Dalton's Law is named for John Dalton, who stated the law in 1801. The law states that the pressure exerted by a mixture of gases is equal to the sum of the pressures which would be exerted by the gases individually.
P = p(1) + p(2) + p(3) ... + p(n)
Where P is the total pressure exerted by the sum of pressures p.
Dalton's discovery was all gases tend to compress similarly. If you have a mixture of nitrogen and oxygen and you add 100lbs of pressure both the nitrogen and oxygen will compress equally.
In other words, mixed gases will stay in the same proportions under pressure - you will not find some gasses compressing more than others. For instance, imagine squeezing a cloth bag equally full of marbles and popcorn. You know that the popcorn will compress more than the marbles and with sufficient pressure the proportion of marbles and popcorn in the bag (by volume) will change. Dalton's law assures us that among gases it will not happen.
To a scuba diver this assures us that our bodies absorb gases in the same proportions at any depth. It is this principle which makes it possible to estimate gas levels in our body, plan repetitive dives and avoid the bends.
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