Activity Coefficients of Dissolved Species

1
Activity Coefficients of Dissolved Species

• In natural waters, solubilities can be increased
  by complexing and by ionic strength effects.
• Ionic strength effects arise from the coulombic
  interaction between ions (like charges repel,
  opposite charges attract) the coulombic force is
  ? to the square of the charge, thus I ½?mizi2.
  
• Increasing I decreases the effective
  concentration (activity) of dissolved species ai
  ?imi, thereby decreasing their chemical
  potentials ?i ?i? RT ln ai ?i? RT ln?i
  RTln mi
• For all charged ions the value of ?i decreases
  with increasing ionic strength. The decrease is
  greatest for highly charged species and is
  similar for all species of a given charge,
  regardless of sign.
• A mineral (salt) that dissolves in H2O to form
  charged species should be more soluble when other
  salts are present in solution. Salts usually
  dissolve as charged species, increasing the ionic
  strength and decreasing the activities of other
  ions in solution.

2
Mean ion activity coefficients

• Solutions must be electrically neutral ?mizi
  0. Impossible to measure activity coefficients
  independently because each ion must be
  accompanied by an ion of the opposite charge.
• Mean ion activity coefficients represent the net
  effect of the cation and anion from a salt on the
  solution, and they can be measured (e.g., effect
  on solubility, or by measuring transport
  properties, such as conductivity and diffusion).
• Mean ion activity coefficients are useful for
  chemists investigating simple (single salt)
  electrolyte solutions, but for natural waters
  containing a mixture of several electrolytes,
  need a way to obtain individual ion activity
  coefficients.
• MacInnes convention ?K ?Cl ??KCl Can use
  this relationship to calculate individual ion
  activity coefficients of strong electrolytes
  (completely dissociated, no complexing) measured
  at the same ionic strength. The effect of ionic
  strength on activity coefficients is measured
  relative to that on KCl. (see pp. 126-7, CRC mean
  salt values). Method only accurate at low
  concentrations no ion pairing.

3
Equations for calculating individual ion activity
coefficients

• Dilute solutions Debye-Huckel equation.
  Assumptions ion interaction purely coulombic,
  ion size does not vary with ionic strength, ions
  of the same sign do not interact. At internediate
  and high ionic strengths these assumptions become
  invalid.
• Example calculate fluorite solubility in pure
  H2O and in 1M SrCl2. Solve for 1) Ionic strength
  2) activity coefficients 3) concentrations from
  Ksp 4) repeat.
• Stoichiometric and effective ionic strength
• Effect of ionic strength on trace element
  partitioning melt/fluid partition coefficients
  (Ayers Eggler, 1995)
• Intermediate ionic strengths The Davies and
  Truesdell-Jones equations
• High ionic strengths (brines) the Pitzer model