A sample of air contains only nitrogen and oxygen gases whose partial pressures are 0.80 atm and 0.20 atm, respectively. Calculate the total pressure and the mole fractions of the gases.

The concept of partial pressure is key when dealing with mixtures of gases. It refers to the pressure that a single gas component in a mixture would exert if it alone occupied the entire volume of the container at the same temperature. In a mixture, each gas exerts pressure independently of the others. This idea is crucial in understanding how gases behave in mixtures, such as the air we breathe, which is a mixture primarily of nitrogen and oxygen.

For instance, if air contains nitrogen and oxygen in a container, the partial pressure of nitrogen is the pressure it would contribute to the total pressure in the container. If you measure a partial pressure of 0.80 atm for nitrogen, that means nitrogen alone accounts for 0.80 atm of the total pressure exerted by the air inside the container. This is exactly the situation seen in the exercise provided.

When considering a gas mixture, like air, the total gas pressure is the sum of all partial pressures of the individual gases present. In other words, it is what you would register on a pressure gauge if you were to measure the pressure inside a container holding the mixture. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the additive result of all the individual gases' pressures.

As illustrated in the exercise, if you have a sample of air with partial pressures of 0.80 atm for nitrogen and 0.20 atm for oxygen, then the total pressure is simply the sum of these two values, which equals 1.00 atm. This concept is fundamental for determining the behavior and properties of gas mixtures in various scientific and industrial processes.

The mole fraction is a way of expressing the concentration of a particular component in a mixture without the reliance on volume or pressure, using moles as a counting unit instead. It is defined as the ratio of the number of moles of one component to the total number of moles of all components present in the mixture.

In the context of the exercise, the mole fraction is calculated using partial pressures under the assumption that the gases behave ideally. This is possible because, for an ideal gas, the partial pressure is directly proportional to the number of moles. Therefore, if the partial pressure of nitrogen is 0.80 atm and the total pressure is 1.00 atm, the mole fraction of nitrogen is 0.80. This tells us that nitrogen makes up 80% of the total moles of gas in the mixture. The calculation of mole fraction is a vital step in quantifying the composition of gas mixtures in chemistry and engineering.

Understanding the behavior of gases is essential in diverse scientific disciplines, and this involves being familiar with the gas laws. These laws describe the relationship between the pressure, volume, temperature, and amount of gas. They include Boyles's Law (pressure-volume relationship), Charles's Law (temperature-volume relationship), Avogadro's Law (amount-volume relationship), and the Ideal Gas Law, which combines the aforementioned laws into one equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

The calculations in the exercise rely on the principles of these laws—particularly those related to pressure. The Ideal Gas Law helps to understand that assuming a constant temperature and volume, the pressure exerted by a gas is proportional to the number of moles of the gas. Therefore, one can find the mole fraction of gases in a mixture by relating the partial pressures to the total pressure, showcasing a practical application of the gas laws.