Week 06: Excercise Problems Chapter 3 (Surface Processes and Outgassing)

Excercise Problems Chapter 3 (Surface Processes and Outgassing)

3.1 If a monolayer of gas forms on a surface in 3 seconds at 10-6 mbar, how long would it take to form at 5 × 10-8 mbar?
3.2 A cubic vessel of side 10 cm contains a perfect vacuum and its internal walls are covered by a complete monolayer of gas molecules that suddenly desorb and stay in the vacuum space. How many desorb? What pressure will they create in the volume, assumed to be at 295 K?
3.3 For nitrogen gas at 295 K, the expression for the impingement rate of molecules on a surface, is J = 2.9 × 1020 p per cm2 per second, where the pressure p is in mbar. Re express this so that the units of J are per m2 per second, with pressure in Pa.
3.4 Verify that the specification of energies as “eV per molecule” is equivalent to 96.5 kJ per mole and that the value of kT at room temperature is 0.025 = 1 /40 eV.
3.5 For molecules that adsorb on a surface with energy 1.0 eV, estimate the average stay time at (a) 295 K, (b) 285 K, (c) 305 K.
3.6 Molecules whose average stay time on a surface is 1 ms impinge on it with sticking coefficient 0.1 at a rate 1017cm-2s-1. What is the equilibrium population of adsorbed molecules per cm2? To what fraction of a monolayer does this correspond?
3.7 Molecules of helium and carbon dioxide effuse through an aperture into a very high vacuum from an enclosure in which they originally exert equal partial pressures. What is the ratio of the helium and carbon dioxide effusion rates initially,
3.8 The molar adsorption energy of CO2 on carbon is approximately 34 kJ/mol. Calculate the mean stay time of CO2 on carbon at (a) 295 K, (b) 90 K, assuming a pre exponential factor 1013s.
3.9 Estimate the total area of surface in the “sponge-like” structure of a 1cm cube of porous molecular sieve with a 5 nm pore diameter by modeling it as a set of spherical voids packed in a cubic arrangement (i.e., in a simple cubic structure). Assuming that this material presents 1014 adsorption sites per cm2, estimate the maximum number of molecules that might be captured by it. To how many cm3 of gas at room temperature and atmospheric pressure would this correspond?

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