# How to Calculate the Pressure of Hydrogen Gas

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The ideal gas equation discussed below in Step 4 is sufficient for calculating the pressure of hydrogen gas under normal circumstances. Above 150 psi (ten times normal atmospheric pressure) and the van der Waals equation may need to be invoked to account for intermolecular forces and the finite size of the molecules.

Measure the temperature (T), volume (V), and mass of the hydrogen gas. One method to determine the mass of a gas is to completely evacuate a light but strong vessel, then weigh it before and after introducing the hydrogen.

Determine the number of moles, n. (Moles are a way of counting molecules. One mole of a substance equals 6.022×10^23 molecules.) The molar mass of hydrogen gas, being a diatomic molecule, is 2.016g/mol. In other words, it's twice the molar mass of an individual atom, and therefore twice the molecular weight of 1.008 amu. To find the mole count, divide the mass in grams by 2.016. For example, if the mass of the hydrogen gas is 0.5 grams, then n equals 0.2480 moles.

Convert the temperature T into Kelvin units by adding 273.15 to the temperature in Celsius.

Use the ideal gas equation (PV=nRT) to solve for pressure. n is the number of moles and R is the gas constant. It equals 0.082057 L atm / mol K. Therefore, you should convert your volume to liters (L). When you solve for pressure P, it will be in atmospheres. (The unofficial definition of one atmosphere is the air pressure at sea level.)

#### Tips

• For the high pressures in which hydrogen gas is often stored, the van der Waals equation can be used. It is P+a(n/V)^2=nRT. For diatomic hydrogen gas, a=0.244atm L^2/mol^2 and b=0.0266L/mol. This formula throws out some of the assumptions of the ideal gas equation (e.g., that gas molecules are point particles with no cross section, and that they don’t exert an attractive or repulsive force on each other).

#### References

• Raymond Chang; Chemistry; 1984