KEVOS® MAKEOS · Pneumatics
Gas Mixture Properties (Dalton: Molar Mass, Gas Constant, Specific Heats, Density, Partial Pressures, Mixing Entropy)
For a mixture of up to three perfect gases, what are its molar mass, gas constant, specific heats, ratio of specific heats, density, speed of sound and partial pressures, how much work does separating it take, and is one component’s partial pressure inside my limit?
Properties of a mixture of up to three perfect gases from their molar masses, specific heats and mole fractions: the mixture molar mass and mass fractions, gas constant, specific heats and their ratio, density and speed of sound at the pressure and temperature entered, each component’s partial pressure by Dalton’s law, the entropy of mixing and the least work to separate the mixture into its pure gases, and a check of one component’s partial pressure against a maximum or minimum you set.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Gas 1 | ||
| Molar mass of gas 1 | kg/kmol | Molar mass of the first gas, from its chemical formula or a property table. |
| Specific heat of gas 1 at constant pressure | kJ/(kg·K) | Specific heat of the first gas at constant pressure per kilogram at the mixture temperature, from property tables. |
| Mole fraction of gas 1 | % | Share of the first gas by moles (equal to its share by volume for perfect gases), from the gas specification or analysis. |
| Gas 2 | ||
| Molar mass of gas 2 | kg/kmol | Molar mass of the second gas. |
| Specific heat of gas 2 at constant pressure | kJ/(kg·K) | Specific heat of the second gas at constant pressure per kilogram. |
| Mole fraction of gas 2 | % | Share of the second gas by moles; gas 3 makes up the rest to 100 %. |
| Gas 3 (the rest of the mixture) | ||
| Molar mass of gas 3 | kg/kmol | Molar mass of the third gas, which makes up the rest of the mixture. |
| Specific heat of gas 3 at constant pressure | kJ/(kg·K) | Specific heat of the third gas at constant pressure per kilogram. |
| Condition and check | ||
| Mixture pressure | kPa abs | Total absolute pressure of the mixture. |
| Mixture temperature | °C | Temperature of the mixture. |
| Component to check | choice | Which gas’s partial pressure is checked against your limit. |
| Kind of limit | choice | Whether your limit is a maximum (the gas must stay below it) or a minimum (the gas must stay above it). |
| Partial pressure limit | kPa | Your partial pressure limit for that gas, from the process specification, an exposure standard or a corrosion criterion. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
Gas 1
What this means: Molar mass of gas 1
- What it is
- The mass of one kilomole of the first gas, from its chemical formula. Molar masses weighted by mole fraction give the mixture molar mass, and with the universal gas constant the mixture gas constant.
- Units and format
- Enter a number in kg/kmol: kg/kmol. The form accepts 1 kg/kmol to 1000 kg/kmol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 39.948 kg/kmol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A heavier gas raises the mixture molar mass and density and lowers the mixture gas constant.
- Get it right
- Argon is 39.948, carbon dioxide 44.01 and nitrogen 28.014 kg/kmol; do not use a molecular weight in grams for one molecule.
What this means: Specific heat of gas 1 at constant pressure
- What it is
- The heat needed to warm one kilogram of the first gas by one kelvin at constant pressure, at the mixture temperature. Specific heats per kilogram are averaged by mass fraction.
- Units and format
- Enter a number in kJ/(kg·K): kilojoules per kilogram per kelvin. The form accepts 0.01 kJ/(kg·K) to 100 kJ/(kg·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5203 kJ/(kg·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the mixture c_p and so lowers γ when this gas has a large share.
- Get it right
- Use the per-kilogram value: a molar value in kJ/(kmol·K) must be divided by the molar mass.
What this means: Mole fraction of gas 1
- What it is
- The share of the first gas by number of molecules, which for perfect gases equals its share by volume. Gases 1 and 2 together must not exceed 100 %; gas 3 makes up the rest.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 82% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes every mixture property and the partial pressure of gas 1, which equals this share of the total pressure.
- Get it right
- Gas specifications are usually by volume (mole) percent; convert a mass percentage before entering it.
Gas 2
What this means: Molar mass of gas 2
- What it is
- The mass of one kilomole of the second gas, from its chemical formula. It is weighted by the second gas’s mole fraction in the mixture molar mass.
- Units and format
- Enter a number in kg/kmol: kg/kmol. The form accepts 1 kg/kmol to 1000 kg/kmol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 44.01 kg/kmol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A heavier second gas raises the mixture density and lowers the gas constant.
- Get it right
- Check the formula: carbon dioxide (44.01) and carbon monoxide (28.01) are easily confused.
What this means: Specific heat of gas 2 at constant pressure
- What it is
- The heat needed to warm one kilogram of the second gas by one kelvin at constant pressure, at the mixture temperature, averaged into the mixture by mass fraction.
- Units and format
- Enter a number in kJ/(kg·K): kilojoules per kilogram per kelvin. The form accepts 0.01 kJ/(kg·K) to 100 kJ/(kg·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.846 kJ/(kg·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the mixture c_p in proportion to the second gas’s mass fraction.
- Get it right
- Take it at the mixture temperature; for carbon dioxide it changes markedly between room temperature and a few hundred degrees.
What this means: Mole fraction of gas 2
- What it is
- The share of the second gas by number of molecules, equal to its share by volume for perfect gases. Gas 3 takes whatever share of 100 % is left after gases 1 and 2.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes every mixture property and the partial pressure of gas 2.
- Get it right
- If the mixture has only two gases, enter 100 % minus gas 1 here so that gas 3 is zero.
Gas 3 (the rest of the mixture)
What this means: Molar mass of gas 3
- What it is
- The mass of one kilomole of the third gas, which fills the rest of the mixture after gases 1 and 2. It has no effect when their shares add up to 100 %.
- Units and format
- Enter a number in kg/kmol: kg/kmol. The form accepts 1 kg/kmol to 1000 kg/kmol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 28.014 kg/kmol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Matters only in proportion to the third gas’s share of the mixture.
- Get it right
- Leave any value when there is no third gas; with a zero share it does not change the result.
What this means: Specific heat of gas 3 at constant pressure
- What it is
- The heat needed to warm one kilogram of the third gas by one kelvin at constant pressure, used in proportion to its mass fraction in the mixture.
- Units and format
- Enter a number in kJ/(kg·K): kilojoules per kilogram per kelvin. The form accepts 0.01 kJ/(kg·K) to 100 kJ/(kg·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.04 kJ/(kg·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Matters only in proportion to the third gas’s mass fraction.
- Get it right
- For air as a single component use about 1.005 kJ/(kg·K) near room temperature.
Condition and check
What this means: Mixture pressure
- What it is
- The total absolute pressure of the mixture. Each gas’s partial pressure is its mole fraction times this pressure (Dalton’s law), and the density is proportional to it.
- Units and format
- Enter a number in kPa abs: kPa abs. The form accepts 0.001 kPa abs to 100000 kPa abs. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 101.325 kPa abs as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Partial pressures and density rise in proportion; γ, the gas constant and the mixing entropy do not change.
- Get it right
- Add atmospheric pressure to a gauge reading; a cylinder regulator outlet at 2 bar gauge is about 301 kPa absolute.
What this means: Mixture temperature
- What it is
- The temperature of the mixture, converted to kelvin. It sets the density and speed of sound, and the least separation work, which is the absolute temperature times the entropy of mixing.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -270 °C to 3000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher temperature lowers the density and raises the speed of sound and the least separation work.
- Get it right
- Enter the specific heats for this temperature too; they are not adjusted automatically.
What this means: Component to check
- What it is
- Which of the three gases has its partial pressure checked against the limit below, for example an active gas in a shielding blend or oxygen in a breathing or inerting mixture.
- Units and format
- Choose one of 3 options from the list: Gas 1; Gas 2; Gas 3.
- Example
- The form opens with “Gas 2” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Selects which partial pressure is compared with the limit; the mixture properties do not change.
- Get it right
- Check the numbering: gas 3 is the remainder after gases 1 and 2.
What this means: Kind of limit
- What it is
- Whether the limit is a ceiling the partial pressure must stay under, such as a toxic or corrosive component, or a floor it must stay above, such as oxygen needed for breathing or combustion.
- Units and format
- Choose one of 2 options from the list: Maximum partial pressure; Minimum partial pressure.
- Example
- The form opens with “Maximum partial pressure” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Reverses the direction of the pass and fail test.
- Get it right
- Oxygen for breathing is a minimum; an inerting atmosphere sets a maximum oxygen level.
What this means: Partial pressure limit
- What it is
- The partial pressure, in kilopascals, that the chosen gas must stay under or above, from your process specification, an exposure standard or a corrosion criterion.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 0 kPa to 100000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moves the pass and fail line only; the calculated properties do not change.
- Get it right
- A limit given as a volume percentage at atmospheric pressure converts to kPa by multiplying by 1.01325.
Method and formulas
- Gas 3 mole fraction y₃ = 100 % − y₁ − y₂; molar mass M = Σ yᵢ Mᵢ and mass fractions xᵢ = yᵢ Mᵢ ÷ M.
- Gas constant R = R̄ ÷ M, equal to Σ xᵢ Rᵢ (Bryan §124, equation (166)); c_p = Σ xᵢ c_p,ᵢ and c_v = c_p − R (Bryan §124, equations (168)–(169), and §121, c_p − c_v = R); γ = c_p ÷ c_v.
- Dalton’s law: each partial pressure pᵢ = yᵢ p (Bryan §124); density ρ = p ÷ (R T); speed of sound a = √(γ R T) (Bryan §121).
- Entropy of mixing per kilogram Δs = −R Σ yᵢ ln yᵢ, the constant C of Bryan §127 equation (179); the least work to separate the mixture into its pure gases at T is T Δs (Bryan §§126–128).
- Example: 82 % argon and 18 % carbon dioxide at 101.325 kPa and 20 °C has M = 40.68 kg/kmol, R = 0.2044 kJ/(kg·K), γ = 1.539, ρ = 1.691 kg/m³ and a CO₂ partial pressure of 18.24 kPa.
Limitations
- Perfect gases with constant specific heats: at high pressure, low temperature or near condensation of a component use real-gas data.
- The least separation work is for complete separation into pure gases; a process taking out one product at partial recovery has a different (smaller) minimum.
- Specific heats must be entered for the mixture temperature; they are not looked up.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find γ, R and density of a shielding, process or fuel gas blend for flow and compressor calculations
- Check a component’s partial pressure against a process, exposure or corrosion limit
- Estimate the least work any separation (membrane, PSA) can take
Who it is for
- Process and pneumatic engineers
- Welding and fabrication engineers
- Gas system designers
What you get
- Molar mass and mass fractions
- Gas constant, c_p, c_v and γ
- Density and speed of sound
- Partial pressures
- Entropy of mixing and least separation work
- Verdict on the partial pressure limit
Interpreting the result
- Mixing a monatomic gas such as argon with a polyatomic one lowers γ from 1.67 towards the polyatomic value, which changes nozzle and compressor behaviour.
- The separation work is the reason gas separation always needs energy input; a real membrane or PSA unit uses much more than this minimum.
Before relying on the result
- Confirm the mixture analysis from the gas supplier’s certificate before using a partial pressure for a safety decision.
References
- Bryan G. H., Thermodynamics: An Introductory Treatise Dealing Mainly with First Principles and Their Direct Applications (B. G. Teubner, Leipzig, 1907), Chapter XII §§121, 124–128 (specific heats and adiabatics of perfect gases; gas mixtures, Dalton’s law, gain of entropy and loss of available energy by diffusion), pp. 119, 121–126. Public-domain source; the method is restated in original words and no text, tables or figures are reproduced.
- Çengel Y. A. and Boles M. A., Thermodynamics: An Engineering Approach (McGraw-Hill): gas mixtures, Dalton’s law and properties of ideal-gas mixtures.
- NIST Chemistry WebBook, https://webbook.nist.gov/chemistry/: molar masses and specific heats of the component gases.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · KEVOS® original book
Shielding and purging gases
In Industrial Gases by the Numbers
What it covers: Compare argon, helium, carbon dioxide and their mixtures, find where a workshop's shielding gas really goes, and calculate how long a pipe purge takes.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.