In a gas mixture with 30% oxygen, what is the partial pressure of the oxygen at 3 atmospheres absolute?

To determine the partial pressure of oxygen in a gas mixture, you can use Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is equal to the sum of the partial pressures of its individual components. The formula to calculate the partial pressure of a gas within a mixture is:

[ P_{gas} = P_{total} \times \text{Fraction of gas} ]

In this case, the total pressure is 3 atmospheres absolute, which is equivalent to 3 ata (atmospheres absolute), and the fraction of oxygen in the mixture is 30%, or 0.30 in decimal form.

Applying the numbers:

[ P_{O2} = 3 , ata \times 0.30 = 0.9 , ata ]

This calculation confirms that the partial pressure of oxygen in the mixture is 0.9 ata. This aligns with the understanding that as the percentage of a gas in a mixture increases, its partial pressure also increases in relation to the total atmospheric pressure. This principle is crucial in diving and scientific diving environments, as understanding gas mixtures and their partial pressures can significantly impact safety and physiological responses under varying pressure conditions.