Gas Mixture Partial Pressure Calculator

Dalton's Law says the total pressure of a non-reacting gas mixture is the sum of the partial pressures of its components: P_total = Σ P_i. Each component behaves as if it had the container to itself, because ideal-gas molecules don't see each other at distances larger than a few collision diameters. The classic demonstration is mixing 1 atm of nitrogen with 1 atm of oxygen in the same fixed-volume vessel at constant temperature: the gauge reads 2 atm, not some weighted average. The law breaks for reactive mixtures (NH₃ plus HCl gives NH₄Cl smoke and the pressure drops as the salt deposits), and for any condensable component near its dew point. For routine general-chem problems, room temperature and pressures under 5 atm, the deviation from ideality is well under 1%.

Two routes work. If you have mole fractions and total pressure, use P_i = x_i · P_total directly. If you have moles, temperature, and volume, apply the ideal gas law to each component as if it were alone: P_i = n_i · R · T / V. The two routes agree when the gases are ideal because they're algebraically equivalent. Worked example: 0.40 mol N₂ and 0.60 mol O₂ in a 10.0 L vessel at 298.15 K. P(N₂) = (0.40 × 0.08206 × 298.15) / 10.0 = 0.978 atm. P(O₂) = 1.467 atm. P_total = 2.45 atm. Check with mole fractions: x(N₂) = 0.40 / 1.00 = 0.40, so P(N₂) = 0.40 × 2.45 = 0.978 atm. Same answer.

Mole fraction is the ratio of one component's moles to the total moles in the mixture: x_i = n_i / n_total. Dimensionless, always between 0 and 1, and the fractions sum to exactly 1 across all components. Air, simplified: 0.78 N₂, 0.21 O₂, 0.0093 Ar, plus trace CO₂ and water vapor. The numbers work out because they're counting molecules, not weighing them. A common student error swaps mole fraction with mass fraction. They aren't equal except when all molar masses match. For a 50/50-by-moles mixture of H₂ and CO₂, the mass fractions are 4.4% and 95.6% because CO₂ molecules weigh 22 times more than H₂. Mole fraction is what enters Dalton's law and what the gas-law equations expect.

Dalton's law uses mole fraction. P_i = x_i · P_total where x_i = n_i / n_total. Mass fraction (w_i = m_i / m_total) is a different number and will give you the wrong partial pressures if you plug it in. Worked case: 8.00 g O₂ and 4.00 g He at a total pressure of 1.00 atm. By mass, O₂ is dominant (8 / 12 = 67%). By moles, O₂ contributes 8 / 32.00 = 0.250 mol and He contributes 4 / 4.003 = 1.00 mol. Total moles = 1.25. So x(He) = 0.80 and x(O₂) = 0.20, and P(He) = 0.80 atm, P(O₂) = 0.20 atm. Helium dominates the pressure because moles, not mass, set the count of independently moving particles. That counter-intuitive flip is why this question shows up on every general-chem midterm.

Pressure is the time-averaged force per area exerted by molecular collisions with the container walls. If two species of gas share a container and don't interact, the collisions from each species add up independently. There's no cross-term, no mutual reduction. P_total = Σ P_i comes straight out of that linearity. The microscopic picture: an O₂ molecule and an N₂ molecule fly through each other's space without noticing, until both eventually hit a wall. The wall counts both impacts. This breaks when molecules attract or repel meaningfully, which happens for polar gases (water vapor, ammonia) and at high pressure where molecules spend more time within each other's force ranges. For routine N₂ / O₂ / Ar mixtures at 1 atm, the deviation from strict additivity is below the third decimal place.

Partial pressure is what one component of a gas mixture contributes to the total pressure. Vapor pressure is the equilibrium pressure of a substance's gas phase over its own liquid or solid at a given temperature, a property of the pure substance. They're related when the gas phase contains the substance and the liquid/solid is also present. In that case, the partial pressure of the volatile component equals its vapor pressure (the system has reached vapor-liquid equilibrium). For water at 25 °C, the saturation vapor pressure is 23.8 mmHg (NIST WebBook). If you collect any gas over water at 25 °C in a sealed tube and wait for equilibrium, the partial pressure of water vapor in the gas phase reaches 23.8 mmHg. Below equilibrium, the water keeps evaporating. Above, it condenses. The numerical convergence is what makes gas-collection labs work.

Gas collected by water displacement (the standard general-chem setup: an inverted graduated cylinder over a water bath) contains the gas of interest plus water vapor at the bath temperature. The eudiometer reads total pressure, which is P(gas of interest) + P(water vapor). Subtract the water vapor contribution before reporting the gas alone. NIST WebBook tabulates the values: 17.5 mmHg at 20 °C, 23.8 mmHg at 25 °C, and 31.8 mmHg at 30 °C. Worked example: hydrogen collected over water at 25 °C, total pressure 752 mmHg. P(H₂) = 752 − 23.8 = 728.2 mmHg, which then goes into n = PV / RT for the moles of H₂ calculation. Skipping this correction overstates the H₂ yield by roughly 3% at 25 °C, more on a hot day. In practice, the bigger error on a freshman gas-collection experiment is parallax in reading the eudiometer.

Divide mass by molar mass: n = m / M. The mass goes in grams, the molar mass in g/mol, and n comes out in moles. 28.00 g of N₂ at M = 28.014 g/mol (IUPAC 2021) gives 0.9995 mol. 1.00 g of methane (CH₄, M = 16.043 g/mol) gives 0.0623 mol. The number that trips students is hydrogen: H₂ has M = 2.016 g/mol, not 1.008, because the diatomic form has two atoms. The atomic weight (1.008) applies to one H atom; the molecular weight applies to the actual gas species you're working with. For mixtures, do the conversion separately for each component, then sum the moles to get the total before applying mole-fraction logic.

Pick a unit and stick with it. 1 atm = 101.325 kPa = 760 mmHg = 760 Torr = 1.01325 bar = 14.696 psi. The calculator accepts any of these as long as all inputs share one unit. Mixing atm and kPa silently gives garbage. General-chem problems usually run in atm or mmHg. Engineering work prefers bar or Pa. The pascal (Pa) is the SI unit but is awkwardly small (1 atm = 101,325 Pa), so kPa is the practical scale. For Dalton's law, units cancel in the mole-fraction equation P_i = x_i · P_total, so you can compute partial pressures in whatever the total is given in. For ideal-gas-law calls (P_i = n_i R T / V), pick R to match: R = 0.08206 L·atm·mol⁻¹·K⁻¹ for atm-and-liters, R = 8.314 J·mol⁻¹·K⁻¹ for Pa-and-cubic-meters.

Use the ideal-gas-law form: ρ_mixture = (P_total · M_avg) / (R · T), where M_avg is the mole-fraction-weighted molar mass M_avg = Σ x_i · M_i. Worked example: dry air at sea level, 1.00 atm and 25 °C (298.15 K). Using the simplified composition x(N₂) = 0.78, x(O₂) = 0.21, x(Ar) = 0.01: M_avg = 0.78 · 28.014 + 0.21 · 31.998 + 0.01 · 39.948 = 28.96 g/mol. ρ = (1.00 · 28.96) / (0.08206 · 298.15) = 1.184 g/L. NIST's tabulated density of dry air at the same conditions is 1.184 g/L, so the match is exact to four figures. Humid air is less dense than dry air at the same temperature and pressure because water (M = 18.0) is lighter than the N₂/O₂ average, which is one reason hot humid days feel oppressive: the air can carry less oxygen per liter.

Dalton's law assumes ideal gas behavior, which means no intermolecular forces and zero molecular volume. Real gases violate both assumptions, and the violations get serious above roughly 10 atm or near a gas's condensation temperature. Attractive forces pull molecules slightly toward each other, reducing wall collisions and giving an effective partial pressure below the ideal value. Finite molecular volume reduces the free space, raising the effective partial pressure for the same mole count. The two effects partially cancel; van der Waals quantifies both via the a and b constants for each gas. At room temperature and pressures up to 5 atm with N₂, O₂, Ar, or CO₂, the deviation from ideality is under 1%. For CO₂ near its 60 atm critical pressure, or for low-temperature industrial work, switch to Peng-Robinson or van der Waals. The /tools/chemistry/ideal-gas page covers the general formulation. Atkins handles the deviation calculations.

Gas exchange in the alveoli is driven entirely by partial-pressure gradients. Alveolar P(O₂) sits near 100 mmHg, while venous blood arriving at the lungs is around 40 mmHg P(O₂). The 60 mmHg gradient pushes oxygen across the alveolar-capillary membrane until the blood leaves arterialized at roughly 95 mmHg P(O₂). CO₂ runs the opposite direction: venous P(CO₂) of 46 mmHg unloads into alveolar P(CO₂) of 40 mmHg, then exhalation refreshes the gradient. Henry's law converts gas-phase partial pressures to dissolved-blood concentrations, with hemoglobin binding then dominating O₂ transport beyond the simple solubility curve. Anesthesiology and pulmonary medicine spend their careers tuning these numbers. For altitude and hyperbaric calculations, the partial pressures change with total atmospheric pressure but the membrane physics is the same. Guyton's textbook covers the physiological details that go beyond Dalton's law itself.

The calculator checks that the sum of the computed partial pressures matches the total pressure you provided as input. Σ P_i should equal P_total to within rounding (typically the fourth decimal place). A larger gap means something upstream is off: mole fractions that don't sum to 1.0000, mismatched units between inputs, or a typo in one of the masses or moles. A 0.1% gap is usually rounding. A 5% gap means a real input error. Worked example: if you enter mole fractions of 0.45 N₂, 0.40 O₂, and 0.10 Ar (sum 0.95, missing 0.05), the calculator flags the inconsistency rather than silently pretending the missing 5% doesn't exist. In a real eudiometer reading the bigger error source is usually parallax in reading the water level, not Dalton's-law deviation, but the consistency check still catches data-entry mistakes.