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In gas mixtures, each individual gas exerts its own pressure, known as partial pressure. It's as if each gas in the mixture is acting independently. Partial pressure is an essential concept in understanding gas behavior in mixtures. When we talk about the partial pressure of a gas, we are referring to the pressure that gas would exert if it occupied the entire volume by itself at the same temperature. This concept helps break down the individual contributions that different gases make to the overall pressure of the mixture. For example, in our exercise, the partial pressures of oxygen (\(\mathrm{O}_2\)) and nitrogen (\(\mathrm{N}_2\)) in the air are given as a ratio, 0.21:0.79. This ratio indicates how the pressure exerted by each gas compares when combined within the same system.

The mole fraction provides a simple way to express the composition of a gas mixture based on the number of moles. It is the ratio of the number of moles of a particular component to the total number of moles in the mixture. Mathematically:

• Mole fraction (\(X\)) = number of moles of gas / total number of moles

In our context, since the partial pressures are given, we can use Dalton’s Law. The mole fraction of oxygen (\(X_{O_2}\)) is calculated as 0.21, and for nitrogen (\(X_{N_2}\)) as 0.79. These values come from the ratio of the partial pressures. The mole fraction plays a crucial role when determining other properties of the gas mixture, such as mass fraction.

Mass fraction represents the proportion of a substance's mass compared to the total mass of the mixture. This is useful when you need to know how much of the total mass is made up by each component.

• Mass fraction = mass of component / total mass of mixture

In the exercise, the mass contributions of both oxygen and nitrogen were calculated based on their mole fractions and molar masses. Using these mass contributions, the mass fraction of oxygen was found to be approximately 0.233, while for nitrogen, it was about 0.767. These fractions help us understand the weight distribution of each component within the mixture.

Oxygen is a diatomic molecule (\(\mathrm{O}_2\)) and a crucial component of the Earth's atmosphere. It is highly reactive, combining with most elements and playing a vital role in processes like combustion and respiration. In our exercise, oxygen was considered with its partial pressure at 0.21 times the total pressure, reflecting its presence in the air mixture. Knowing its molar mass (32 g/mol) is important when determining its mass contribution and exactly understanding its role within the gas mixture. Oxygen's role, both in the exercise and in real life, illustrates its importance in maintaining balance and functionality within different systems, including biological and chemical ones.

Nitrogen, like oxygen, is diatomic (\(\mathrm{N}_2\)) and comprises a significant portion of the Earth's atmosphere. It is relatively inert compared to other gases, which makes it a stabilizing presence in the air. In our example, its partial pressure, which is 0.79 of the system, demonstrates its dominance in the gaseous mixture of air. With a molar mass of 28 g/mol, nitrogen contributes significantly to the total mass, resulting in a higher mass fraction compared to oxygen. This inertness and abundance make nitrogen essential in processes like the nitrogen cycle and applications requiring non-reactive environments, illustrating its versatility and importance on the global scale.