An air sample contains \(0.038 \% \mathrm{CO}_{2}\). If the total pressure is \(758 \mathrm{~mm} \mathrm{Hg}\), what is the partial pressure of \(\mathrm{CO}_{2}\) ?

When we talk about gas mixtures, we're referring to a combination of different gases that share a common space, like the atmosphere, a balloon, or a container in a chemistry lab. Each gas in a mixture behaves independently and contributes to the total pressure inside the container. This behavior is key to understanding how gas mixtures operate, and it allows us to calculate the pressure that a specific gas exerts within a mixture.

In our daily lives, we're surrounded by gas mixtures. The air we breathe, for example, is a mixture of nitrogen, oxygen, carbon dioxide, and other trace gases. These gas mixtures are not chemically bonded but exist together and their individual molecules move around freely. This free movement means that each gas in the mixture exerts pressure as if the other gases were not present. The concept of partial pressures is built on this understanding.

Pressure conversions are crucial in the study of gases because different measurements might be used in different contexts. It's not uncommon to express pressure in units of millimeters of mercury (mmHg), atmospheres (atm), pascals (Pa), or pounds per square inch (psi), among others. For students and scientists alike, being comfortable with converting between these units ensures accurate calculations and comprehension of gas behavior.

For example, the standard atmospheric pressure at sea level is considered to be approximately 760 mmHg, which is also equivalent to 101,325 Pa or 1 atm. When solving problems, one might need to convert mmHg to atm or vice versa to align with the given data or required solution units. It's a simple ratio conversion, but it's vital to accuracy in calculations involving gases.

Dalton's Law of Partial Pressures is a foundational concept in chemistry, particularly when dealing with gas mixtures. The law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases. This means each gas contributes to the total pressure independently of the other gases present.

To apply Dalton's Law to our example, we calculated the partial pressure of CO₂ by considering the total pressure of the air sample and the percentage of CO₂ it contains. The CO₂, though only a tiny fraction of the mixture, exerts a pressure we can find by multiplying the total pressure by the fraction of CO₂. In a classroom setting, this law helps students predict the behavior of gas mixtures in different conditions, and it's essential for various real-world applications, including environmental science and engineering.