c12 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come
BOILING POINT ELEVATION 189pT1 atmTbpTΔpΔTbFIGURE 12.5 Boiling of pure solvent (left) and a solution of solvent and nonvolatile solute
(right). The temperature of the solution must be increased byTbto restore its vapor pressure
to 1 atm.Addition of a nonvolatile solute causes a change in the vapor pressure of the solution
according to the amount of solute added because( 1 −X 1 )=X 2 for a binary solution:p=p 1 ◦−p=p◦ 1 −X 1 p◦ 1 =p◦ 1 (1−X 1 )=p◦ 1 X 2The statementp=p◦ 1 X 2 is true only in the limit of very dilute solutions.
To see that addition of a small amount of nonvolatile solute causes an elevation of
the boiling point of the solution relative to the pure solvent, consider a solvent that
has an exponential variation ofpwithTas in Fig. 12.5 (left). Its boiling point is the
temperature at which the vapor pressure is equal to the pressure of the atmosphere
bearing down on the surface of the liquid (dotted line).
When a nonvolatile solute is added to the solvent, its entire vapor pressure curve
is displaced downward byp. An increase in temperature is necessary to restore the
vapor pressure to 1 atm. The vapor pressure of the solution moves along the lower
exponential curve with increasing temperature until it arrives once again at 1 atm and
Tb, whereupon boiling recommences. It is evident that a functional relationship
must exist amongp,X 2 , andTb. To find the relation between the amount of
nonvolatile solute andTbwe have recourse to the Clausius–Clapeyron equationlnp=−vapH
R(
1
T
)
+constDifferentiating, we obtaindlnp=dp
p=
vapH
R(
1
T^2
)
dTIf we takedp/pasp/pfor a very small but finite and measurablep, brought
about by addition of the solute, we must increase the temperature by an amount