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Partial Pressure Calculator

Q: What is Dalton's Law of Partial Pressures?

Dalton's Law of Partial Pressures states that the total pressure of a gas mixture equals the sum of the partial pressures of all component gases: P_total = P1 + P2 + P3 + ... + P?. This law, formulated by John Dalton in 1801, assumes ideal gas behavior where gas molecules do not interact with each other. It is foundational to understanding gas mixtures in chemistry, physiology, and engineering.

Q: How do you calculate partial pressure from mole fraction?

Use the formula P_A = ?_A × P_total, where ?_A is the mole fraction of gas A and P_total is the total pressure of the mixture. The mole fraction is ?_A = n_A / n_total, where n_A is the moles of gas A and n_total is the total moles of all gases. Example: if ?_N2 = 0.78 and P_total = 1 atm, then P_N2 = 0.78 × 1 = 0.78 atm.

Q: How do you find total pressure from partial pressures?

Add all the partial pressures together using Dalton's Law: P_total = P1 + P2 + P3 + ... + P?. Make sure all partial pressures are in the same units before adding. Example: if P_N2 = 0.78 atm, P_O2 = 0.21 atm, and P_Ar = 0.01 atm, then P_total = 0.78 + 0.21 + 0.01 = 1.00 atm.

Q: What is the formula for partial pressure?

There are three main partial pressure formulas: (1) From Dalton's Law: P_i = P_total - (sum of all other partial pressures); (2) From mole fraction: P_A = ?_A × P_total where ?_A = n_A / n_total; (3) From the ideal gas law: P_A = n_A × R × T / V, where R = 0.08206 L·atm/(mol·K), T is in Kelvin, and V is in litres.

Q: How do you find partial pressure from moles?

Step 1: Find moles of each gas (convert from grams if needed: n = mass ÷ molar mass). Step 2: Sum all moles to get n_total. Step 3: Calculate mole fraction: ?_A = n_A / n_total. Step 4: Multiply by total pressure: P_A = ?_A × P_total. Example: 3 mol N2 and 1 mol O2 at P_total = 4 atm ? ?_N2 = 3/4 = 0.75 ? P_N2 = 0.75 × 4 = 3 atm.

Q: What is the partial pressure of oxygen in air?

The partial pressure of oxygen in dry air at sea level is approximately 0.2095 atm, or 21.22 kPa, or 159.2 mmHg. This is calculated from oxygen's mole fraction in dry air (0.2095) multiplied by standard atmospheric pressure (1 atm = 101.325 kPa). In the lungs, the partial pressure of oxygen is lower (about 13.3 kPa) due to water vapor and carbon dioxide.

Q: How does partial pressure relate to the ideal gas law?

Each gas in a mixture independently obeys the ideal gas law: P_A × V = n_A × R × T, so P_A = n_A RT/V. This means you can calculate the partial pressure of any gas if you know its moles, the container volume, and the temperature. The total pressure is the sum of all individual gas pressures, consistent with Dalton's Law.

Q: What are the units of partial pressure?

Partial pressure uses the same units as total pressure: atmospheres (atm), kilopascals (kPa), pascals (Pa), millimetres of mercury (mmHg or torr), bar, and pounds per square inch (psi). Standard conversions: 1 atm = 101.325 kPa = 760 mmHg = 1.01325 bar = 14.696 psi = 101,325 Pa.

Q: How do you convert between pressure units?

Key conversion factors from 1 atm: 1 atm = 101.325 kPa = 101,325 Pa = 760 mmHg = 760 torr = 1.01325 bar = 14.696 psi. To convert any pressure to atm first, then multiply by the target unit factor. Example: 500 mmHg ÷ 760 = 0.6579 atm; 0.6579 × 101.325 = 66.67 kPa.

This partial pressure calculator finds partial pressure using Dalton's Law, mole fractions, and the ideal gas law. Learn how to find partial pressure for gas mixtures with multiple components — results shown instantly in atm, kPa, mmHg, bar, and all common pressure units.

∑ Dalton's Law — Total Pressure Calculator

P_total = P₁ + P₂ + P₃ + … + P_n

Add the partial pressure of each gas component to find the total pressure

Enter the name and partial pressure of each gas. All pressures are converted to the same unit before summing.

χ Partial Pressure from Mole Fraction — P_A = χ_A × P_total

P_A = χ_A × P_total = (n_A / n_total) × P_total

Mole fraction χ is dimensionless — always between 0 and 1

Mole Fraction χ_A

χ format

Total Pressure P_total

Unit

🌡 Partial Pressure from Ideal Gas Law — P_A = n_ART/V

P_A = n_A × R × T / V

R = 0.082057 L·atm/(mol·K) | Temperature must be in Kelvin

Moles of gas n_A (mol)

Volume V

Volume unit

Temperature unit

Temperature T

🧪 Gas Mixture Partial Pressure Calculator

Enter each gas component. Common gas molar masses are auto-filled when you type the gas name (e.g. "O2", "N2", "CO2"). P_A = χ_A × P_total

Total Pressure P_total

Unit

What is Partial Pressure? — Dalton's Law of Partial Pressures

Partial pressure is the pressure that a single gas in a mixture would exert if it alone occupied the entire volume of the container at the same temperature. It represents that individual gas's contribution to the total pressure of the mixture. John Dalton formulated his Law of Partial Pressures in 1801: the total pressure of a gas mixture is the sum of the partial pressures of all component gases.

P_total = P₁ + P₂ + P₃ + … + P_n

Dalton's Law of Partial Pressures

P_i = χ_i × P_total

Mole fraction χ_i = n_i / n_total (dimensionless, always between 0 and 1, sum of all = 1)

This law assumes ideal gas behaviour — gas molecules do not interact with one another and occupy negligible volume themselves. In practice it is highly accurate for most gases under ordinary conditions.

Real-World Example: Atmospheric Air at Sea Level

N2 contributes ~78% → P_N2 ≈ 0.7808 atm
O2 contributes ~21% → P_O2 ≈ 0.2095 atm
Ar contributes ~1% → P_Ar ≈ 0.00934 atm
P_total = 0.7808 + 0.2095 + 0.00934 ≈ 1.000 atm ✓

Applications of Dalton's Law

Scuba diving: partial pressure of O2 and N2 increase with depth; narcosis and oxygen toxicity depend on their partial pressures.
Respiratory physiology: partial pressure of O2 in alveoli drives gas exchange across the lung membrane.
Industrial gas: storage and handling of gas mixtures require calculating individual partial pressures for safety limits.
Anesthesiology: anesthetic gases exert their effect proportional to their partial pressure in the blood.

Partial Pressure Formula — Mole Fraction Method

The mole fraction method is the most common way to calculate partial pressure in chemistry. It directly connects the amount of each gas to the pressure it exerts. P_A = χ_A × P_total

χ_A = n_A / n_total

Mole fraction of gas A — dimensionless, between 0 and 1

P_A = χ_A × P_total

Partial pressure from mole fraction

P_A = (n_A / n_total) × P_total

Combined formula — substituting mole fraction definition

Key properties of mole fraction: it is dimensionless (no units), always between 0 and 1, and the sum of all mole fractions in a mixture exactly equals 1: Σχ_i = 1. For ideal gases at the same T and P, mole fraction equals volume fraction and pressure fraction. Mole% = χ × 100%.

Example — Dry air: N2 mole fraction = 0.7809 = 78.09 mol%. At 1 atm: P_N2 = χ_N2 × P_total = 0.7809 × 1 atm = 0.7809 atm = 79.12 kPa.

How to Find Partial Pressure — Step by Step

There are three main methods for how to find partial pressure. The correct method depends on what information you are given.

Method 1: From Known Partial Pressures (Dalton's Law) — P_total = P₁ + P₂ + P₃

List all partial pressures in the same units.
Add them: P_total = P₁ + P₂ + … + P_n.
Unknown partial pressure = P_total − (sum of all known partial pressures).

Method 2: From Moles and Total Pressure

Find moles of each gas.
n_total = Σn_i.
χ_A = n_A / n_total.
P_A = χ_A × P_total.

Method 3: From Ideal Gas Law

Note n_A (mol), V (L), T (K).
P_A = n_A × R × T / V.
Use R = 0.082057 L·atm/(mol·K).

Worked Example — Air Composition: 3.12 mol N2, 0.84 mol O2, 0.04 mol Ar, P_total = 4.00 atm

n_total = 3.12 + 0.84 + 0.04 = 4.00 mol
χ_N2 = 3.12 / 4.00 = 0.780 → P_N2 = 0.780 × 4.00 = 3.120 atm
χ_O2 = 0.84 / 4.00 = 0.210 → P_O2 = 0.210 × 4.00 = 0.840 atm
χ_Ar = 0.04 / 4.00 = 0.010 → P_Ar = 0.010 × 4.00 = 0.040 atm
Check: 3.120 + 0.840 + 0.040 = 4.000 atm ✓ | χ sum: 0.780 + 0.210 + 0.010 = 1.000 ✓

How to Calculate Partial Pressure from Moles

When you know the mass or moles of each gas and the total pressure, use this four-step method to calculate partial pressure from moles. This is the most common exam scenario.

Step 1: Convert grams to moles if needed: n = mass(g) ÷ molar mass(g/mol)
Step 2: Sum all moles: n_total = Σn_i
Step 3: Calculate mole fraction: χ_A = n_A / n_total
Step 4: Partial pressure: P_A = χ_A × P_total

Example 1: 14 g N2 and 16 g O2, P_total = 2.00 atm

n_N2 = 14 ÷ 28.014 = 0.4998 mol
n_O2 = 16 ÷ 31.998 = 0.5000 mol
n_total = 0.4998 + 0.5000 = 0.9998 mol
χ_N2 = 0.4998 / 0.9998 = 0.4999 → P_N2 = 0.4999 × 2.00 = 1.000 atm
χ_O2 = 0.5000 / 0.9998 = 0.5001 → P_O2 = 0.5001 × 2.00 = 1.000 atm

Example 2: 0.5 mol H2, 0.3 mol He, 0.2 mol Ar, P_total = 5.00 atm

n_total = 0.5 + 0.3 + 0.2 = 1.00 mol
χ_H2 = 0.50 → P_H2 = 0.50 × 5.00 = 2.50 atm
χ_He = 0.30 → P_He = 0.30 × 5.00 = 1.50 atm
χ_Ar = 0.20 → P_Ar = 0.20 × 5.00 = 1.00 atm

Example 3: Partial Pressure of Nitrogen in Dry Air at Sea Level

Dry air: 78.09% N2 by mole → χ_N2 = 0.7809
P_total = 101.325 kPa (1 atm)
P_N2 = χ_N2 × P_total = 0.7809 × 101.325 = 79.12 kPa = 0.7809 atm

⚗

Need to convert grams to moles first? Our Grams to Moles Calculator handles any element or compound with step-by-step working.

Grams to Moles Calculator →

Pressure Unit Conversion Table

Standard atmospheric pressure: 1 atm = 101.325 kPa = 760 mmHg = 1.01325 bar = 14.696 psi = 101,325 Pa

Unit	= atm	= kPa	= mmHg	= bar	= Pa	= psi
1 atm	1	101.325	760	1.01325	101,325	14.696
1 kPa	0.009869	1	7.5006	0.01	1,000	0.14504
1 mmHg (torr)	0.001316	0.13332	1	0.001333	133.32	0.01934
1 bar	0.98692	100	750.06	1	100,000	14.504
1 Pa	9.869×10?6	0.001	0.0075	0.00001	1	0.000145
1 psi	0.068046	6.8948	51.715	0.068948	6,894.8	1

Partial Pressure of Gases in Dry Air at Sea Level

At standard sea-level pressure (1 atm = 101.325 kPa = 760 mmHg), the partial pressures of the main atmospheric gases are:

Gas	Mole Fraction (χ)	P (atm)	P (kPa)	P (mmHg)
Nitrogen (N2)	0.78084	0.7808 atm	79.12 kPa	593.4 mmHg
Oxygen (O2)	0.20946	0.2095 atm	21.22 kPa	159.2 mmHg
Argon (Ar)	0.00934	0.00934 atm	0.946 kPa	7.10 mmHg
Carbon dioxide (CO2)	0.000421	0.000421 atm	0.0427 kPa	0.320 mmHg
Total (dry air)	1.00000	1.0000 atm	101.325 kPa	760.0 mmHg

Note: partial pressure of oxygen in the alveoli of the lungs is lower (~13.3 kPa) due to dilution by water vapour (~6.3 kPa) and CO2 (~5.3 kPa) in the alveolar air. Partial pressure of nitrogen at sea level: P_N2 = 0.7808 atm = 79.12 kPa = 593.4 mmHg.

Worked Examples

1. Finding Partial Pressure Using Dalton's Law (P_total = P₁ + P₂ + P₃)

Three gases are in a container: P_N2 = 0.78 atm, P_O2 = 0.21 atm, P_Ar = 0.01 atm. By Dalton's Law, P_total = P_N2 + P_O2 + P_Ar = 0.78 + 0.21 + 0.01 = 1.00 atm. To find an unknown partial pressure, rearrange: P_unknown = P_total − (sum of known pressures).

2. Partial Pressure from Mole Fraction — P_A = χ_A × P_total

A gas mixture has P_total = 3.00 atm. Gas A has χ_A = 0.40. Apply the formula: P_A = χ_A × P_total = 0.40 × 3.00 = 1.20 atm = 121.6 kPa. Verify: if χ_B = 0.60, then P_B = 0.60 × 3.00 = 1.80 atm; 1.20 + 1.80 = 3.00 atm ✓.

3. Partial Pressure from Moles and Total Pressure

3 mol N2 and 1 mol O2 at P_total = 4 atm. n_total = 4 mol. χ_N2 = 3/4 = 0.75 → P_N2 = 0.75 × 4 = 3.00 atm. χ_O2 = 1/4 = 0.25 → P_O2 = 0.25 × 4 = 1.00 atm. Check: 3.00 + 1.00 = 4.00 ✓.

4. Finding Total Pressure from Partial Pressures

Given P_H2 = 250 mmHg, P_He = 375 mmHg, P_Ar = 135 mmHg. Convert to same unit (already in mmHg). P_total = P₁ + P₂ + P₃ = 250 + 375 + 135 = 760 mmHg = 1.00 atm. Dalton's Law requires all pressures in the same unit before summing.

5. Partial Pressure Using the Ideal Gas Law — P_A = n_ART/V

n = 0.5 mol O2, V = 10 L, T = 25°C = 298.15 K. P_O2 = (0.5 × 0.082057 × 298.15) / 10 = 12.232 / 10 = 1.223 atm = 123.9 kPa. Always convert °C to K by adding 273.15 before using PV = nRT.

6. Partial Pressure of Oxygen in Air

Oxygen makes up 20.946% of dry air by mole. χ_O2 = 0.20946. At P_total = 1 atm: P_O2 = χ_O2 × P_total = 0.20946 × 1 = 0.2095 atm = 21.22 kPa = 159.2 mmHg. In the lungs this drops to ~13.3 kPa due to water vapour and CO2.

7. Partial Pressure of Nitrogen at Sea Level

N2 mole fraction in dry air = 0.78084. At 1 atm: P_N2 = 0.78084 × 1 atm = 0.7808 atm = 0.7808 × 101.325 = 79.12 kPa = 0.7808 × 760 = 593.4 mmHg. This is the partial pressure of nitrogen that causes nitrogen narcosis in scuba diving at depth.

8. Partial Pressure from Grams of Each Gas

32 g O2 and 28 g N2 in a container at P_total = 3 atm. n_O2 = 32/31.998 = 1.000 mol; n_N2 = 28/28.014 = 0.9995 mol; n_total = 1.9995 mol. χ_O2 = 1.000/1.9995 = 0.5001; P_O2 = 0.5001 × 3 = 1.500 atm. χ_N2 = 0.4999; P_N2 = 0.4999 × 3 = 1.500 atm.

9. Mole Fraction from Partial Pressure

If P_total = 5.00 atm and P_CO2 = 0.75 atm, find χ_CO2. Rearrange P_A = χ_A × P_total: χ_CO2 = P_CO2 / P_total = 0.75 / 5.00 = 0.150 = 15.0 mol%. This confirms that mole fraction = pressure fraction for ideal gases.

10. Partial Pressure in a Three-Component Gas Mixture

2 mol CH4, 1 mol CO2, 0.5 mol H2, P_total = 7.00 atm. n_total = 3.5 mol. χ_CH4 = 2/3.5 = 0.5714 → P_CH4 = 0.5714 × 7 = 4.000 atm. χ_CO2 = 1/3.5 = 0.2857 → P_CO2 = 2.000 atm. χ_H2 = 0.5/3.5 = 0.1429 → P_H2 = 1.000 atm. Sum: 4+2+1 = 7.00 ✓.

Frequently Asked Questions

What is partial pressure? ▼

Partial pressure is the pressure a single gas in a mixture would exert if it alone occupied the entire container volume at the same temperature. It represents that gas's individual contribution to the total mixture pressure. Calculated as P_i = χ_i × P_total.

What is Dalton's Law of Partial Pressures? ▼

Dalton's Law states that the total pressure of a gas mixture equals the sum of all partial pressures: P_total = P₁ + P₂ + P₃ + … + P_n. Formulated by John Dalton in 1801, it assumes ideal gas behaviour with no interactions between molecules.

How do you calculate partial pressure from mole fraction? ▼

Use the formula P_A = χ_A × P_total. First find the mole fraction: χ_A = n_A / n_total. Multiply by the total pressure of the mixture. Example: χ_O2 = 0.21, P_total = 1 atm → P_O2 = 0.21 × 1 = 0.21 atm.

How do you find total pressure from partial pressures? ▼

Add all partial pressures in the same unit: P_total = P₁ + P₂ + P₃ + …. Convert to a common unit first if needed. Example: P_N2 + P_O2 + P_Ar = 0.78 + 0.21 + 0.01 = 1.00 atm.

What is the formula for partial pressure? ▼

Three formulas: (1) Dalton's Law: P_total = P₁ + P₂ + …; (2) Mole fraction: P_A = χ_A × P_total where χ_A = n_A/n_total; (3) Ideal gas law: P_A = n_ART/V with R = 0.082057 L·atm/(mol·K).

How do you find partial pressure from moles? ▼

(1) Sum all moles: n_total. (2) Find χ_A = n_A/n_total. (3) Multiply: P_A = χ_A × P_total. If you have grams instead of moles, convert first: n = mass ÷ molar mass.

What is the partial pressure of oxygen in air? ▼

In dry air at sea level: P_O2 = 0.2095 atm = 21.22 kPa = 159.2 mmHg. Calculated from χ_O2 = 0.20946 and P_total = 1 atm. In the lungs, it drops to ~13.3 kPa due to water vapour and CO2 dilution.

How does partial pressure relate to the ideal gas law? ▼

Each gas in a mixture individually obeys PV = nRT: P_AV = n_ART, so P_A = n_ART/V. The total pressure is the sum of all individual gas pressures, consistent with Dalton's Law. This connection means mole fraction equals pressure fraction for ideal gases.

What are the units of partial pressure? ▼

Same as total pressure: atm, kPa, Pa, mmHg (torr), bar, or psi. Standard conversion: 1 atm = 101.325 kPa = 760 mmHg = 1.01325 bar = 14.696 psi = 101,325 Pa.

How do you convert between pressure units? ▼

Convert to atm first, then to target unit. Key factors: divide mmHg by 760 to get atm; divide kPa by 101.325 for atm; divide bar by 1.01325 for atm. Then multiply atm by the target factor (e.g., ×101.325 for kPa, ×760 for mmHg).

Related Calculators

📐 Key Formulas

Dalton's Law: P_total = P₁ + P₂ + P₃ + …

Mole Fraction: P_A = χ_A × P_total

Ideal Gas: P_A = n_ART/V

Mole fraction: χ_A = n_A/n_total

Σχ = 1 always — mole fractions sum to exactly 1

💡 Quick Conversions

1 atm	= 101.325 kPa
1 atm	= 760 mmHg
1 atm	= 1.01325 bar
1 atm	= 14.696 psi
1 atm	= 101,325 Pa

🔬 Gas Molar Masses

N2	28.014 g/mol
O2	31.998 g/mol
CO2	44.009 g/mol
H2	2.016 g/mol
He	4.003 g/mol
Ar	39.948 g/mol
CH4	16.043 g/mol
NH3	17.031 g/mol

📊 Air Composition

χ = 0.7808 → 79.12 kPa

χ = 0.2095 → 21.22 kPa

χ = 0.00934 → 0.946 kPa

CO2

χ = 0.000421 → 0.043 kPa

Partial Pressure Calculator – Dalton’s Law, Mole Fraction & Gas Mixtures

Partial Pressure Calculator

What is Partial Pressure? — Dalton's Law of Partial Pressures

Real-World Example: Atmospheric Air at Sea Level

Applications of Dalton's Law

Partial Pressure Formula — Mole Fraction Method

How to Find Partial Pressure — Step by Step

Method 1: From Known Partial Pressures (Dalton's Law) — P_total = P₁ + P₂ + P₃

Method 2: From Moles and Total Pressure

Method 3: From Ideal Gas Law

Worked Example — Air Composition: 3.12 mol N2, 0.84 mol O2, 0.04 mol Ar, P_total = 4.00 atm

How to Calculate Partial Pressure from Moles

Example 1: 14 g N2 and 16 g O2, P_total = 2.00 atm

Example 2: 0.5 mol H2, 0.3 mol He, 0.2 mol Ar, P_total = 5.00 atm

Example 3: Partial Pressure of Nitrogen in Dry Air at Sea Level

Pressure Unit Conversion Table

Partial Pressure of Gases in Dry Air at Sea Level

Worked Examples

1. Finding Partial Pressure Using Dalton's Law (P_total = P₁ + P₂ + P₃)

2. Partial Pressure from Mole Fraction — P_A = χ_A × P_total

3. Partial Pressure from Moles and Total Pressure

4. Finding Total Pressure from Partial Pressures

5. Partial Pressure Using the Ideal Gas Law — P_A = n_ART/V

6. Partial Pressure of Oxygen in Air

7. Partial Pressure of Nitrogen at Sea Level

8. Partial Pressure from Grams of Each Gas

9. Mole Fraction from Partial Pressure

10. Partial Pressure in a Three-Component Gas Mixture

Frequently Asked Questions

Related Calculators

Pages

Newsletter

Partial Pressure Calculator – Dalton’s Law, Mole Fraction & Gas Mixtures

Partial Pressure Calculator

What is Partial Pressure? — Dalton's Law of Partial Pressures

Real-World Example: Atmospheric Air at Sea Level

Applications of Dalton's Law

Partial Pressure Formula — Mole Fraction Method

How to Find Partial Pressure — Step by Step

Method 1: From Known Partial Pressures (Dalton's Law) — Ptotal = P1 + P2 + P3

Method 2: From Moles and Total Pressure

Method 3: From Ideal Gas Law

Worked Example — Air Composition: 3.12 mol N2, 0.84 mol O2, 0.04 mol Ar, Ptotal = 4.00 atm

How to Calculate Partial Pressure from Moles

Example 1: 14 g N2 and 16 g O2, Ptotal = 2.00 atm

Example 2: 0.5 mol H2, 0.3 mol He, 0.2 mol Ar, Ptotal = 5.00 atm

Example 3: Partial Pressure of Nitrogen in Dry Air at Sea Level

Pressure Unit Conversion Table

Partial Pressure of Gases in Dry Air at Sea Level

Worked Examples

1. Finding Partial Pressure Using Dalton's Law (Ptotal = P1 + P2 + P3)

2. Partial Pressure from Mole Fraction — PA = χA × Ptotal

3. Partial Pressure from Moles and Total Pressure

4. Finding Total Pressure from Partial Pressures

5. Partial Pressure Using the Ideal Gas Law — PA = nART/V

6. Partial Pressure of Oxygen in Air

7. Partial Pressure of Nitrogen at Sea Level

8. Partial Pressure from Grams of Each Gas

9. Mole Fraction from Partial Pressure

10. Partial Pressure in a Three-Component Gas Mixture

Frequently Asked Questions

Related Calculators

Pages

Newsletter

Method 1: From Known Partial Pressures (Dalton's Law) — P_total = P₁ + P₂ + P₃

Worked Example — Air Composition: 3.12 mol N2, 0.84 mol O2, 0.04 mol Ar, P_total = 4.00 atm

Example 1: 14 g N2 and 16 g O2, P_total = 2.00 atm

Example 2: 0.5 mol H2, 0.3 mol He, 0.2 mol Ar, P_total = 5.00 atm

1. Finding Partial Pressure Using Dalton's Law (P_total = P₁ + P₂ + P₃)

2. Partial Pressure from Mole Fraction — P_A = χ_A × P_total

5. Partial Pressure Using the Ideal Gas Law — P_A = n_ART/V