains the denominator even after ingredients are mixed.

Real-world example

A chemist comparing freezing behavior of solutions may report molality because weighed solvent mass remains well defined despite temperature-dependent volume changes during careful experimental measurements.

Why?

Why is solvent mass used instead of whole-solution mass? That is the defining concentration basis; it measures solute amount relative to the medium into which it is dissolved.

Common misconception

“One molal means one mole per kilogram of solution.” It means one mole of solute per kilogram of solvent, excluding the solute's own mass from the denominator.

Worked example

Calculate molality for 5.85 g NaCl dissolved in 100.0 g water. NaCl amount = 5.85/58.44 = 0.100 mol formula units. Water mass = 0.1000 kg. Therefore b = 0.100/0.1000 = 1.00 mol kg⁻¹ NaCl to three significant figures. This does not tell the final solution volume.

Quick check

1. What is molality for 0.20 mol solute in 0.50 kg solvent? Answer: 0.20/0.50 = 0.40 mol kg⁻¹.

Exam focus

Underline “solvent” in the denominator and convert grams to kilograms. Do not confuse the symbol b or unit mol kg⁻¹ with molarity M.

Advanced insight

For very concentrated solutions, particle interactions can make ideal colligative-property predictions inaccurate even when molality itself is measured correctly. The concentration definition and the ideal physical model are separate statements.

Summary

Molality divides solute moles by kilograms of solvent. It differs from molarity in both denominator and temperature behavior under fixed composition, so always read the concentration label before calculating.

Practice questions

1. What mass basis belongs in a molality denominator? Answer: Kilograms of solvent, not kilograms of total solution. 2. Find b for 0.75 mol solute in 1.50 kg solvent. Answer: 0.75/1.50 = 0.500 mol kg⁻¹. 3. If solvent evaporates while solute stays, does molality rise or fall? Answer: It rises because the solvent-mass denominator decreases.