126. Solving a chemistry problem

27. To verify the validity of the Kelvin equation, the following experiments were carried out (at 20 C). A narrow layer of cyclohexane (density 0.7785 g/cm3) was raised between two flat mica plates spaced at a controlled distance of less than 1 µm between them. Above the liquid meniscus formed, the equilibrium vapor pressure was measured, and the curvature radius of the meniscus was also measured (by the interferometric method). The following table shows the results of these experiments.
-rk, nm 22.3 16.6 11.6 7.95 6.33 4.22
p/ps 0.943 0.930 0.899 0.864 0.834 0.761
Calculate the surface tension from these data and find its percentage deviation from the result of a direct measurement on a flat surface of cyclohexane (25.3 mN/m). Note that the surface of the meniscus in this experiment is concave and not spherical, but parabolic. In this case, the Kelvin equation has the form ln(p/ps)=σVm/RTrk, where rk is the radius of curvature.