x_i = n_i / Σ n_j
Mole fraction of component i equals its amount divided by the total amount of all components.
Mole fraction of component i.
- n_i
- amount of component i (mol)
- Σ n_j
- total amount of all components (mol)
Use when — Composition needs to be expressed independently of temperature and volume.
Common trap — Using masses instead of amounts of substance.
M = n_solute / V_solution
Molarity equals amount of solute divided by volume of solution.
Molarity of the solute.
- n_solute
- amount of solute (mol)
- V_solution
- volume of solution (L)
Use when — Solution volume is known and available; note this is temperature-sensitive because solution volume can change.
Common trap — Dividing by solvent volume instead of solution volume.
m = n_solute / m_solvent
Molality equals amount of solute divided by mass of solvent in kilograms.
Molality of the solute.
- n_solute
- amount of solute (mol)
- m_solvent
- mass of solvent (kg)
Use when — Solvent mass is known; ordinarily temperature-independent, unlike molarity.
Common trap — Using solution mass instead of solvent mass.
p_i = x_i × p_i^0
Partial vapour pressure of component i equals its mole fraction times the vapour pressure of the pure component.
Raoult relation for volatile component i in an ideal solution.
- p_i
- partial vapour pressure of component i (matches p_i^0)
- x_i
- mole fraction of component i in solution (dimensionless)
- p_i^0
- vapour pressure of pure component i (pressure unit)
Use when — The solution is ideal at the stated temperature.
Common trap — Using the solute mole fraction where the solvent partial pressure is required.
(p^0 - p) / p^0 = x_solute
Relative lowering of vapour pressure equals the mole fraction of the non-volatile solute.
Relative lowering of solvent vapour pressure caused by a non-volatile solute.
- p^0
- vapour pressure of the pure solvent (pressure unit)
- p
- vapour pressure of the solution (pressure unit)
- x_solute
- mole fraction of the non-volatile solute (dimensionless)
Use when — The solution is ideal, the solute is non-volatile, and dilute approximation is used in standard molar-mass work.
Common trap — Applying this relation when the solute is volatile, without a full component treatment.
p = K_H × x
Pressure equals the Henry constant times the mole fraction of dissolved gas.
Henry relation for a gas dissolved in a liquid, in the NCERT convention.
- K_H
- Henry constant (pressure unit)
- x
- mole fraction of dissolved gas (dimensionless)
Use when — A dilute gas is dissolved in liquid at fixed temperature, with the constant's convention stated.
Common trap — Assuming every textbook uses the same Henry-constant convention.
ΔT_b = i × K_b × m
Boiling-point elevation equals van't Hoff factor times the ebullioscopic constant times molality.
Boiling-point elevation for a dilute solution.
- i
- van't Hoff factor (dimensionless)
- K_b
- ebullioscopic constant (K kg mol^-1 (common))
- m
- molality (mol kg^-1)
Use when — The solution is dilute and molality is used consistently.
Common trap — Using molarity or Celsius as an absolute temperature input.
ΔT_f = i × K_f × m
Freezing-point depression equals van't Hoff factor times the cryoscopic constant times molality.
Magnitude of freezing-point depression for a dilute solution.
- K_f
- cryoscopic constant (K kg mol^-1 (common))
- m
- molality (mol kg^-1)
Use when — The solution is dilute and molality is used consistently.
Common trap — Losing the fact that the freezing point decreases, not increases.
π = i × C × R × T
Osmotic pressure equals van't Hoff factor times molar concentration times the gas constant times absolute temperature.
Osmotic pressure of a dilute ideal solution.
- C
- molar concentration (mol m^-3 or matched alternative)
- T
- absolute temperature (K)
Use when — The solution is dilute and ideal, with absolute temperature used.
Common trap — Mixing litre-atmosphere and SI units.
i = observed colligative effect / effect for no association or dissociation
Van't Hoff factor equals the observed colligative effect divided by the effect expected with no association or dissociation.
Effective particle-count factor comparing observed behaviour to the undisturbed formula-unit model.
- i
- van't Hoff factor (dimensionless)
Use when — Association, dissociation, or non-ideal behaviour must be captured; the model is not universal.
Common trap — Setting i equal to the stoichiometric ion count without the complete-dissociation assumption.