When moist air cools, a cloud can form. This much is true. The process is responsible for the cumulus cloud over Vancouver and the cap cloud over Rainier, shown above. Ascending air always cools. The cumulus cloud formed when air over the sun-warmed ground became buoyant and rose; the cap cloud, when the wind (coming from the right) blew against the sloping side of the mountain and was forced up.

But did the clouds form because the colder air had a lower holding capacity for water vapor than the warm air? If you believe a legion of teachers (from grade school to university), TV weather broadcasters, and endless textbook writers, this is the reason. They speak of the air being saturated and one even published an illustration of the air being wrung out like a sponge as the temperature dropped (sigh...). Unfortunately, it is not true. Sure, a cloud may form as the temperature drops, but not because some mystical holding capacity of the air has decreased.

 To claim that a temperature-dependent holding capacity of the air caused the cloud to form in cold air is to get (approximately) the right answer for the wrong reason. It is like trying to reduce the fraction, 19 / 95, by imagining that you can cancel the 9s. The right answer ensues, but for the wrong reason. And, if the process was wrong, it is unlikely to work the next time you try it in a slightly different situation.

 The air (mainly nitrogen and oxygen) no more has a holding capacity for water vapor, than, say, water vapor has for nitrogen. The atmosphere is a mixture of gases. While saturation (which involves bonds between different molecules) is a real phenomenon in liquids it does not describe the interaction of atmospheric constituents.
 
 

So, what is going on?
Water molecules are constantly coursing back and forth between phases (another word for the three states: vapor, liquid, and solid). If more molecules are leaving a liquid surface than arriving, there is a net evaporation; if more arrive than leave, a net condensation. It is these relative flows of molecules which determine whether a cloud forms or evaporates, not some imaginary holding capacity that nitrogen or oxygen have for water vapor.

The rate at which vapor molecules arrive at a surface of liquid (cloud drop) or solid (ice crystal) depends upon the vapor pressure.

 The rate at which vapor molecules leave the surface depends upon the characteristics of the surface. The number escaping varies with:

1. the phases involved --- molecules can escape from liquid more readily than from the solid (ice);
2. the shape of the boundary --- molecules escape more readily from highly curved (small) drops or ice crystals (convex);
3. the purity of the boundary --- foreign substances dissolved in the liquid or ice diminish the number of water molecules which can escape;
4. the temperature of the boundary --- at higher temperatures the molecules have more energy and can more readily escape.

So, what do you tell your students?
What appears to be cloud-free air (virtually) always contains sub microscopic drops, but as evaporation exceeds condensation, the drops do not survive long after an initial chance clumping of molecules. As air is cooled, the evaporation rate decreases more rapidly than does the condensation rate with the result that there comes a temperature (the dew point temperature) where the evaporation is less than the condensation and a droplet can grow into a cloud drop.

Evaporation increases with temperature, not because the holding capacity of the air changes, but because the more energetic molecules can evaporate more readily (with, of course, the caveat that evaporation is also influenced by things other than temperature, as described above).

If that explanation is not simple enough for your students, just present the facts: when the temperature drops below the dew-point temperature, there is a net condensation and a cloud forms.

But don't ever teach nonsense by claiming that the air has a temperature-dependent holding capacity for water vapor.
 

A little history
The idea that it is the air which determines the amount of water vapor which can be present through some sort of holding capacity is an eighteenth century idea which was shown to be false both empirically and theoretically about two hundred years ago! The fact that it is still taught in our schools and defended by teachers and (gulp) professors, is a testimony to the mindless persistence of myth. A discussion of some of the history of this bankrupt idea is offered by Steven M. Babin.