Question

The saturated vapour pressure above an aqueous solution of sugar is known to be lower than that above pure water, where it is equal to psat, by Δp = 0.05psatc, where c is the molar concentration of the solution. A cylindrical vessel filled to height h1 =10 cm with a sugar solution of concentration c1 = 2 x 10-3 is placed under a wide bell. The same solution of concentration c2 = 10-3 is poured under the bell to a level h2 < h1 (Fig. 66)

Determine the level h of the solution in the cylinder after the equilibrium has been set in. The temperature is maintained constant and equal to 20 °C. The vapour above the surface of the solution contains only water molecules, and the molar mass of water vapour is μ = 18 x 10-3 kg/mol.

Answer 1

The concentration of the solution of sugar poured above a horizontal surface practically *** unchanged.

After the equilibrium sets in, the concentration of the solution in the vessel will be

The concentration changes as a result of evaporation of water molecules from the surface (concentration increases) or as a result of condensation of vapour molecules into the vessel (concentration decreases). The saturated vapour pressure above the solution in the cylindrical vessel is lower than that above the solution at the bottom by Δp = 0.05psat(c - c2). This difference in pressure is balanced by the pressure of the vapour column of height h:

The density ρv of vapour at a temperature T = 293 K can be found from the equation of state for an ideal gas:

Thus, the height h of vapour column satisfies the quadratic equation

Substituting the numerical values and solving the quadratic equation, we obtain

h ≈ 16.4 cm.

It is interesting to note that, as follows from the problem considered above, if two identical vessels containing solutions of different concentrations are placed under the bell, the liquid will evaporate from the solution of a lower concentration. Conversely, water vapour will condense to the solution of a higher concentration. Thus, the concentrations tend to level out. This phenomenon explains the wetting of sugar and salt in an atmosphere with a high moisture content.