91Ó°ÊÓ

When dealing with a gas mixture, each gas component exerts its own pressure, which is known as its partial pressure. The partial pressure is proportional to its mole fraction in the mixture. This relationship is crucial for understanding gas behavior in mixtures.
In the original exercise, we have a mixture containing 75% COâ‚‚ and 25% Hâ‚‚O by volume. To find the partial pressure of COâ‚‚, we use the formula:

• \( P_{\text{CO}_2} = X_{\text{CO}_2} \times P_{\text{total}} \)

Here, \( X_{\text{CO}_2} = 0.75 \) is the mole fraction, and \( P_{\text{total}} = 225 \) kPa is the total pressure. Hence, the initial partial pressure of COâ‚‚ is 168.75 kPa.
Understanding partial pressure helps us segregate how much each gas in a mixture contributes to the total pressure.

A gas mixture consists of multiple gases that are mixed together but not chemically bonded. Each gas within a mixture behaves independently.
In our example, we have CO₂ and H₂O gases. These gases coexist under an initial condition of a rigid container with a total pressure of 225 kPa and a temperature of 175°C. The properties of the mixture depend on the individual proprietaries of the gases involved.

• Each gas contributes to the total pressure.
• The contribution is dependent on its fractional volume and partial pressure.

Analyzing gas mixtures helps in situations where gas separation or collection is required, such as environmental gas analysis and chemical reactions.

Condensation is the process where a substance in gas form transforms into a liquid. This occurs when the gas is either cooled or compressed to reach its dew point.
In the problem provided, when the gas mixture was cooled to 0°C, the water vapor condenses. At this point, liquid water forms, leaving CO₂ as the only gas present in the vessel. This process reduces the total pressure of the system since the partial pressure contributed by the water vapor is now zero.

• Condensation removes gas volume, affecting pressures in mixtures.
• It helps transition between gas phases in thermodynamic cycles.

Understanding condensation is essential for studying climatic processes and designing systems like refrigerators and dehumidifiers.

Temperature change impacts gas behavior significantly, altering volume and pressure conditions according to the Ideal Gas Law. Lowering the temperature of a gas usually reduces its kinetic energy, causing a decrease in pressure if the volume is constant.
In the scenario given, the temperature of the gas mixture is reduced from 175°C (448 K) to 0°C (273 K). Assuming volume and amount of CO₂ remain unchanged, the pressure change can be calculated using:

• \[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]

Substituting known values leads to a new COâ‚‚ pressure of 102.65 kPa. This principle helps in understanding gas expansion and contraction, crucial for engines, weather predictions, and pressure vessels.