Problem 9: Determine the minimum of the relative humidity, which is necessary to stabilize a supercooled water droplet of water with the
diameter of 10 nm at -10 $^\circ$C, using the following information only.
the saturated vapour pressure ($P_0$ 273K) of water at 273 K: 4.7 Torr, surface tension of liquid water at 263K: 77 Dyne/cm; the density of water and
the molecular weight are respectively 1 g/ml, and 18 amu.
Requirements: As always, use the Word program's equation tools to present your solution. Derive the analytical expression for the relative humidity first
(before the actual calculation).
Problem 10: An organic compound is synthesized in an advanced gas-phase reactor. Upon synthesis, a fraction of volatile products condenses into
a \"fog\" of nanoscale droplets, which are in equilibrium with vapour phase molecules at 310 K. The partial pressure of the organic vapor at this
temperature is 68.5 mBar, and the saturated vapor pressure of the liquid is approximately 62 mBar. The molar density of the liquid phase is
approximately 0.001 mol/cm$^3$. Using this information, determine the maximum pore diameter of a filter, which will be able to trap all the \"fog\"
particles. Note that the surface energy of the liquid surface has been estimated as 58 mJ/cm$^2$.
