Henry's Law Calculator
Find how much gas dissolves in water at a given partial pressure, or the pressure a dissolved gas needs.
What it does
Henry's law is the rule that connects a gas floating above a liquid with the amount of that gas that ends up dissolved in it. At a fixed temperature the dissolved concentration is proportional to the partial pressure of the gas above the liquid, and the constant in the middle depends on the gas, the solvent and the temperature. It is the rule behind carbonated drinks, the oxygen content of a fish tank and the way a lake holds carbon dioxide.
The constant has to be quoted with its units, or the number is meaningless. The EPA has to spell this out in its own materials, where the constants come in several flavours: partial pressure over solubility in atmosphere cubic metres per mole, and dimensionless concentration ratios between the gas phase and the water. This page uses the NIST Chemistry WebBook form, solubility in moles per kilogram of water per bar, because that is the version published with a temperature correction for each gas.
The NIST form also shows the temperature dependence. The constant at any temperature follows from the value at 25 °C and a single parameter for that gas, using an exponential in the inverse of the absolute temperature. Warm water holds less gas, which is why a warm lake loses oxygen faster and why a chilled bottle keeps its fizz longer.
For dilute solutions the number of moles per kilogram of water is close enough to moles per liter to read as a concentration, and multiplying by the molar mass turns it into milligrams per liter, which is how dissolved oxygen and dissolved carbon dioxide are reported in water quality work.
The calculation ignores everything except the equilibrium. Real water is rarely in equilibrium with a clean gas, and a sample that has been sitting open has already lost some of what it held. It also treats the gas as ideal, which is a good approximation at these pressures.
How to use
- Pick the gas you are working with.
- Enter the water temperature.
- Choose whether you know the partial pressure or the dissolved concentration.
- Enter the pressure in bar, or the concentration in moles per liter.
- Read the Henry constant at that temperature and the matching concentration.
- Switch the units to imperial if you work in pounds per square inch.
Formula
- k
- Henry constant, moles of gas per kilogram of water per bar.
- B
- Temperature parameter for that gas, in kelvin.
- T
- Absolute temperature in kelvin.
- p
- Partial pressure of the gas above the water, in bar.
- c
- Dissolved concentration, moles per kilogram of water.
The molar masses used to turn moles into milligrams are the standard atomic weights, and the mole fraction of the gas in a mixture of gases is the partial pressure over the total pressure, so a gas at 21 percent of the atmosphere has a partial pressure of 0.21 bar, not 1 bar. The NIST compilation lists more than one measured value for several gases, and the values used here are the ones the WebBook prints for each gas with its temperature parameter.
Worked example
Example: oxygen at 25 °C under one atmosphere
Defaults: metric units, oxygen, 25 °C, concentration from partial pressure, and a partial pressure of 1.01325 bar, which is one atmosphere.
- At 25 °C the temperature correction is exp(0) = 1, so the constant stays at 0.0013 mol/(kg bar).
- Concentration: 0.0013 x 1.01325 = 0.001317 mol/L.
- In milligrams per liter: 0.001317 x 31.998 x 1000 = 42.15 mg/L.
- The partial pressure is 1.013 bar, which is the value entered.
- Running it the other way with 0.001317 mol/L gives the same 1.013 bar back.
- The tool shows 0.00130 mol/(kg bar), 0.001317 mol/L, 42.15 mg/L and 1.013 bar.
Reference table
| Gas | Constant mol/(kg bar) | Temperature parameter | At 1 atm |
|---|---|---|---|
| Oxygen | 0.0013 | 1500 K | 42.15 mg/L |
| Nitrogen | 0.00065 | 1300 K | 18.45 mg/L |
| Carbon dioxide | 0.035 | 2400 K | 1,560.76 mg/L |
| Methane | 0.0014 | 1600 K | 22.76 mg/L |
| Hydrogen sulfide | 0.10 | 2000 K | 3,453.26 mg/L |
| Carbon monoxide | 0.00099 | 1300 K | 28.10 mg/L |
Limits
- Describes an equilibrium between a clean gas and water, not a sample that has been sitting in the open.
- Treats the gas as ideal and the water as pure, so salts and organic matter change the answer.
- Reads moles per kilogram of water as moles per liter, which is close for dilute water but not exact.
- The constants are compiled values with scattered accuracy, and the NIST entries list more than one measurement for several gases.
Common mistakes
- Using the total pressure of the gas instead of its partial pressure, which overstates the dissolved amount by the mole fraction.
- Reading a constant in atm cubic metres per mole as if it were in moles per liter per bar, which inverts the answer.
- Forgetting that the constant changes with temperature and using a 25 °C value for cold water.
- Treating a concentration in milligrams per liter as the same as the constant, when the molar mass is missing.
- Assuming the water is saturated when the sample was capped, which is the normal case for field work.
Try it yourself
Quick checks. Answers sit tucked under each question.
How much oxygen does water hold at 20 °C under one atmosphere?
The constant at 20 °C is 0.001416 mol/(kg bar), so the concentration is 0.001435 mol/L, which is 45.93 mg/L. Cold water holds more oxygen than warm water.
A sample holds 0.035 mol/L of carbon dioxide at 25 °C. What partial pressure does that need?
The partial pressure is 0.035 / 0.035 = 1.000 bar, which is close to one atmosphere of carbon dioxide.
What is the dissolved concentration of methane at 25 °C under one atmosphere?
0.0014 x 1.01325 = 0.001419 mol/L, which is 22.76 mg/L of methane.
Questions
What is Henry's law?
At a fixed temperature, the concentration of a dissolved gas is proportional to the partial pressure of that gas above the liquid. The constant of proportionality is the Henry constant.
Why are the units on the constant so important?
Because a number without units can be read the wrong way round. The same constant can be written as solubility, as pressure over solubility or as a dimensionless ratio, and getting the convention wrong gives an answer off by a factor of thousands.
How much oxygen can water hold?
About 42.15 mg/L at 25 °C under one atmosphere of oxygen, and about 45.93 mg/L at 20 °C. That is why a warm lake holds less oxygen, and why a fish tank needs aeration in summer.
What is the difference between Henry's law and Raoult's law?
Raoult's law is for a liquid mixture of volatile components, while Henry's law is for a gas dissolving in a liquid. They meet at the limit where the solvent follows ideal behaviour.
Does salt change the answer?
Yes. Salts lower the solubility of a gas in water, which is the salting out effect, and organic matter in the water binds dissolved gases as well. The values here are for clean water.
Can I use this for a gas other than the six listed?
Not with the built in data, but the same arithmetic works with any Henry constant. Take the constant and its temperature parameter from the NIST WebBook entry for the gas and use the same formula.
Sources
- NIST Chemistry WebBook: Henry's law constants for oxygen
- NIST Chemistry WebBook: Henry's law constants for carbon dioxide
- US EPA: Henry's law constants, definitions and conventions