Dalton’s Law of Partial Pressure

Dalton’s Law of Partial Pressure states that the total pressure exerted by a mixture of gases is equal to the sum of the pressures of the different gases making up the mixture --- each gas acting as if it alone were present and occupied the total volume.  The pressure exerted by each gas is proportional to the number of molecules of that gas that are present in the total volume.  Therefore, the pressure exerted by each gas is proportional to the percentage of the volume made up by that gas and is called the Partial Pressure.  Dalton’s Law can be expressed as:

 

                         P(Total) = pp(A) + pp(B) + pp(C) + . . . . = 100%

 

And, therefore, the partial pressure exerted by gas A is:

 

                                          P(Total)  x  % Vol(A)

                          Pp(A) =  -------------------------

                                                       100%

 

An understanding of Dalton’s Law is crucial in mixed-gas diving.  For example, in air at the surface, the partial pressure of oxygen is:

 

                                           1 ATA  x  21%

                         ppO2  =  ------------------  =  0.21 ATA

                                                  100%

 

At what depth would the partial pressure of oxygen in air be equal to 1.6 ATA?  The solution can be calculated as follows:

 

                                                     ppO2  x  100%                    1.6 ATA  x  100%

                        P(Total)      =        -----------------       =       ---------------------   =   7.62 ATA

                                                          % Vol(A)                                  21%

 

Atmospheric pressure is equal to 1 ATA, therefore the water pressure at the depth where the ppO2 = 1.6 ATA in air is

 

                       7.62 ATA  -  1.0 ATA  =  6.62 ATA

 

Therefore, the depth where the ppO2 = 1.6 ATA in an air mixture is:

 

                                                   33 fsw

                      6.62 ATA    x       --------   =  218 fsw

                                                   1 ATA

 

Henry’s Law of Solubility

 This type of calculation will have to be carried out for every mixed-gas mixture to determine the maximum safe depth at which it can be used because of the problem of oxygen toxicity.

 

Henry’s Law of Solubility states that the amount of gas that will dissolve in a liquid at a given temperature is almost directly proportional to the partial pressure of that gas.  The partial pressure of a gas is determined by the total pressure (depth) and the percentage of the total volume made up by that gas as seen in Dalton’s Law.  In mixed gas diving, the percentage of the total volume made up by the component gases is always different than air and, therefore, every different gas mixture requires its own decompression schedule.  The problem of decompression will be discussed later in the chapter.

 

Henry’s Law is only valid at a constant temperature, but in diving the temperature of the tissues in the body often changes.  The solubility of a gas in a liquid as the temperature changes is counter-intuitive in that, the solubility og a gas increases as the temperature decreases.  Therefore, a diver who gets cold curing a dive will absorb more inert gas than a diver who stays warm, and will have to spend more time decompressing before surfacing to have the same risk of developing decompression sickness.