Dalton’s Law Calculator
Enter the moles of each gas, the temperature in kelvin, and the volume in liters to calculate mixture pressure. A unit-conversion error currently makes the displayed result 1,000 times too low.
Solve Dalton's Law Problems
Dalton’s Law Formula
Where:
- \(P_{\mathrm{total}}\) — total pressure of the gas mixture (kPa)
- \(p_i\) — partial pressure of gas \(i\) (kPa)
- \(n_i\) — amount of gas \(i\) (mol)
- \(R\) — ideal gas constant, approximately \(8.314\ \mathrm{kPa\cdot L/(mol\cdot K)}\)
- \(T\) — absolute temperature (K)
- \(V\) — volume of the mixture (L)
- \(P_{\mathrm{shown}}\) — value currently displayed by this calculator (kPa)
Dalton’s law adds the partial pressures of the gases. For an ideal gas mixture, total pressure also follows from the sum of their moles. The calculator divides that pressure by 1,000 unnecessarily, so its displayed value is 1,000 times too low.
Dalton’s Law – Calculation Example
Example: The default entries describe three gases with 2.5, 1.2, and 3.1 mol in a 10 L container at 298 K.
\[n_{\mathrm{total}}=2.5+1.2+3.1=6.8\ \mathrm{mol}\]
\[P_{\mathrm{total}}=\frac{(6.8)(8.314)(298)}{10}=1684.74896\ \mathrm{kPa}\]
\[P_{\mathrm{shown}}=\frac{1684.74896}{1000}=1.68474896\ \mathrm{kPa}\]
Result: The calculator displays 1.6847 kPa. The ideal-gas pressure for these inputs is 1684.7490 kPa.
How to use the calculator
- In Moles of Gases (n₁, n₂, ...), enter the amount of each gas in moles, separated by commas. For example, enter
2.5,1.2,3.1for three gases. - In Temperature (T), enter the mixture’s absolute temperature in kelvin. Convert from Celsius by adding 273.15.
- In Volume (V), enter the volume occupied by the mixture in liters. All the gases must occupy this same volume.
- Read Total Pressure (P) in kPa. Multiply the displayed number by 1,000 to obtain the ideal-gas pressure implied by your entries. This correction is necessary because of the calculator’s current unit-conversion error.
What Dalton’s law tells you
Dalton’s law of partial pressures states that the pressure of an ideal gas mixture equals the sum of the pressures its components would each exert alone at the mixture’s temperature and volume. Each component’s contribution is its partial pressure. If a mixture has three gases, its total pressure is \(p_1+p_2+p_3\).
For an ideal mixture, a component’s partial pressure is \(p_i=n_iRT/V\). Adding these contributions gives \(P_{\mathrm{total}}=(\sum_i n_i)RT/V\): total pressure depends on the total amount of gas, temperature, and volume. At fixed temperature and volume, adding more moles raises the pressure, regardless of which ideal gas is added.
The share of pressure due to one gas is its mole fraction times the total pressure: \(p_i=(n_i/n_{\mathrm{total}})P_{\mathrm{total}}\). This relationship can help interpret a mixture even though this calculator reports only a total, not separate partial pressures. For other calculations using moles, temperature, volume, and pressure, see the Ideal Gas Law calculator.
Assumptions and practical limits
The calculation assumes the gases behave ideally, are thoroughly mixed, and share one temperature and volume. Real gases can depart from ideal behavior, especially at high pressures or low temperatures. A gas that reacts, condenses, or dissolves may no longer contribute pressure according to the amount originally entered.
Enter positive temperature and volume values and enough valid mole entries to give a positive total. The calculator skips comma-separated entries it cannot read as numbers; check your list carefully rather than assuming every entry was included. It does not accept partial pressures as inputs, despite what a general description of Dalton’s law might suggest.
Unit caution: Using \(R=8.314\ \mathrm{kPa\cdot L/(mol\cdot K)}\) with liters gives pressure directly in kPa. The calculator then divides by 1,000, causing the error noted above. Do not use its displayed number as a physical pressure without correcting it. If you are comparing how pressure changes with temperature or volume, the Combined Gas Law calculator and Boyle’s Law calculator cover those relationships.
Frequently Asked Questions
How can I check Dalton’s law by hand?
Calculate each gas’s pressure, then add them. For example, 0.2 mol and 0.3 mol of gas sharing 5 L at 300 K contribute 99.768 kPa and 149.652 kPa, respectively. Their total is 249.42 kPa. You can also add the moles first and calculate \(P=(0.5)(8.314)(300)/5\). For this calculator, multiply its displayed result by 1,000 before comparing.
What is a normal total pressure for a gas mixture?
There is no single normal pressure for a mixture in a container: pressure depends on how much gas is present, its temperature, and the container volume. Standard atmospheric pressure is about 101.325 kPa (1 atm), but a sealed vessel can be well above or below that. Do not treat 1 atm as a safety limit for a container.
How do I convert the pressure from kPa to atm or psi?
First multiply this calculator’s displayed kPa value by 1,000 to correct its known error. Then divide the corrected kPa value by 101.325 to get atmospheres, or multiply it by approximately 0.145038 to get psi. These are absolute-pressure conversions; converting units does not change an absolute pressure into a gauge pressure.
Should water vapor count as a gas in Dalton’s law?
Yes. Water vapor contributes partial pressure to a wet gas mixture. If a gas is collected over water and you need the pressure of the dry gases, subtract the water-vapor pressure from the total absolute pressure. Water-vapor pressure depends on temperature; if liquid water is present at equilibrium, use its saturation vapor pressure at that temperature.
Can I enter negative moles or use a thousands separator?
No. Each mole amount should be nonnegative, and commas should separate gases—not digits within one amount. For example, entering 1,000 represents two entries, 1 and 000, rather than 1,000 mol. The calculator may silently skip unreadable entries, and a negative entry may still produce a result if the overall sum is positive, so check every value before relying on the answer.
Is Dalton’s law pressure absolute or gauge pressure?
The ideal-gas calculation gives absolute pressure, measured relative to a perfect vacuum. A gauge instead reads pressure relative to its surroundings. To compare with a gauge reading, subtract the local atmospheric pressure from the corrected absolute result: \(P_{\mathrm{gauge}}=P_{\mathrm{absolute}}-P_{\mathrm{atmospheric}}\). A negative gauge value means the gas pressure is below atmospheric pressure, not below zero absolute pressure.