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Partial Pressure Calculator

Chemistry

Calculate partial pressure of gas components using Dalton's law: P_i = x_i × P_total. Supports up to 4 gas components with mole fraction shown.

Reviewed by the thecalcu.com team · Last updated October 20, 2024

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Partial Pressure Gas 1 (atm)

0.5
Partial Pressure Gas 2 (atm)
0.5
Partial Pressure Gas 3 (atm)
0
Partial Pressure Gas 4 (atm)
0
Mole Fraction Gas 1
0.5

Breakdown

How the total splits

Partial Pressure Gas 1 (atm)
0.5
Partial Pressure Gas 2 (atm)
0.5
Partial Pressure Gas 3 (atm)
0
Partial Pressure Gas 4 (atm)
0

This calculator computes your Partial Pressure Gas 1 (atm), Partial Pressure Gas 2 (atm), Partial Pressure Gas 3 (atm), Partial Pressure Gas 4 (atm), Mole Fraction Gas 1 from the values you enter.

Inputs
Total Pressure (atm)Moles of Gas 1Moles of Gas 2Moles of Gas 3 (optional)Moles of Gas 4 (optional)
Outputs
Partial Pressure Gas 1 (atm)Partial Pressure Gas 2 (atm)Partial Pressure Gas 3 (atm)Partial Pressure Gas 4 (atm)Mole Fraction Gas 1

What is a Partial Pressure?

The Partial Pressure Calculator computes the partial pressure of each component in a gas mixture using Dalton's law: P_i = x_i × P_total, where x_i = n_i / n_total is the mole fraction of component i. Enter the total pressure (in atm) and the number of moles of up to four gas components to get the partial pressure of each gas and the mole fraction of the first component.

Dalton's law of partial pressures, that each gas in a mixture exerts pressure independently and the total pressure is the sum of partial pressures, is a foundational result of the kinetic theory of ideal gases. It is used across gas stoichiometry (equilibrium constant Kp calculations), atmospheric science (oxygen partial pressure at altitude), physiology (alveolar gas exchange), industrial gas processes, and analytical chemistry.

Partial pressure links directly to the equilibrium constant Kp (see Kp Calculator), which is expressed in terms of equilibrium partial pressures of reacting gases. It also links to Raoult's law (see Raoult's Law Calculator), which gives the partial pressure of each liquid component above an ideal solution.

Why Use a Partial Pressure Calculator?

The mole fraction calculation is multi-step: sum all moles, divide each component by the total, then multiply by total pressure. For four-component mixtures, tracking four mole fractions simultaneously while verifying they sum to 1 is error-prone. This calculator does it in one step for all components.

For NCERT Class 11 Chapter 5 (States of Matter) and JEE problems, partial pressure calculations frequently appear as part of gas stoichiometry: after a reaction, finding the partial pressures of products and reactants at equilibrium requires computing mole fractions from the equilibrium mole amounts.

Who Should Use This Calculator?

Chemistry students at Class 11 (NCERT, States of Matter chapter) and JEE preparation level computing partial pressures in gas law and equilibrium problems.

Atmospheric scientists and meteorologists computing partial pressures of atmospheric components (O₂, N₂, CO₂, H₂O vapour) at different altitudes and humidity conditions.

Physiologists and respiratory scientists calculating alveolar oxygen and carbon dioxide partial pressures for gas exchange analysis, altitude physiology, and anaesthesiology.

Chemical engineers designing gas separation processes (pressure swing adsorption, membrane separation) where partial pressure drives is the fundamental driving force for separation.

Scuba diving instructors and hyperbaric medicine specialists computing gas partial pressures at depth to assess oxygen toxicity and nitrogen narcosis risks.

What Insights Does the Partial Pressure Calculator Give You?

Partial Pressure Gas 1 (atm) is the primary highlighted output, the pressure that gas 1 contributes to the total mixture pressure. This is the quantity used in Kp expressions and Henry's law (which relates partial pressure to dissolved gas concentration).

Partial Pressures Gas 2, 3, 4 (atm) complete the picture for all components. The four partial pressures sum to the total pressure.

Mole Fraction Gas 1 is the proportion of gas 1 in the mixture by moles, the fundamental compositional variable. Mole fractions are dimensionless and always sum to 1 for all components combined.

How to use this Partial Pressure calculator

  1. Enter the Total Pressure of the gas mixture in atm.
  2. Enter Moles of Gas 1 and Moles of Gas 2, the required components.
  3. Enter Moles of Gas 3 and Moles of Gas 4 if present, or leave at 0 for a simpler mixture.
  4. Read Partial Pressure Gas 1 (atm) as the highlighted primary result.
  5. Note the Mole Fraction Gas 1 for use in Raoult's law, Kp expressions, or Henry's law calculations.
Show formula & methodology ↓Show less ↑

Formula & Methodology

Dalton's law of partial pressures:

P_i = x_i × P_total  x_i = n_i / n_total     (mole fraction) n_total = n₁ + n₂ + n₃ + n₄ Σ P_i = P_total          (verification)

Worked example, alveolar gas mixture at sea level:

Gas mixture: N₂ (78.09%), O₂ (20.95%), CO₂ (0.04%), H₂O vapour (0.92%) by mole fraction at 760 mmHg. Use mole fractions directly as effective "moles" relative to 100:

n_N₂ = 78.09, n_O₂ = 20.95, n_CO₂ = 0.04, n_H₂O = 0.92 n_total = 100  P(N₂) = 78.09/100 × 760 = 593.5 mmHg = 0.781 atm P(O₂) = 20.95/100 × 760 = 159.2 mmHg = 0.209 atm P(CO₂) = 0.04/100 × 760 = 0.30 mmHg ≈ 0.0004 atm P(H₂O) = 0.92/100 × 760 = 7.0 mmHg = 0.009 atm

For inspired air in the lungs at body temperature (37°C), water vapour saturates at 47.1 mmHg, giving actual inspired PO₂ = (760 − 47.1) × 0.2095 = 149.3 mmHg, the quantity used in the alveolar gas equation for respiratory physiology.

Frequently Asked Questions

What is partial pressure?
The partial pressure of a gas in a mixture is the pressure that gas would exert if it alone occupied the entire volume of the mixture at the same temperature. It is proportional to the mole fraction of that gas: P_i = x_i × P_total, where x_i = n_i / n_total. The sum of all partial pressures equals the total pressure, this is Dalton's law of partial pressures.
What is Dalton's law of partial pressures?
Dalton's law states that the total pressure of a mixture of non-reacting ideal gases equals the sum of the partial pressures of the individual gases: P_total = P₁ + P₂ + P₃ + ... Each gas exerts pressure independently, as if the other gases were not present. Dalton's law holds well at low to moderate pressures where gases behave ideally. At high pressures where intermolecular interactions are significant, real gas deviations become important.
How do I calculate partial pressure from mole fractions?
Partial pressure = mole fraction × total pressure. Mole fraction of gas i = (moles of i) / (total moles of all gases). Example: a mixture of 2 mol N₂ and 3 mol O₂ at 1 atm total pressure. Mole fraction N₂ = 2/5 = 0.4; P(N₂) = 0.4 × 1 atm = 0.4 atm. Mole fraction O₂ = 3/5 = 0.6; P(O₂) = 0.6 × 1 atm = 0.6 atm. Sum = 0.4 + 0.6 = 1.0 atm. ✓
What are the partial pressures of gases in air?
Dry air at sea level (total pressure 760 mmHg) has approximately: N₂ = 78.09% → P = 593.5 mmHg; O₂ = 20.95% → P = 159.2 mmHg; Ar = 0.93% → P = 7.1 mmHg; CO₂ = 0.04% → P = 0.3 mmHg. In humid air, water vapour occupies part of the total pressure (e.g., at 37°C, water vapour pressure = 47.1 mmHg), so oxygen partial pressure in the lungs at sea level is approximately (760 − 47.1) × 0.209 = 149 mmHg, the physiological PO₂ driving oxygen uptake.
How do I use the Partial Pressure Calculator?
Enter the total pressure of the gas mixture in atm, then enter the number of moles of each gas component (1 to 4 components). The calculator computes the mole fraction of each gas and multiplies by the total pressure to give the partial pressure in atm. For Gas 3 and Gas 4, enter 0 if there are fewer than 4 components.
What is the partial pressure of oxygen at altitude and why does it matter?
As altitude increases, total atmospheric pressure decreases, and so does the partial pressure of oxygen (pO₂) even though the mole fraction of O₂ in air remains constant at 20.95%. At sea level: pO₂ = 0.2095 × 760 = 159 mmHg. At 3,500 m (Leh): pO₂ = 0.2095 × 490 = 103 mmHg, 35% lower. At 8,849 m (Everest summit): pO₂ = 0.2095 × 253 = 53 mmHg, only 33% of sea level. This low pO₂ causes altitude sickness, hypoxia, and requires supplemental oxygen above approximately 7,000 m.
How does partial pressure apply to anaesthesiology?
Anaesthetic gases are administered in known partial pressures, not volumes. The minimum alveolar concentration (MAC) of an anaesthetic like isoflurane is 1.15% of 1 atm = 8.74 mmHg, the partial pressure that prevents movement in 50% of patients. Nitrous oxide (N₂O) is commonly used at 50% (380 mmHg partial pressure) mixed with oxygen. The ratio of partial pressure to pure vapour pressure gives the fraction of saturation, used to calculate depth of anaesthesia. Indian anaesthesiologists at sea level and high-altitude hospitals calculate partial pressures identically, but high-altitude conditions require higher flow rates to achieve the same MAC.
What is the relationship between partial pressure and Kp?
The equilibrium constant Kp for a gas-phase reaction is expressed in terms of partial pressures (in atm or bar) of reactants and products at equilibrium: Kp = ΠP_products^n / ΠP_reactants^m. The partial pressures used in Kp are calculated exactly as in this calculator, mole fraction × total pressure for each gas component. The [Kp Calculator](/kp-calculator/) computes Kp from partial pressures, and the [Equilibrium Constant Calculator](/equilibrium-constant-calculator/) relates Kp to Kc via the equation Kp = Kc(RT)^Δn.
How is partial pressure used in scuba diving safety?
Scuba divers breathe compressed air at elevated pressure (approximately 1 atm per 10 m of depth, so at 30 m = 4 atm total). The partial pressure of oxygen at 30 m = 0.21 × 4 = 0.84 atm, still safe. The partial pressure of nitrogen at 30 m = 0.79 × 4 = 3.16 atm, causes nitrogen narcosis above approximately 2.5 atm pN₂ (30 m depth). Beyond 60 m, pO₂ = 0.21 × 7 = 1.47 atm → oxygen toxicity. Deep diving uses helium-oxygen (heliox) mixtures to control partial pressures of both oxygen and nitrogen.