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3.10.4    Crysocopic and ebullioscopic constants and enthalpies of fusion and of evaporation of some common solvents

The lowering ΔT_fus,A = |T^*_fus,A − T_fus,A| of the freezing temperature T^*_fus,A of a mass m_A of the solvent substance A by a dissolved amount n_B of solute substance B is given by the formula:

         ΔT_fus,A = (n_B/m_A)T^*_fus,A(RT^*_fus,A/Δ¹_sh^*_A) = (n_B/m_A)k_fus,A,

where R denotes the gas constant (R = 8.314 51 J·K⁻¹· mol⁻¹), Δ¹_sh^*_A denotes the massic (formerly ‘specific’) enthalpy of fusion of the pure (*) solvent A, and k_fus,A is called the cryoscopic constant of A, and where it has been assumed that the solution is ideal-dilute and that the solid phase is that of the pure solvent.
    Similarly, the corresponding elevation ΔT_vap,A = |T_vap,A − T^*_vap,A| of the boiling temperature at a given pressure is given by the formula:

         ΔT_vap,A = (n_B/m_A)T^*_vap,A(RT^*_vap,A/Δ₁^gh*_A) = (n_B/m_A)k_vap,A,

where Δ₁^gh^*_A is now the massic enthalpy of evaporation of the pure solvent A and k_vap,A is called the ebullioscopic constant of A, and where it has been assumed that the solution is ideal-dilute and that the solute B is involatile.

Enthalpies of evaporation at several temperatures

Approximate values of the molar enthalpy of evaporation can be computed from tables of vapour pressure against temperature (see section 3.4.4) by the use of Clapeyron's equation. For conditions where the molar volume of the liquid is small compared with the molar volume of the vapour and where the vapour can be treated as an ideal gas, the molar enthalpy of evaporation Δ₁^g H_A can be calculated from the expression:

         Δ₁^g H_A = RT²p ^{− 1}(dT/dp) ^{− 1}.

Values of dT/dp for p = 101 325 kPa are given for many substances in Section 3.4.4.
    The following table gives values for the massic enthalpy of evaporation, Δ₁^g h_A/(J·g⁻¹), for several substances A at several temperatures. Some values at the normal boiling temperatures are given in the preceding table.

Δ_l^gh_A/(J·g ^{− 1})

The following highly accurate massic enthalpies of evaporation of water were calculated, with temperatures T₉₀ on the International Temperature Scale of 1990 (ITS-90), from those measured by Osborne, Stimson, and Ginnings (1939) J. Res. Nat. Bur. Stand., 23, 197, 261.

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