0.17 Phase equilibrium in solutions  (Page 3/9)

We should check this result by comparing it to other aqueous solutions of nonvolatile solutes. Ethylene glycol, commonly used in antifreeze solutions, is soluble in water but has a very small vapor pressure at 25 ºC, less than 0.1 torr. When we prepare ethylene glycol solutions with molarities in the range of 1.0 M to 3.0 M and measure the vapor pressures as before, we discover a remarkable result. The vapor pressures follow the same graphs as shown in Figures 1 and 2. There is no discernible difference within the accuracy of our measurements. This means that, in our equation P _vap =P ^* _vap *X _water , the vapor pressure of the aqueous solution does not depend on the identity of the nonvolatile solute. It depends only on the number of moles of the nonvolatile solute. This is not at all an intuitive result. However, it is quite general, and these experimental results and the equation above both go by the name “Raoult’s Law.” Raoult’s measurements showed that this equation works for almost all solvent and nonvolatile solute combinations, provided only that the concentration of the solute is not too high.

Given this surprising result, we need to generate a model which can account for it. Before doing so, we will consider an additional aspect of our observation. Imagine that we start with pure liquid water in equilibrium with its vapor at the normal boiling point. This means that the temperature is 100 ºC, and the applied pressure and the vapor pressure are both 1 atm. Now imagine that we add some amount of glucose to the water. According to Raoult’s law, the vapor pressure of the solution we just formed must be less than the vapor pressure of the pure water. Therefore, the vapor pressure is less than 1 atm, which is less than the applied pressure. Since the applied pressure is greater, all of the vapor must now condense into the liquid, and we no longer have liquid-vapor equilibrium. The solution is not at its boiling point, even though the temperature is 100 ºC. The addition of the nonvolatile solute has disrupted the liquid-vapor equilibrium.

How can we restore the equilibrium? There are two ways. The obvious way would be to lower the applied pressure to the vapor pressure of the solution. A less obvious way would be to increase the temperature without changing the applied pressure. To see this, remember that Raoult’s law gives the vapor pressure of the solution in terms of the vapor pressure of the pure liquid: P _vap =P ^* _vap *X _water . If we need P _vap to be 1 atm even though X _water is less than 1, we can increase P _vap ^* by increasing the temperature. This means that we can find a normal boiling point for the solution, but it will be at a higher temperature than the boiling point of the pure liquid at the same applied pressure. The boiling point is elevated by the presence of the nonvolatile solute. The amount by which the boiling point changes is typically quite small, about 0.5 ºC for a 1 M solution, but it is easily observable.

Dynamic equilibrium and vapor pressure lowering

There are really two interesting observations in Raoult’s law. One is that the vapor pressure is lowered when a nonvolatile solute is dissolved in a volatile solvent. The other is that the amount of that lowering does not depend on what the nonvolatile solute is. It depends only on the mole fraction of the nonvolatile solute in the solution. We need to develop a model which accounts for both of these observations.