8.1 Properties of Gas Mixtures and Dalton's Law

Gas mixtures are crucial in thermodynamics, combining multiple gases that keep their individual properties. Understanding their composition and behavior is key for analyzing air conditioning processes and other applications involving mixed gases.

Dalton's Law is a fundamental principle for gas mixtures, stating that the total pressure equals the sum of partial pressures. This concept is essential for calculating properties of gas mixtures and plays a vital role in air conditioning and ventilation systems.

Gas mixtures and their characteristics

Composition and properties of gas mixtures

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• A gas mixture combines two or more gases that retain their individual properties without chemically reacting with each other
• The composition of a gas mixture can be expressed using mole fractions (ratio of moles of a component gas to total moles), mass fractions (ratio of mass of a component gas to total mass), or volume fractions (ratio of volume of a component gas to total volume)
• Gas mixture properties, such as density, specific heat, and viscosity, depend on the properties and proportions of the individual component gases (nitrogen and oxygen in air)
• Each component gas in a mixture behaves independently and exerts its own partial pressure, contributing to the total pressure of the mixture (oxygen and carbon dioxide in exhaled breath)

Classification of gas mixtures

• Gas mixtures can be classified as homogeneous, having a uniform composition throughout (well-mixed air in a room), or heterogeneous, where the composition varies with position (stratified layers of gases in the atmosphere)

Dalton's Law for gas mixtures

Statement and mathematical expression of Dalton's Law

• Dalton's Law states that the total pressure of a gas mixture equals the sum of the partial pressures of the individual component gases
• Mathematically, Dalton's Law is expressed as $P_{total} = P_1 + P_2 + ... + P_n$, where $P_{total}$ is the total pressure of the mixture and $P_1$, $P_2$, ..., $P_n$ are the partial pressures of the component gases
• The partial pressure of each component gas is the pressure it would exert if it occupied the entire volume of the mixture alone at the same temperature (nitrogen partial pressure in air at sea level is about 0.78 atm)

Assumptions and limitations of Dalton's Law

• Dalton's Law assumes that the gases in the mixture are ideal and do not interact with each other
• Deviations from Dalton's Law can occur in real gas mixtures due to intermolecular forces and non-ideal behavior (high-pressure gas mixtures in industrial processes)
• The mole fraction of a component gas is the ratio of the number of moles of that gas to the total number of moles in the mixture
• The partial pressure of a component gas can be calculated by multiplying its mole fraction by the total pressure of the mixture ($P_i = y_i \times P_{total}$, where $P_i$ is the partial pressure of component $i$ and $y_i$ is its mole fraction)

Composition and partial pressures of gas mixtures

Determining composition using mole, mass, and volume fractions

• Mole fraction ($y_i$) is the ratio of the number of moles of a component gas ($n_i$) to the total number of moles in the mixture ($n_{total}$), expressed as $y_i = \frac{n_i}{n_{total}}$
• Mass fraction ($w_i$) is the ratio of the mass of a component gas ($m_i$) to the total mass of the mixture ($m_{total}$), expressed as $w_i = \frac{m_i}{m_{total}}$
• Volume fraction ($v_i$) is the ratio of the volume of a component gas ($V_i$) to the total volume of the mixture ($V_{total}$), expressed as $v_i = \frac{V_i}{V_{total}}$

Calculating partial pressures using mole fractions and total pressure

• The partial pressure of a component gas ($P_i$) can be calculated using its mole fraction ($y_i$) and the total pressure of the mixture ($P_{total}$), expressed as $P_i = y_i \times P_{total}$
• The partial pressures of the component gases can be used to determine the composition of the gas mixture and analyze its properties (partial pressure of water vapor in humid air affects comfort and air conditioning requirements)

Ideal vs real gas mixtures

Characteristics of ideal gas mixtures

• Ideal gas mixtures follow the assumptions of the ideal gas law, where the molecules are considered as non-interacting point particles with negligible volume
• In ideal gas mixtures, the properties of the mixture can be accurately predicted using Dalton's Law and the ideal gas equation ($PV = nRT$)
• Ideal gas mixtures exhibit no intermolecular forces and have zero volume occupied by the gas molecules (helium-neon mixture at low pressure and high temperature)

Deviations from ideal behavior in real gas mixtures

• Real gas mixtures deviate from ideal behavior due to intermolecular forces, such as van der Waals forces, and the finite volume occupied by the gas molecules
• The deviations from ideal behavior become more significant at high pressures and low temperatures, where the intermolecular forces and molecular size effects are more pronounced (natural gas mixtures in pipelines)
• Equations of state, such as the van der Waals equation and the Redlich-Kwong equation, describe the behavior of real gas mixtures by accounting for the non-ideal effects

Compressibility factor for real gas mixtures

• The compressibility factor ($Z$) quantifies the deviation of a real gas mixture from ideal behavior, expressed as $Z = \frac{PV}{nRT}$, where $Z = 1$ for an ideal gas and $Z \neq 1$ for a real gas
• The compressibility factor varies with pressure and temperature and can be used to correct the ideal gas equation for real gas mixtures (Z-factor charts for natural gas mixtures)