Page 251 - Physical chemistry understanding our chemical world

218 PHASE EQUILIBRIA

The figure shows how adding salt to the water has caused both the lines for liquid
and for gas to drop down the page, thus causing the intersection temperature to change.
Therefore, a second consequence of adding salt to water, in addition to changing its
chemical potential, is to change the temperature at which boiling occurs. Note that
the boiling temperature is raised, relative to that of pure water.

Why does the ice on a path melt when sprinkled
with salt?

Quantitative cryoscopy

The ice on a path or road is slippery and dangerous, as we saw when considering
black ice and ice skaters. One of the simplest ways to make a road or path safer is to
sprinkle salt on it, which causes the ice to melt. In practice, rock salt is preferred to
table salt, because it is cheap (it does not need to be purified) and because its coarse
grains lend additional grip underfoot, even before the salt has dissolved fully.
The depression of freezing temperature occurs because ions from the salt enter the
lattice of the solid ice. The contaminated ice melts at a lower temperature than does
pure ice, and so the freezing point decreases. Even at temperatures below the normal
melting temperatures of pure ice, salted water remains a liquid – which explains why
the path or road is safer.
We must appreciate, however, that no chemical reaction occurs
The ‘molaLity’ m is the between the salt and the water; more or less, any ionic salt, when
number of moles of put on ice, will therefore cause it to melt. The chemical identity of
solute dissolved per the salt is irrelevant – it need not be sodium chloride at all. What
unit mass of solvent; matters is the amount of the salt added to the ice, which relates
‘molaRity’ (note the eventually to the mole fraction of salt. So, what is the magnitude
different spelling) is of the freezing-point depression?
the number of moles
Let the depression of the freezing point be T , the magnitude
of solute dissolved per of which depends entirely on the amount of solute in the solvent.
unit volume.
Re-interpreting Blagden’s law gives

T ∝ molality (5.15)
We prefer ‘molaL-
ity’ m to ‘molaRity’
(i.e. concentration c) The amount is measured in terms of the molality of the solute.
Molality (note the spelling) is defined as the amount of solute
because the volume
of a liquid or solution dissolved per unit mass of solvent:
changes with temper-
ature, whereas that moles of solute
molality,m = (5.16)
of a mass does not. mass of solvent
Accordingly, molal-
ity is temperature where the number of moles of solute is equal to ‘mass of solute ÷
independent whereas molar mass of solute’. The proportionality constant in Equation
concentration is not. (5.15) is the cryoscopic constant K (cryoscopic) . Table 5.3 contains a
few typical values of K (cryoscopic) , from which it can be seen that