Q1(f). Debye–Hückel limiting law for γ±

Answer in brief

log₁₀ γ± = −A|z₊z₋|√I. It is exact only in the limit I → 0 (in practice I < about 0.01 mol kg⁻¹ for 1:1 electrolytes), hence “limiting”.

Key points

• γ±: mean ionic activity coefficient, γ± = (γ₊^ν₊ γ₋^ν₋)^1/ν; z₊, z₋: charge numbers.
• I: ionic strength (mol kg⁻¹), counting every ion present; A = 0.509 (mol kg⁻¹)⁻¹ᐟ² for water at 25 °C.
• Why “limiting”: the model holds exactly only as I → 0: point-charge ions, complete dissociation, Coulomb forces only, continuum solvent.
• The law fails as I rises (NaCl 0.1 m: 0.690 against 0.778 measured); the extended law −A|z₊z₋|√I/(1 + Ba√I) is then used.