Molality Calculators

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Molality (m) is a concentration unit defined as the moles of solute per kilogram of solvent: m = n_solute / m_solvent (kg). Unlike molarity, which is based on solution volume, molality is based on solvent mass and is therefore independent of temperature — making it the preferred unit for colligative property calculations involving temperature changes (boiling point elevation, freezing point depression). Molality is most useful when working with solutions that undergo significant temperature changes or when precise concentration comparisons at different temperatures are needed.

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Molality Formula

m = moles of solute / kilograms of solvent

Note: kilograms of SOLVENT, not solution. Example: dissolve 10.0 g NaCl (MW = 58.44 g/mol) in 200 g of water: n = 10.0/58.44 = 0.171 mol; m = 0.171/0.200 kg = 0.855 m.

Molality vs. Molarity

  • Molarity (M) = mol/L solution — changes with temperature (volume expands/contracts)
  • Molality (m) = mol/kg solvent — temperature-independent (masses don't change)
  • For dilute aqueous solutions at 25°C: m ≈ M (density of dilute water ≈ 1 kg/L)
  • For concentrated solutions or at extreme temperatures: m ≠ M significantly

Colligative Property Calculations

Molality is used for boiling point elevation and freezing point depression:

ΔT_b = K_b × m × i (K_b water = 0.512°C/m)

ΔT_f = K_f × m × i (K_f water = 1.86°C/m)

Example: 2.0 m NaCl (i=2): ΔT_f = 1.86 × 2.0 × 2 = 7.44°C → freezes at −7.44°C.

Converting Between Molality and Molarity

m = M / (ρ − M × MW_solute/1000), where ρ = solution density (g/mL). For dilute solutions: m ≈ M. For concentrated solutions: a density measurement is required for conversion.

Glossary

Molality (m)
Moles of solute per kilogram of solvent: m = n/kg_solvent; temperature-independent; used for colligative property calculations (ΔT_b = K_b×m×i; ΔT_f = K_f×m×i).
Ebullioscopic Constant (K_b)
The boiling point elevation per molal concentration: K_b = 0.512°C/m for water; ΔT_b = K_b × m × i; characteristic of the solvent, not the solute.
Cryoscopic Constant (K_f)
The freezing point depression per molal concentration: K_f = 1.86°C/m for water; ΔT_f = K_f × m × i; basis for determining molecular weight by freezing point depression osmometry.

Frequently Asked Questions

Molality (m) = moles of solute / kilograms of solvent. Example: dissolve 25.0 g of glucose (MW = 180.16 g/mol) in 500 g of water: moles = 25.0/180.16 = 0.1388 mol; molality = 0.1388/0.500 kg = 0.278 m. Key: use mass of solvent (water), not total solution mass. The unit is mol/kg, sometimes written as mol kg⁻¹ or m (lowercase italic m for molality, to distinguish from m for meters).

Molarity (M) = moles/liter of solution — temperature-dependent because liquid volume changes with temperature. Molality (m) = moles/kilogram of solvent — temperature-independent because mass doesn't change with temperature. For dilute aqueous solutions at room temperature, M ≈ m since 1 L of dilute water ≈ 1 kg. For concentrated solutions: a 6 M H₂SO₄ solution has a very different molality because the density is ~1.34 g/mL. For colligative property calculations involving temperature changes, always use molality.

Colligative property calculations involve temperature changes — boiling point elevation and freezing point depression measure exactly how much the temperature changes. Since molarity is volume-based, it changes as the solution cools (volume decreases) or heats (volume increases). Molality is mass-based and remains constant regardless of temperature, providing a stable concentration reference for calculations involving temperature change. The formulas ΔT_b = K_b × m and ΔT_f = K_f × m are derived assuming molality as the concentration unit.

M = m × ρ × (1 / (1 + m × MW_solute/1000)), where ρ is solution density in g/mL. For dilute aqueous solutions (ρ ≈ 1.00 g/mL): M ≈ m. Example: 0.5 m NaCl in water (density ≈ 1.018 g/mL, MW_NaCl = 58.44): M = 0.5 × 1.018 / (1 + 0.5 × 58.44/1000) ≈ 0.509/1.029 ≈ 0.495 M. For concentrated solutions, density must be measured experimentally or looked up in tables for accurate conversion.