What are the mole fraction and the mole percent of oxygen in exhaled air if \(P_{\mathrm{O}_{2}}\) is 116 torr and \(P_{\text {total }}\) is 788 torr?

Partial pressure is a term used in chemistry to describe the pressure exerted by a single gas component in a mixture of gases. It is proportional to the number of moles of the gas and is an important concept when analyzing the behavior of gas mixtures, such as the air we breathe.

In a mixture, each gas behaves as if it occupies the entire volume alone and exerts pressure independently. This is known as Dalton’s Law of Partial Pressures. For example, in exhaled air, the partial pressure of oxygen (\(P_{\text{O}_2}\)) is one part of the total pressure exerted by all gases present. Understanding partial pressure is essential when working with gas laws and calculations involving gas mixtures.

The mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a particular substance to the total number of moles of all substances in the mixture. To calculate the mole fraction of oxygen in exhaled air, you would use the formula \(X_{\text{O}_2} = \frac{P_{\text{O}_2}}{P_{\text{total}}}\) where \(P_{\text{O}_2}\) is the partial pressure of oxygen and \(P_{\text{total}}\) is the total pressure of the gas mixture.

The mole fraction is dimensionless and always between 0 and 1. It is a useful concentration measure in various chemical calculations because it does not change with temperature or pressure, unlike other concentration measures such as molarity or mass percent.

Gas composition refers to the quantitative makeup of a gas mixture. It is crucial information when studying chemical reactions involving gases, environmental science, and industrial processes. The composition can be expressed in different ways, including mole fraction and partial pressures.

Understanding the composition of gas mixtures like exhaled air allows us to explore respiratory physiology. In our practical example, knowing the mole fraction and partial pressure of oxygen in exhaled air can be useful in medical diagnostics, scuba diving, and many other applications where gas mixtures are critical. The key to these calculations lies in accurately measuring or predicting the component pressures and translating them into meaningful concentrations.

Mole percent is another way to describe the concentration of a component within a mixture, representing the mole fraction in terms of percentage. To convert a mole fraction to mole percent, simply multiply the mole fraction by 100%. For instance, if the mole fraction of oxygen in exhaled air is calculated to be 0.147, then the mole percent would be \(0.147 \times 100\% = 14.7\%\).

This conversion is very straightforward and allows for easy comparison of component concentrations when discussing the composition of mixtures in terms such as 'percent composition,' which is more commonly used and understood outside the field of chemistry.