A deep-sea diver should breathe a gas mixture that has the...

A deep-sea diver should breathe a gas mixture that has the same oxygen partial pressure as at sea level, where dry air contains $20.9 \%$ oxygen and has a total pressure of $1.01 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} .$ (a) What is the partial pressure of oxygen at sea level? (b) If the diver breathes a gas mixture at a pressure of $2.00 \times 10^{6} \mathrm{N} / \mathrm{m}^{2},$ what percent oxygen should it be to have the same oxygen partial pressure as at sea level?

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Key Concepts

Partial Pressure

Partial pressure is the pressure contributed by a single component in a mixture of gases, determined by its mole fraction multiplied by the total pressure. It is essential for understanding how individual gases behave in a mixture, irrespective of the other gases present.

Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure exerted by a gas mixture is the sum of the partial pressures of its individual components. This principle is key for calculating the specific pressures of gases within a mixture when the overall pressure and composition are known.

Gas Mixtures and Composition

Understanding gas mixtures involves analyzing the proportions of different gases in a blend and how these proportions affect properties like partial pressures. Adjusting the composition is crucial in practical applications, such as ensuring that breathing mixtures provide the appropriate partial pressure of oxygen, especially under varying total pressure conditions.

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