ΔT = Kfm ,where ΔT is the freezing point depression, m the molality of the solute, and Kf a constant characteristic of the solvent. Arrhenius hypothesized that in electrolyte solutions some portion of the solute dissociates into ions, making the molality of particles im rather than m; thus i is the average number of particles into which a solute molecule dissociates. For electrolyte solutions, then,
ΔT = Kfim ,where i depends on the nature of the solute and its extent of dissociation. (Note: i need not be an integer.)
1) How can one find i from freezing point depression experiments? Write an expression for i as a function of quantities measurable in a freezing point depression experiment.
2) To see that i need not be an integer, consider a solute of formula MX. Suppose that half of the MX formula units dissociate into M+ and X- ions and half remain intact as MX molecules. What is the value of i for this MX solution? What if the fraction that dissociates is not one half but an arbitrary fraction α?
3) Continue to suppose that the fraction of molecules that dissociate is α Suppose that the solute molecules that do dissociate yield k ions each (where k is a known integer, e.g., 2 for NaCl, 3 for MgCl2, 4 for FeCl3, etc.). Write an expression for i in terms of k and α.
In fact, α and i can be measured independently (from conductance and freezing-point depression experiments respectively). Comparing i from freezing-point depression experiments with i computed from the expression derived from exercise 3 can serve as a check on the validity of the hypothesis of electrolyte dissociation. This comparison was an important part of Arrhenius's landmark paper on electrolyte solutions.
|
| Back to the Classic Calculations home page |
| Back to the top of the Classic Chemistry site |