91Ó°ÊÓ

The mole fraction is a crucial concept when dealing with gas mixtures. It represents the proportion of moles of a particular gas in a mixture relative to the total number of moles of all gases present. To calculate the mole fraction, divide the moles of the individual gas by the total number of moles in the mixture. For example, in our exercise, we have:

- The mole fraction of \text{O}_2: \footnotesize{\text{\( \frac{8 \text{~mol}}{12 \text{~mol}} = \frac{2}{3} \)}}
- The mole fraction of \text{CH}_4: \footnotesize{\text{\( \frac{3 \text{~mol}}{12 \text{~mol}} = \frac{1}{4} \)}}
- The mole fraction of \text{CO}_2: \footnotesize{\text{\( \frac{1 \text{~mol}}{12 \text{~mol}} = \frac{1}{12} \)}}

Understanding mole fractions allows us to relate the properties of each individual gas to the whole gas mixture. It's an essential step in applying gas laws, such as Dalton's Law of Partial Pressures.

Partial pressure refers to the pressure that a single gas in a mixture would exert if it occupied the entire volume by itself. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. To find the partial pressure of each gas in our exercise, we multiply the mole fraction of the gas by the total pressure. Hence:

- The partial pressure of \text{O}_2: \footnotesize{\text{\( \frac{2}{3} \times 240 \text{~atm} = 160 \text{~atm} \)}}
- The partial pressure of \text{CH}_4: \footnotesize{\text{\( \frac{1}{4} \times 240 \text{~atm} = 60 \text{~atm} \)}}
- The partial pressure of \text{CO}_2: \footnotesize{\text{\( \frac{1}{12} \times 240 \text{~atm} = 20 \text{~atm} \)}}

This concept helps us understand how each gas contributes to the total pressure in a mixture. It simplifies complex gas behavior into manageable parts by focusing on individual gases.

Gas laws describe the behavior of gases under various conditions of pressure, volume, and temperature. Several important gas laws interact and are foundational to understanding the properties and behavior of gases. These include:

- **Boyle's Law:** States that the pressure of a gas is inversely proportional to its volume, at constant temperature.
- **Charles's Law:** States that the volume of a gas is directly proportional to its temperature, at constant pressure.
- **Avogadro's Law:** States that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules.

Dalton's Law of Partial Pressures, which was applied in the exercise, states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in the mixture. It's a useful tool in chemical calculations when dealing with gas mixtures, making it easier to predict how each gas will behave independently and within a mixture. These laws help us to predict and calculate the outcomes of changing conditions in gas-related scenarios, providing a comprehensive understanding of gaseous behavior.