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Molality Calculator

Ready to calculate
m = mol solute / kg solvent.
Temperature-independent.
Colligative-property ready.
100% Free.
No Data Stored.

How it Works

01Determine Moles of Solute

Either enter moles directly, or check the box to expose mass + molar mass for n = m / MW.

02Weigh the SOLVENT (not solution)

Mass of solvent only — the key distinction from molarity. Accept kg, g, mg, lb, oz.

03Apply m = n / mass_solvent (kg)

Mass-based denominator means molality is temperature-independent — unlike volume-based molarity.

04Use for Colligative Properties

ΔT_b = K_b·m (boiling-point elevation); ΔT_f = K_f·m (freezing-point depression). Standard temperature-independent reference.

What is a Molality Calculator?

Molality (m, mol/kg) is the temperature-independent concentration unit of choice for colligative-property work and high-precision physical chemistry. The defining identity is m = moles of solute / kg of SOLVENT — note: kilograms of solvent, not solution. This is the critical distinction from molarity (mol/L of solution), and it is exactly what makes molality temperature-independent: mass doesn't change with temperature, but volume does. Every freezing-point depression and boiling-point elevation calculation, every osmotic-pressure problem in non-dilute solutions, and every NIST-traceable certified reference material is specified in molality precisely because the value doesn't drift with thermal expansion.

Our Molality Calculator implements this in two modes. Direct mode — enter moles of solute and mass of solvent, get molality. Mass-and-MW mode — check the box to expose mass of solute and molar mass; the calculator computes moles internally via n = mass / MW, then divides by the solvent mass. Solvent mass accepts kg / g / mg / µg / lb / oz; solute mass accepts g / mg / µg / kg; molar mass in g/mol. Output: molality in mol/kg (m), mmol/kg, and µmol/kg. Smart warnings flag MW < 1 g/mol (unphysical), MW > 1 MDa (verify), and concentrations beyond solubility limits of common solutes.

Designed for physical-chemistry coursework (the colligative-property unit), analytical chemists preparing NIST-traceable reference solutions, biochemists working with high-precision freezing-point osmolality (clinical osmometers report osmolality not osmolarity), and any researcher needing a concentration that doesn't drift across the working temperature range — runs entirely in your browser, no account, no data stored.

Pro Tip: Pair this with our Molarity Calculator for volume-based concentrations, our Mole Calculator for the mass↔moles conversion, or our Mass Percent Calculator for w/w percentages.

How to Use the Molality Calculator?

Pick a Mode: by default, the calculator expects you to enter moles of solute directly. If you have mass and molar mass instead, check the "Show mass of solute and molar mass" box to expose the alternative input fields; the calculator computes moles internally.
Direct Mode — Enter Moles of Solute: in mol. Get this from a previous mole calculation (n = mass / MW) or from a primary stoichiometry calculation. The calculator accepts any positive value.
Mass + MW Mode — Enter Both: mass of solute (g, mg, µg, kg) and molar mass (g/mol). Look up MW on PubChem (pubchem.ncbi.nlm.nih.gov), CRC Handbook, or supplier datasheet. Critical: for hydrate forms, use the hydrate MW (CuSO₄·5H₂O 249.69 vs anhydrous 159.61) — using the wrong form gives 30-50% errors.
Enter Mass of Solvent (NOT Solution): the most common error in molality calculations is using the mass of solution instead of solvent. Mass of solvent = (mass of solution) − (mass of solute). For dilute aqueous solutions (< 0.1 mol/kg), the difference is negligible; for concentrated solutions, this matters significantly.
Apply m = n / mass_solvent (kg): the calculator converts solvent mass to kg internally. Output in mol/kg (the SI unit), with mmol/kg and µmol/kg for cleaner display of dilute solutions.
Use for Colligative Properties: molality is the canonical input for freezing-point depression (ΔT_f = K_f × m × i) and boiling-point elevation (ΔT_b = K_b × m × i), where K_f and K_b are solvent-specific cryoscopic and ebullioscopic constants and i is the van't Hoff factor (accounts for ionization: NaCl i ≈ 2, CaCl₂ i ≈ 3).
Cross-Check Against Common References: 1.0 mol/kg NaCl in water has freezing-point depression ΔT_f = 1.86 × 1.0 × 2 = 3.72 °C (i.e. freezes at −3.72 °C). 0.5 mol/kg sucrose ΔT_f = 1.86 × 0.5 × 1 = 0.93 °C. 2.0 mol/kg ethylene glycol ΔT_f = 1.86 × 2 = 3.72 °C — basis of automotive antifreeze.

How is molality calculated?

Molality is one of the four canonical concentration units of physical chemistry — distinguished by being temperature-independent and the natural scale for colligative properties. The math is simple; the conceptual distinction (mass of SOLVENT, not solution) is what catches students.

References: IUPAC Compendium of Chemical Terminology (Gold Book): "molality"; Atkins' Physical Chemistry (12th ed., Chapter 5); Levine's Physical Chemistry (7th ed.).

Core Formula

Molality m (mol/kg) = moles of solute n / mass of solvent in kg

Equivalently: m = (mass_solute / MW) / mass_solvent_kg = mass_solute_g / (MW × mass_solvent_kg).

Worked Example — NaCl in Water (Saline-Like)

Dissolve 5.844 g NaCl (MW 58.44) in 1000 g of water.

  • n(NaCl) = 5.844 / 58.44 = 0.1000 mol.
  • m_solvent = 1000 g = 1.000 kg.
  • Molality = 0.1000 / 1.000 = 0.1000 mol/kg = 0.1 m NaCl.
  • Compare to molarity: 0.1 mol in roughly 1.003 L of solution (slight volume increase from dissolved salt) ≈ 0.0997 M. For dilute aqueous, m ≈ M; for concentrated, they diverge.

Worked Example — Antifreeze (Ethylene Glycol)

2 mol ethylene glycol (62.07 g/mol) dissolved in 1.0 kg water.

  • m_solute = 2 × 62.07 = 124.14 g.
  • Molality = 2.0 / 1.0 = 2.0 mol/kg = 2.0 m.
  • Freezing-point depression: ΔT_f = K_f × m × i = 1.86 × 2.0 × 1 = 3.72 °C (ethylene glycol is non-ionic, i = 1).
  • Solution freezes at −3.72 °C (vs pure water 0 °C). Real automotive antifreeze 50% w/w ≈ 8 mol/kg → ΔT_f ≈ 15 °C theoretical (real systems also include propylene glycol; non-ideal effects reduce this somewhat).

Worked Example — Phosphate Buffer

17.42 g K₂HPO₄ (MW 174.18) in 1000 g water → "0.10 m K₂HPO₄ buffer".

  • n = 17.42 / 174.18 = 0.1000 mol.
  • Molality = 0.1000 / 1.0 = 0.10 mol/kg = 0.10 m.
  • Note: as the solution warms from 4 °C (cold storage) to 37 °C (assay temp), the molality stays exactly 0.10 m — but molarity would change by ~1% from water expansion.

Colligative Properties — Why Molality Matters

Four colligative properties depend on molality (×van't Hoff factor i for ionic compounds):

  • Freezing-point depression: ΔT_f = K_f × m × i. Water K_f = 1.86 °C·kg/mol.
  • Boiling-point elevation: ΔT_b = K_b × m × i. Water K_b = 0.512 °C·kg/mol.
  • Vapor pressure lowering: ΔP = P°₁ × x₂ (where x₂ is mole fraction; for dilute solutions x₂ ≈ m × MW_solvent / 1000).
  • Osmotic pressure: π = i × M × R × T (for dilute aqueous, M ≈ m, so π also tracks molality).

Cryoscopic and Ebullioscopic Constants for Common Solvents

  • Water: K_f = 1.86 °C·kg/mol; K_b = 0.512 °C·kg/mol.
  • Benzene: K_f = 5.12; K_b = 2.53.
  • Cyclohexane: K_f = 20.0; K_b = 2.79.
  • Camphor: K_f = 39.7 (very large — used historically for molecular-mass determination via Rast method).
  • Ethanol: K_f = 1.99; K_b = 1.22.
  • Acetic acid: K_f = 3.90; K_b = 3.07.
  • Carbon tetrachloride: K_f = 30; K_b = 5.03.

Van't Hoff Factor (i) for Ionic Solutes

  • Non-electrolyte (sucrose, glucose, urea): i = 1.
  • 1:1 electrolyte (NaCl, KCl, KNO₃): i ≈ 2 (slightly less due to ion pairing).
  • 1:2 electrolyte (CaCl₂, MgCl₂): i ≈ 3 (1 cation + 2 anions).
  • 2:1 electrolyte (Na₂SO₄): i ≈ 3.
  • 1:3 electrolyte (AlCl₃): i ≈ 4.
  • Weak electrolytes (HF, NH₃, acetic acid): i depends on degree of dissociation α; i = 1 + α(ν − 1) where ν is total ions per formula unit.
Real-World Example

Worked Example — Predict Freezing Point of Saltwater

Question: What is the freezing point of an aqueous solution prepared by dissolving 23.4 g of NaCl in 500 g of water?

Step 1 — Compute moles of NaCl.

  • MW(NaCl) = 58.44 g/mol.
  • n = 23.4 / 58.44 = 0.400 mol NaCl.

Step 2 — Compute molality.

  • mass_solvent = 500 g = 0.500 kg.
  • m = n / mass_solvent = 0.400 / 0.500 = 0.800 mol/kg.

Step 3 — Apply ΔT_f = K_f · m · i.

  • K_f(water) = 1.86 °C·kg/mol.
  • i(NaCl) ≈ 2.0 (1:1 strong electrolyte, accounting for slight ion-pairing closer to 1.9 in real solutions).
  • ΔT_f = 1.86 × 0.800 × 2.0 = 2.98 °C.

Step 4 — Predict the freezing point.

  • Pure water freezes at 0 °C.
  • Solution freezes at 0 − 2.98 = −2.98 °C.

Step 5 — Interpret.

  • This is roughly the chemistry of brining and road de-icing. Salt depresses water's freezing point — at 0.8 m NaCl (~4.7% w/w), water freezes near −3 °C.
  • Maximum NaCl-water freezing-point depression occurs at the eutectic: −21.1 °C at ~23.3% w/w NaCl (~5.4 mol/kg), beyond which NaCl·2H₂O hydrate co-precipitates.
  • For higher freezing-point depression, use CaCl₂ (i ≈ 3, eutectic −51 °C at 30% w/w) or NaCl/MgCl₂ blends.

Who Should Use the Molality Calculator?

1
Molality is the canonical concentration unit for colligative-property problems — freezing-point depression, boiling-point elevation, vapor-pressure lowering, osmotic pressure. Every undergrad p-chem course tests it.
2
Predict freezing point of glycol-water and salt-water mixtures from molality. Engineering antifreeze blends for automotive radiators, aircraft de-icing, refrigeration brines.
3
Certified reference materials are specified in molality (not molarity) because molality is temperature-independent. Use the calculator for traceable solution preparation.
4
Clinical osmometers measure freezing-point depression and report osmolality (mOsm/kg). The calculator converts back to molality via osmolality = m × i × osmolality_factor.
5
DMSO, glycerol, and other cryoprotectants in cell freezing media are quantified by molality for reproducible freezing rates and post-thaw viability.
6
Subsurface brines and oilfield-produced waters often have mol/kg concentrations of dissolved salts (Cl⁻, Na⁺, Ca²⁺) too high for the dilute-solution molarity approximation. Molality is the standard unit.
7
Drug solubility in solvent mixtures, tonicity adjustment for parenteral injections, and stability studies across temperature ranges all use molality as the preferred concentration unit.

Technical Reference

IUPAC Definition. Per IUPAC Compendium of Chemical Terminology (Gold Book): molality (b or m) of solute B = n_B / m_A, where n_B is the amount of solute B and m_A is the mass of solvent A. SI units: mol/kg. Equivalent older notation: molal (m), as in "1 molal NaCl" = "1 m NaCl" = "1 mol/kg".

Why Mass-Based Instead of Volume-Based? Mass is conserved; volume changes with temperature (typical thermal expansion of liquids: ~0.0002-0.001 K⁻¹). A 1.000 M solution at 25 °C becomes ~0.998 M at 35 °C from solvent thermal expansion. A 1.000 m solution stays exactly 1.000 m at any temperature. This is why molality is preferred for: (a) high-precision colligative-property work; (b) NIST-traceable certified reference materials; (c) any application where the solution is used at a different temperature from where it was prepared; (d) extreme temperature ranges (cryopreservation at −80 °C; geothermal brines at 200 °C).

Molality vs Molarity Conversion. For an aqueous solution at temperature T, molality and molarity are related by: M = m × ρ_solution / (1 + m × MW_solute / 1000), where ρ_solution is solution density in g/mL and MW_solute is in g/mol. For dilute aqueous (m × MW ≪ 1000): M ≈ m × ρ_solution ≈ m (when ρ ≈ 1 g/mL for water). For concentrated solutions: M can be 10-30% different from m. Inverse: m = M / (ρ_solution − M × MW_solute / 1000). Solving these requires knowing the solution density at T.

Cryoscopic Constants K_f (°C·kg/mol). The freezing-point depression per molal of solute. Solvent-specific:

  • Water: 1.86
  • Acetic acid: 3.90
  • Benzene: 5.12
  • Cyclohexane: 20.0
  • Camphor: 39.7 (very large — used historically for molecular mass determination via Rast method)
  • Naphthalene: 6.94
  • Phenol: 7.27
  • Carbon tetrachloride: 30.0

Ebullioscopic Constants K_b (°C·kg/mol).

  • Water: 0.512
  • Benzene: 2.53
  • Carbon tetrachloride: 5.03
  • Acetic acid: 3.07
  • Cyclohexane: 2.79
  • Ethanol: 1.22
  • Chloroform: 3.63

Van't Hoff Factor (i) for Common Ionic Solutes. The effective number of particles per formula unit. Theoretical (for complete dissociation) and experimental (slightly less due to ion pairing) values for 0.1 mol/kg aqueous solutions at 25 °C:

  • NaCl: theoretical 2; experimental 1.87.
  • KCl: theoretical 2; experimental 1.86.
  • MgSO₄: theoretical 2; experimental 1.32 (significant ion pairing for 2:2).
  • CaCl₂: theoretical 3; experimental 2.71.
  • K₂SO₄: theoretical 3; experimental 2.32.
  • FeCl₃: theoretical 4; experimental ~3.4.
  • For very dilute solutions (< 0.001 mol/kg), i approaches the theoretical limit.

Osmolality vs Osmolarity. Clinical chemistry uses these two unit pairs paralleling molality vs molarity. Osmolality = (number of dissolved particles) × m (mol/kg solvent); reported in mOsm/kg. Osmolarity = same × M (mol/L solution); reported in mOsm/L. Clinical osmometers measure freezing-point depression and report osmolality (because the measurement principle is colligative). Plasma osmolality is normally 285-295 mOsm/kg; isotonic IV fluids match this. Estimated formula: Osmolality = 2[Na⁺] + glucose/18 + BUN/2.8.

Common Reference Molalities.

  • Pure water (as solvent): 55.5 mol/kg (1000 g / 18.015 g/mol).
  • Physiological saline (0.9% NaCl): 0.154 mol/kg.
  • Seawater: ~0.6 mol/kg total dissolved salts (mostly NaCl; ~3.5% w/w salinity).
  • Saturated NaCl in water (25 °C): ~6.1 mol/kg.
  • Saturated KCl in water (25 °C): ~4.6 mol/kg.
  • 50% w/w sucrose (heavy syrup): ~2.9 mol/kg.
  • Concentrated H₂SO₄ (98% w/w): ~10 mol/kg (with self-as-solvent gives different number).
  • Saturated NaOH (50% w/w, 25 °C): ~25 mol/kg.

Limitations of Ideal Molality Behavior. Colligative-property formulas (ΔT_f = K_f·m·i, etc.) assume ideal-solution behavior — solute particles do not interact with each other beyond random mixing. Real solutions deviate at concentrations above ~0.1-0.5 mol/kg due to: ion pairing (reduces effective i); ion-water interactions (specific solvation); non-ideal mixing of polar molecules. Activity coefficients (γ) correct for non-ideality: m_effective = m × γ; γ approaches 1 at infinite dilution and decreases at higher concentrations (typically γ = 0.8-0.95 at 0.1 mol/kg for 1:1 electrolytes). For high-precision work in the > 0.5 mol/kg range, use Debye-Hückel theory or extended formulations (Davies equation, Pitzer equations). References: IUPAC Compendium of Chemical Terminology; Atkins' Physical Chemistry; Levine's Physical Chemistry; CRC Handbook of Chemistry and Physics.

Conclusion

Molality is the temperature-independent concentration unit. The math is one formula — m = moles of solute / kg of solvent — but the conceptual point is critical: per kg of solvent, not solution. This mass-only basis (no volume term) makes molality immune to thermal expansion, and that's why every colligative-property calculation uses it: ΔT_f = K_f × m × i, ΔT_b = K_b × m × i. Get molality right and you can predict freezing points, boiling points, osmotic pressures, and vapor pressures without worrying about the temperature at which the measurement is taken.

Two things to remember: (1) Mass of SOLVENT, not solution — the most common error in molality problems is dividing by the mass of solution. For dilute aqueous (< 0.1 mol/kg), the distinction is negligible; for concentrated solutions, it matters significantly. (2) For ionic solutes, the effective colligative concentration is m × i (van't Hoff factor): NaCl i ≈ 2, CaCl₂ i ≈ 3, AlCl₃ i ≈ 4. Forgetting i underestimates colligative effects by 2-4× for typical strong electrolytes. The calculator handles the molality math; the i factor is your responsibility — but once you know it, the colligative properties are one multiplication away.

Frequently Asked Questions

What is the Molality Calculator?
It implements the foundational identity m = moles solute / kg of SOLVENT in two modes: (1) Direct mode — enter moles of solute and mass of solvent. (2) Mass + MW mode — check the box to expose mass of solute + molar mass; the calculator computes moles internally. Output: molality in mol/kg, mmol/kg, µmol/kg with full breakdown.

Pro Tip: Pair this with our Molarity Calculator for volume-based concentrations.

What is molality?
Moles of solute per kilogram of SOLVENT (not solution). Symbol m or b; units mol/kg. The defining feature is the mass-only denominator — because mass doesn't change with temperature (volume does), molality is temperature-independent, unlike molarity (mol/L of solution). Used as the canonical concentration unit for colligative-property calculations: ΔT_f = K_f·m·i (freezing-point depression), ΔT_b = K_b·m·i (boiling-point elevation).
What's the formula for molality?
m = moles of solute / kg of solvent. Equivalently when you have mass + MW: m = (mass_solute / MW) / mass_solvent_kg = mass_solute_g / (MW × mass_solvent_kg). Worked example: 5.844 g NaCl (MW 58.44) in 1000 g water → n = 5.844/58.44 = 0.1 mol; m = 0.1 / 1.0 = 0.1 mol/kg.
What's the difference between molality and molarity?
Molality (m, mol/kg) divides by mass of SOLVENT; molarity (M, mol/L) divides by volume of SOLUTION. Two key differences: (1) Molality is temperature-independent (mass doesn't change with T); molarity drifts ~0.5-1% per 10 °C from thermal expansion. (2) For dilute aqueous (< 0.1 mol/kg), m ≈ M numerically; for concentrated solutions they diverge significantly. Use molality for: colligative properties, NIST-traceable standards, wide-temperature work. Use molarity for: bench chemistry at controlled lab T, stoichiometry of solutions.
Why is molality temperature-independent?
Because mass doesn't change with temperature. The molality formula m = n / mass_solvent has only mass terms in the denominator — and mass is conserved across thermal expansion (a 1 kg sample is 1 kg at 4 °C and at 80 °C). In contrast, molarity divides by volume, and volumes expand: 1.0 L of water at 4 °C becomes 1.029 L at 100 °C, so a 1.000 M solution at 4 °C becomes 0.972 M at 100 °C. For high-precision work or wide-temperature applications (cryopreservation, geothermal brines), molality avoids these drifts entirely.
How is molality used for freezing-point depression?
ΔT_f = K_f × m × i, where K_f is the cryoscopic constant of the solvent (water 1.86 °C·kg/mol) and i is the van't Hoff factor (1 for non-electrolyte, 2 for NaCl, 3 for CaCl₂, etc.). Example: 0.5 mol/kg sucrose in water: ΔT_f = 1.86 × 0.5 × 1 = 0.93 °C; freezes at −0.93 °C. 0.5 mol/kg NaCl in water: ΔT_f = 1.86 × 0.5 × 2 = 1.86 °C; freezes at −1.86 °C. 1.0 mol/kg ethylene glycol (antifreeze): ΔT_f = 1.86 × 1 × 1 = 1.86 °C — basis of road salt and automotive antifreeze chemistry.
How is molality used for boiling-point elevation?
ΔT_b = K_b × m × i, where K_b is the ebullioscopic constant of the solvent (water 0.512 °C·kg/mol). Example: 1.0 mol/kg sucrose in water: ΔT_b = 0.512 × 1 × 1 = 0.512 °C; boils at 100.512 °C (vs pure water 100 °C). 1.0 mol/kg NaCl: ΔT_b = 0.512 × 1 × 2 = 1.02 °C; boils at 101.02 °C. The effect is much smaller than freezing-point depression because K_b is smaller than K_f for water (0.512 vs 1.86).
What's the molality of seawater?
~0.6 mol/kg total dissolved species (mostly NaCl). Seawater salinity is typically 3.5% w/w, dominated by NaCl with smaller amounts of MgCl₂, MgSO₄, CaSO₄, KCl. Total ionic strength ~0.7 mol/kg. This produces a freezing-point depression of ~1.9 °C (seawater freezes at −1.9 °C, not 0 °C) and an osmotic pressure equivalent to ~1.0 mol/kg of NaCl. Open-ocean salinity is fairly uniform; estuaries and brackish waters are 5-30% of seawater concentration.
How do I convert mass percent to molality?
m = (% w/w × 10) / [MW × (100 − % w/w)/100], with MW in g/mol. Derivation: in 100 g of solution, you have % w/w grams of solute and (100 − % w/w) grams of solvent. Moles solute = % / MW; mass solvent in kg = (100 − %)/1000. Example: 10% w/w NaCl: m = (10 × 10) / (58.44 × 0.90) = 100 / 52.6 = 1.90 mol/kg. For dilute solutions (< 1% w/w): m ≈ % w/w × 10 / MW (since 100 − % ≈ 100). This is the same simplification used to convert ppm to mol/kg: ppm × 10⁻⁶ × 1000 / MW.
What is the van't Hoff factor i?
The effective number of dissolved particles per formula unit of solute — accounts for ionic compounds dissociating into multiple ions. Theoretical values: non-electrolyte i = 1; NaCl, KCl (1:1) i = 2; CaCl₂, MgCl₂ (1:2) i = 3; Na₂SO₄ (2:1) i = 3; AlCl₃ (1:3) i = 4. Real (experimental) values are slightly less than theoretical due to ion pairing; for 0.1 m solutions: NaCl 1.87, CaCl₂ 2.71, MgSO₄ 1.32 (significant pairing for 2:2). For weak electrolytes: i = 1 + α(ν − 1), where α is degree of dissociation and ν is total ions per formula unit; for acetic acid at 0.1 mol/kg, α ≈ 1.3% so i ≈ 1.013.
Why does my molality differ from molarity?
For dilute aqueous solutions (< 0.1 mol/kg), they're numerically nearly equal because 1 L of water ≈ 1 kg of water and the solute adds negligible mass. For concentrated solutions, they diverge because: (1) the solute adds significant mass to the solution (so kg solvent < kg solution); (2) the dissolved solute changes density. Rule of thumb: for typical aqueous solutions at room T, M ≈ m × ρ / (1 + m·MW/1000) where ρ is solution density. For 1.0 m glucose (MW 180, ρ ≈ 1.05 g/mL): M = 1 × 1.05 / 1.18 = 0.89 M. For 1.0 m NaCl (MW 58.44, ρ ≈ 1.04): M = 1 × 1.04 / 1.058 = 0.98 M. The denser the solute and the more concentrated, the bigger the divergence.

Author Spotlight

The ToolsACE Team - ToolsACE.io Team

The ToolsACE Team

Our ToolsACE chemistry team built this calculator to handle the temperature-independent concentration unit used for all colligative-property calculations: <strong>molality m = moles of solute / kg of SOLVENT (not solution)</strong>. The calculator works in two modes: <strong>(1) Direct mode</strong> — enter moles of solute and mass of solvent. <strong>(2) Mass-and-MW mode</strong> — check the box to expose mass of solute + molar mass fields; the calculator computes moles internally via n = mass / MW. Solvent mass accepts kg / g / mg / µg / lb / oz; solute mass in g / mg / µg / kg; molar mass in g/mol. Output: molality in mol/kg (m), mmol/kg, and µmol/kg. Smart warnings flag MW &lt; 1 g/mol (unphysical) and unrealistic concentrations beyond the saturation limits of common solutes (NaOH ~25 mol/kg, H₂SO₄ ~10 mol/kg).

IUPAC Compendium of Chemical Terminology (Gold Book)Atkins' Physical Chemistry (12th ed.)Levine's Physical Chemistry (7th ed.)

Disclaimer

Molality is moles of solute per kg of SOLVENT (not solution) — the most common error in molality problems is using mass of solution. For dilute aqueous (< 0.1 mol/kg), m ≈ M numerically; for concentrated solutions they diverge. Molality is temperature-independent because mass doesn't change with T (volume does). For colligative-property calculations: ΔT_f = K_f·m·i; ΔT_b = K_b·m·i; cryoscopic constant K_f(H₂O) = 1.86, K_b(H₂O) = 0.512 °C·kg/mol. Van't Hoff factor i accounts for ionic dissociation: NaCl ≈ 2, CaCl₂ ≈ 3 in dilute solutions; ion-pairing reduces i at higher concentrations. For research-grade work above 0.5 mol/kg, use activity coefficients (Debye-Hückel, Davies, Pitzer). References: IUPAC Compendium of Chemical Terminology; Atkins' Physical Chemistry; Levine's Physical Chemistry; CRC Handbook of Chemistry and Physics.