Question

The pores in a solid consist of cylindrical tubes of radii 16 nm ending with spherical cavities of radii 41 nm. Calculate the relative pressure at which capillary condensation of nitrogen at 77 K (the boiling temperature at atmospheric pressure) would occur in each section. In this experiment, the gas pressure is being gradually increased, so there has been prior adsorption covering the surfaces of both sections with a 1 nm layer of nitrogen (approximately 2 layers and sufficient to give a liquid-like surface). Describe the capillary condensation process for this particular pore structure . The surface tension of nitrogen liquid at this temperature is 8.85 mN

m^-1, the molar volume is 34.7 cm3 mol^-1; atmospheric pressure is 101.3 kPa.

Answer 1

Using the Kelvin equation for the cylindrical part, we can adjust the radius for the adsorbed gas layer thickness. We now have hollow cylinder of liquid, and to use the Kelvin equation, internal radius of the cylinder would be one radius and the other radius would be infinite because it is radius in the plane of the cylinder axis. Therefore, we can write the equation as,

Relative pressure can be calculated as,

Since two radii are same for spherical cavity, we can write,

This gives,

Therefore, as the pressure increases, capillary condensation would take place in the narrow cylindrical neck of the pore. Because of this process, the radius of the liquid surface within the pores will decrease for capillary condensation to occur rapidly. This will fill the neck and block the access to the spherical cavity.