Gas Mixtures and Dalton's Law of Partial Pressures

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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

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIterated Integrals and Fubini's TheoremDouble Integrals in Cartesian CoordinatesDouble Integrals over Rectangular RegionsDouble Integrals in Polar CoordinatesDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsCenter of MassConservation of Linear MomentumElastic CollisionsInelastic CollisionsCoefficient of RestitutionCollision Analysis and Real-World ApplicationsTwo-Body Collisions in the Center-of-Mass FrameReduced Mass and Two-Body ProblemsKinematics in Two DimensionsProjectile MotionCircular Motion: KinematicsRotational KinematicsTorqueMoment of InertiaRotational Kinetic EnergyThe Work-Energy TheoremConservation of Mechanical EnergyFirst Law of ThermodynamicsThermodynamic Systems and System BoundariesGas Mixtures and Dalton's Law of Partial Pressures

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