[orgo814]

I'm confused about KMT-8 in the picture (sorry if it is posted in a slanted view). They want the approximate collision frequency of nitrogen molecules with a 1-cm^2 surface. Now, when I always calculated collision frequency I did it by ratio of mean speed to mean free path. Here they utilize number density with formula z= (1/4)(N/V)c, where c is the mean speed. In the description to how they solved this, they said that number density is approximately 10^19 molecules/cm^3 at room temperature and pressure and average speed is about 10^5 cm/s which is how they arrived at 10^23 as the answer. im not understanding where the 10^19 and 10^5 is coming from (are they calculated, assumed...). Just a little confused. Thank you.

[mjc123]

These are things you shopuld be expected to know or be able to work out. You know that 1 mol of gas occupies 24L, so it is easy to work out N/V ≈ 10¹⁹ cm^-3. And you should just know that typical molecular speeds are of the order of 1 km/s (if you don't, you can estimate it by KE ≈ kT).

[Enthalpy]

Alternately, one can derive the number of collisions per time unit on a surface from the push on this surface by the collisions (=pressure) and from the mean momentum of the molecules.

Detail: books often represent an elastic collision of gas molecules on surfaces. That's wrong: a gas molecule is adsorbed, sticks on the surface for a random duration, and when the solid happens to impart it enough energy, it's desorbed. The computed pressure is the same as soon as the gas and the surface have the same temperature; delayed desorption matters for the operation of some pumps for instance.

The number of collisions per time unit on a surface permits to estimate the evaporation speed of a liquid, if you suppose that the liquid-vapour equilibrium means equal rates of condensation and evaporation and that all vapour molecules stick when impinging the liquid surface.