334
Colllgatlve Properties
the colligative properties are concerned. For every mole of NaCl dissolved we
have 2 moles in solution: a mole of Na
+ ions, and a mole of Cl~ ions. Thus we
get an abru&rmal freezing-point depression.
Accordirig^to modern theory, many strong electrolytes are completely dissociated in dilute solutions. The freezing-point lowering, however, does not
indicate complete^ dissociation. For NaCl, the depression is not quite twice the
amount calculated on the basis of the number of moles of NaCl added. In the
solution, the ions attract one another to some extent; therefore they do not
behave as completely independent particles, as they would if they were
nonelectrolytes. From the colligative properties, therefore, we can compute
only the "apparent degree of dissociation" of a strong electrolyte in solution.
To illustrate, let us consider the freezing-point depression that occurs when
we put 1 mole of NaCl into 1 kg of water. NaCl dissociates according to the
equation
NaCl -» Na
+ + Cl~
Let us assume that a is the fraction of NaCl molecules that appear to dissociate,
and that 1 - a is the fraction that act as if they were still combined as NaCl
molecules. Remember that we are talking about our apparent degree of dissociation, as measured by the colligative properties. Then we have, if we start with
n moles of NaCl,
n(\ - a) mole of undissociated molecules,
no. mole of Na
+ ions, and
na mole of Cl~ ions.
Adding, we get
total moles in solution = n(l - a + 2a) = n(\ + a)
This we can use to compute the value of a from the freezing-point lowering. As
mentioned previously, we find that a solution of 1 mole of NaCl in 1 kg of H 2 0
freezes at -3.50°C. Here n = 1, so we have m = 1 + a moles/kg of water.
Applying Equation 21-2, we obtain
Ar F = mK F
3.50 = (1 + a)(1.86)
1 + a = 1.88
a = 0.88
Colllgatlve Properties
the colligative properties are concerned. For every mole of NaCl dissolved we
have 2 moles in solution: a mole of Na
+ ions, and a mole of Cl~ ions. Thus we
get an abru&rmal freezing-point depression.
Accordirig^to modern theory, many strong electrolytes are completely dissociated in dilute solutions. The freezing-point lowering, however, does not
indicate complete^ dissociation. For NaCl, the depression is not quite twice the
amount calculated on the basis of the number of moles of NaCl added. In the
solution, the ions attract one another to some extent; therefore they do not
behave as completely independent particles, as they would if they were
nonelectrolytes. From the colligative properties, therefore, we can compute
only the "apparent degree of dissociation" of a strong electrolyte in solution.
To illustrate, let us consider the freezing-point depression that occurs when
we put 1 mole of NaCl into 1 kg of water. NaCl dissociates according to the
equation
NaCl -» Na
+ + Cl~
Let us assume that a is the fraction of NaCl molecules that appear to dissociate,
and that 1 - a is the fraction that act as if they were still combined as NaCl
molecules. Remember that we are talking about our apparent degree of dissociation, as measured by the colligative properties. Then we have, if we start with
n moles of NaCl,
n(\ - a) mole of undissociated molecules,
no. mole of Na
+ ions, and
na mole of Cl~ ions.
Adding, we get
total moles in solution = n(l - a + 2a) = n(\ + a)
This we can use to compute the value of a from the freezing-point lowering. As
mentioned previously, we find that a solution of 1 mole of NaCl in 1 kg of H 2 0
freezes at -3.50°C. Here n = 1, so we have m = 1 + a moles/kg of water.
Applying Equation 21-2, we obtain
Ar F = mK F
3.50 = (1 + a)(1.86)
1 + a = 1.88
a = 0.88