Formation of Precipitation based on Saturation

Saturation is the first step in the formation of precipitation.

It is necessary but not really sufficient, but in the formation of precipitation it is necessary to the air to saturated with water vapor. The water vapor tension must reach the saturation value at that or certain temperature. This can be explaining by Clausius-Clapeyron equation. 

The Clausius-Clapeyron equation is used to estimate the vapor pressure at another temperature, if the vapor pressure is known at some temperature, and if the enthalpy of vaporization is known and to estimate the heat of phase transition from the vapor pressures measured at two temperatures.

The vapor pressures of pure liquids or solids can be estimate based on Clausius-Clapeyron equation:

where P is the vapor pressure, P° is a vapor pressure at a known temperature T°, DeltaH is an enthalpy of vaporization if the substance is a liquid or an enthalpy of sublimation if it's a solid, R is the ideal gas law constant, and T is the temperature (in kelvins).

It is noted that several of the assumptions fail at high pressure and near the critical point, and under those conditions the Clausius-Clapeyron equation will give inaccurate results. However, some researcher still like to use the equation because it's good enough in most applications and because it's easy to derive and justify theoretically.

In addition, The Antoine equation is a modified of Clausius-Clapeyron equation and researcher reveals that this equation is a more more reliable to estimate water vapor pressure. The Antoine equation is a simple 3-parameter fit to experimental vapor pressures measured over a restricted temperature range:

where A, B, and C are "Antoine coefficients" that vary from substance to substance. Sublimations and vaporizations of the same substance have separate sets of Antoine coefficients, as do components in mixtures. The Antoine equation is accurate to a few percent for most volatile substances (with vapor pressures over 10 Torr). Antoine coefficients for many substances are tabulated in Lange's Handbook of Chemistry (12th ed., McGraw-Hill, New York, 1979) and they are available online from NIST's Chemistry WebBook.