Ionic Activity

Ionic Activity

For an ideal NaCl solution, the chemical potential, µ_NaCl is given by

           µ_NaCl= µ_Na⁺ +µ_Cl^-                                                                                       (24)

Because cations and anions cannot be studied individually, µ_Na+ and µ_Cl-are not measurable. We can express the chemical potentials of the cation and anion as

µ_Na+ = µ^o_Na⁺ + RT ln m_Na⁺

µ_Cl-  = µ^o_Cl^- + RT ln m_Cl^-

where µ^o_Na⁺ and µ^o_Cl^- are the standard chemical potentials of the ions. Equation 24  can now be written as

µ_NaCl = µ^o_NaCl + RT ln m_Na⁺m_Cl^-

where

µ^o_NaCl = µ^o_Na⁺ + µ^o_Cl^-

In general, a salt with the formula M_v+X_v- dissociates as follows:

M_v+X_v-              v₊M^z+ + v_-X^z-

where v₊ and v_- are the numbers of cations and anions per unit and z₊ and z_- are the numbers of charges on the cation and anion, respectively.

The chemical potential is given by

µ = v₊µ₊ + v_-µ_-                                                                                           (25)

where

µ₊ = µ^o₊ + RT ln m₊

and

µ_- = µ^o_- + RT ln m_-

The molalities of the cation and anion are related to the molality of the salt originally dissolved in solution m, as follows

₊ = v₊m  m_- = v_-m

substituting the expressions for µ₊ and µ_- into equation 25 yields

µ = (v₊µ^o₊ + v-µ^o_-) + RT ln m₊^v+m_-^v-                                                  (26)

we define mean ionic molality (m_±) as a geometric mean of the individual ionic molalities

m_± = (m₊^v+ m_-^v-) ^1/v                                                                            (27)

where v = v₊ + v_- and equation 26 becomes

µ = (v₊µ^o₊ + v_-µ^o_-) + vRT ln m_±                                                              (28)

Mean ionic molality can be expressed in terms of the molality of the solution, m. Because m₊ = v+m and m- = v-m, we have

m_± =[(v₊m)^v+(v_-m)^v-]^1/v

      = m[(v₊^v+)(v_-⁺⁺)]^1/v                                                               (29)

Most electrolyte solutions behave nonideally, molality is thus replaced with activity

mean ionic activity is defined as   

a_± = (a₊^v+a_-^v-)^1/v         (30)

where a₊ and a- are the activities of the cation and anion, respectively. The mean ionic activity and the mean ionic molality are related by the mean activity co-efficient γ_±, that is

a_± = γ_±m_±                                                                                                  (31)

where γ_± = (γ₊^v+γ_-^v-)^1/v                                                         (32)

The chemical potential of a non ideal electrolyte solution is given by

µ = (v₊µ^o₊ + v-µ^o_-) + vRT lna_±

=  (v₊µ^o₊ + v-µ^o_-) + RT lna^v_±

=  (v₊µ^o₊ + v-µ^o_-) + RT lna                                                                 (33)

where the activity of the electrolyte, a is related to its mean ionic activity by

a = a^v_±

At very low concentrations γ_± unity for all types of electrolytes. As the concentrations of electrolytes increases, deviations  from ideality occur