Partial Pressure Calculator - Dalton's Law for Gas Mixtures

A partial pressure calculator is a chemistry tool that turns a gas mixture's total pressure and the mole fraction of one gas into the partial pressure that gas exerts, using Dalton's law. The form covers the forward case (P_i from x_i and P_total) and the mole fraction reverse case, returning the answer in atm, mmHg, and kPa.

• • Gas-mixture homework: Solve textbook partial pressure problems for oxygen, nitrogen, carbon dioxide, or any other component of a gas mixture.
• • Oxygen in air calculations: Find the partial pressure of oxygen in dry air at sea level, at altitude, or inside a sealed container.
• • Lab gas-collection work: Compute the partial pressure of a gas collected over water once the water vapor partial pressure is subtracted from the barometer reading.
• • Reverse mole fraction check: Enter a measured partial pressure and the total pressure to read the mole fraction directly, the most common reverse on a Dalton's-law worksheet.

Partial pressure shows up in three general chemistry places: Dalton's law problems, gas-collection-over-water experiments, and equilibrium calculations such as Kp. Once the partial pressure is in the right unit (atm for Kp, mmHg for medical gas work, kPa for engineering), the rest is usually a one-line plug-in.

Because the partial pressure calculator uses the mole fraction as its main input, the mole fraction calculator is a useful first stop when you only have grams of each component and need to convert to a mole fraction first.

The calculator applies Dalton's law of partial pressures. Leave the partial pressure blank to solve for P_i, or leave the mole fraction at zero and fill in P_i to solve for x_i.

• P_total: Total pressure of the gas mixture in atm, read from a manometer or barometer.
• x_i: Mole fraction of the gas of interest, equal to its moles divided by total moles (dimensionless, 0 to 1).
• P_i: Partial pressure of the gas of interest in atm; the value the calculator solves for by default.

The result panel returns the partial pressure in mmHg and kPa. The conversions are fixed at 1 atm = 760 mmHg = 101.325 kPa, the same factors used in NIST SP 811. Mole percent is x_i times 100, so 0.21 reads as 21.00 percent.

According to ChemPRIME (LibreTexts) - Dalton's Law of Partial Pressures, the partial pressure of a gas in a mixture is the pressure that gas would exert if it alone occupied the container, and partial pressure equals mole fraction times the total pressure of the mixture under the same conditions.

According to OpenStax Chemistry 2e - Stoichiometry of Gaseous Substances, Mixtures, and Reactions, the total pressure of a mixture of non-reacting gases equals the sum of the partial pressures of the individual gases, and the partial pressure of any one gas equals its mole fraction in the mixture times the total pressure.

When the problem gives you moles, volume, and temperature instead of a total pressure, the ideal gas calculator handles the PV=nRT step that turns a single gas into a partial pressure.

Four ideas show up in almost every partial pressure problem. They are the building blocks behind the form and what you need to interpret the result.

Mole fraction is a ratio, not a percentage, so the input is a decimal between 0 and 1 even though the result panel shows the mole percent alongside. Entering 21 thinking it is a percentage will give a partial pressure 21 times the total, the most common misapplication of Dalton's law.

For a quick walk through Boyle's, Charles's, and Gay-Lussac's law while you work a partial pressure problem, the gas laws calculator keeps the same pressure units handy in atm, mmHg, and kPa.

The form maps each input to one of the three variables in P_i = x_i * P_total. Leave the partial pressure blank to solve for it, or leave the mole fraction at zero and fill in P_i to solve for x_i; the form updates the result on every keystroke.

1. 1 Enter the total pressure of the mixture: Type the barometer or manometer reading in atm. If you have mmHg, divide by 760; if you have kPa, divide by 101.325.
2. 2 Enter the mole fraction of the gas of interest: Use a decimal between 0 and 1. For oxygen in dry air, 0.21 is the textbook value. For nitrogen, use 0.78. Leave the field at 0 if you want to solve for the mole fraction instead.
3. 3 Leave the partial pressure blank to solve for it: The form treats a blank partial-pressure field as the unknown and uses Dalton's law to fill it in. The result panel shows the partial pressure in atm, mmHg, kPa, and the equivalent mole percent.
4. 4 Or fill in the partial pressure to back out the mole fraction: If you already know the partial pressure from a measurement, leave the mole fraction field empty and the form divides P_i by P_total to return the mole fraction and mole percent.
5. 5 Read the result in the unit you need: The primary result is in atm, the unit used in Kp and most equilibrium expressions. Use the mmHg row for medical and diving work, the kPa row for engineering and atmospheric science, and the mole percent row for share-of-mixture questions.

To find the partial pressure of oxygen in dry air at 0.85 atm (the cabin pressure of a commercial flight), enter P_total = 0.85 atm and x_i = 0.21. The form returns P_i = 0.1785 atm = 135.7 mmHg.

A two-input form beats a one-line equation when it removes the small mistakes that happen during a long problem. Here is what it saves.

• • Solves forward and the standard reverse case: Enter a total pressure and mole fraction to get the partial pressure, or a total pressure and partial pressure to get the mole fraction, so the same page handles forward homework and the reverse check.
• • Returns the unit you need: The result panel reports atm, mmHg, kPa, and mole percent side by side, which removes the unit conversion step that usually follows a partial pressure calculation.
• • Catches the mole-fraction percentage trap: The mole-fraction input is a decimal between 0 and 1, and the form shows the mole percent next to it, which makes it obvious when the share was meant as a percentage.
• • Pairs with related gas and concentration tools: Once the partial pressure is in atm, the form hands off to the ideal gas calculator, the gas laws calculator, and the concentration calculator.
• • Anchors results to the standard mole fraction: The default 0.21 lets you recheck the textbook example for oxygen in dry air in a single click.

For homework, the calculator is most useful as a check after you finish the problem by hand. For lab work, it turns a barometer reading and a mole fraction into the value that goes into a Kp expression or a respiratory calculation.

If the partial pressure problem lists grams of each gas instead of moles, the mole and molar mass calculator is the cleanest way to convert each mass to moles before forming the mole fraction.

Dalton's law is simple, but a partial pressure result can be off by a large factor if the inputs are wrong. These four things move the result most.

• • The calculator assumes an ideal gas mixture. Real gas corrections, such as compressibility factors, are not applied automatically, so the result can drift at high pressure or near a phase change.
• • The water vapor partial pressure is not subtracted from a wet gas reading. For gas collected over water, look up the water vapor pressure at the lab temperature and subtract it from the barometer reading first.

According to NIST CODATA Fundamental Physical Constants, the molar gas constant is 8.314462618 J/(mol*K), equal to 0.082057366 L*atm/(mol*K) once the standard atmosphere and liter unit conversions are applied; this value is the basis of the atm, mmHg, and kPa pressure conversions used in the calculator.

For gas-collection-over-water problems where the lab gives a mass of dry gas, the grams to moles calculator turns the mass into moles so the mole fraction and partial pressure can be computed correctly.