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Gas Mixtures and Dalton's Law of Partial Pressures

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Thermodynamic Systems and System Boundaries→→Gas Mixture Thermodynamics and Dalton's LawMultistage Compressor Design and Intercooling+1 more
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Core Idea

Dalton's law states total pressure of a non-reacting gas mixture equals the sum of partial pressures (pressure each gas would exert alone). Component properties (enthalpy, entropy) are calculated separately and summed by mass fraction; mixing is ideal when component interactions are negligible. This framework enables analysis of air as a mixture (79% N₂, 21% O₂) and combustion products as mixtures of CO₂, H₂O, O₂, N₂.

Explainer

From your study of thermodynamic systems, you're comfortable analyzing pure substances — a single-component fluid with well-defined properties. Real gases are almost always mixtures: air is nitrogen and oxygen (plus trace argon and CO₂), exhaust gas contains CO₂, H₂O, O₂, and N₂ in varying proportions, and natural gas is methane plus ethane plus impurities. To apply thermodynamics to these mixtures, you need a framework for connecting the mixture's macroscopic properties to the individual components' properties.

Dalton's model of ideal gas mixtures starts with the simplest possible assumption: each gas in the mixture behaves as if it were alone in the entire volume. The partial pressure of component i is the pressure it would exert if it alone occupied the container at the mixture temperature: P_i = y_i · P_total, where y_i = n_i/n_total is the mole fraction of component i. Dalton's law then states P_total = ΣP_i, which is automatically satisfied by this definition. Mole fractions are additive and sum to 1: Σy_i = 1. For dry air, y_N₂ ≈ 0.79 and y_O₂ ≈ 0.21, so at standard atmospheric pressure, P_N₂ ≈ 79.6 kPa and P_O₂ ≈ 21.2 kPa.

Mixture thermodynamic properties follow from the same logic. The enthalpy of an ideal gas mixture is H_mix = Σ(n_i · h_i), where each h_i is the molar enthalpy of component i at the mixture temperature (and its partial pressure, though for ideal gases enthalpy is pressure-independent). On a mass basis, h_mix = Σ(m_f_i · h_i), where m_f_i is the mass fraction. Entropy is slightly more complex: the entropy of a mixture is not simply the sum of component entropies at the mixture temperature — there is an entropy of mixing term that accounts for the irreversibility of mixing distinguishable gases. For ideal mixtures, Δs_mix = −R Σ(y_i ln y_i) per mole, which is always positive, reflecting the irreversibility of mixing.

The practical payoff is that you can analyze air as a mixture with known composition, use ideal gas property tables for N₂ and O₂ separately, and combine the results. When you compute combustion products from burning methane in air, the exhaust stream contains known mole fractions of CO₂, H₂O, O₂ (excess), and N₂ — all calculable from stoichiometry. Each component's contribution to total enthalpy and entropy is computed independently and summed. This separability is what makes mixture analysis tractable: instead of needing a new set of tables for every possible mixture, you reuse the pure-component tables you already have.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Center of Mass → Conservation of Linear Momentum → Elastic Collisions → Inelastic Collisions → Coefficient of Restitution → Collision Analysis and Real-World Applications → Two-Body Collisions in the Center-of-Mass Frame → Reduced Mass and Two-Body Problems → Kinematics in Two Dimensions → Projectile Motion → Circular Motion: Kinematics → Rotational Kinematics → Torque → Moment of Inertia → Rotational Kinetic Energy → The Work-Energy Theorem → Conservation of Mechanical Energy → First Law of Thermodynamics → Thermodynamic Systems and System Boundaries → Gas Mixtures and Dalton's Law of Partial Pressures

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