Calculating the density of an ideal gas is not more complicated than any of its other properties. The only additional task is to express specific volume in terms of density. That's what this calculator does: it's an ideal gas law calculator with density instead of volume as the output.

If you thought the density of all ideal gases was the same, nothing further from reality. Ideal gas densities can be as low as 0.07927 kg/m³ (hydrogen) or as high as 2.281 kg/m³ in the case of butane. In other words, butane is 29 times denser than hydrogen 🙀

Keep reading to learn more about finding density using the ideal gas law!

Deriving density from ideal gas law equation

Using our calculator is the easiest way to find the density using the ideal gas law. Even so, it's essential to know the equations for a better understanding.

Deriving density from the ideal gas law only requires knowing the relationship between specific volume and density and using it in the ideal gas law equation. Let's remember the equation:

Pν=RTPν = RT

where:

  • PP — Absolute pressure of the gas;
  • νν — Specific volume of the gas;
  • RR — Gas constant, different for every gas; and
  • TT — Absolute gas temperature, in kelvin (K).

Specific volume measures how much space a substance occupies per unit mass. It's the inverse of density (ρ\rho):

ν=1ρν = \frac{1}{\rho}

If we insert this density formula in the ideal gas law:

Pρ=RT\frac{P}{\rho} = RT

and solve for ρ\rho, we have:

ρ=PRT\rho = \frac{P}{RT}

Awesome! We derived a density equation using the ideal gas law.

Now, let's calculate density with the ideal gas law for one of the most common fluids: air.

Example: Calculating the density of air ideal gas

Air density is widely known, but we can calculate it with the previous formula. Follow these steps to do it:

  1. Determine the gas constant. For air, it's R=287 J/kg⋅KR = 287 \ \text{J/kg⋅K}.
  2. Determine the pressure and temperature conditions. Suppose we want to find air density at T=15 °C=288.15 KT = 15\ \text{°C} = 288.15 \ \text{K} and P=101325 PaP = 101325 \ \text{Pa}.
  3. Input the values in the equation, taking into account that the density formula for ideal gas law requires temperature in kelvin:
    ρ=PRT=101325 Pa287 J/kg⋅K(288.15 K)=1.225 kg/m³ρ = \frac{P}{RT} = \frac{101325 \ \text{Pa}}{287 \ \text{J/kg⋅K}(288.15 \ \text{K})} = 1.225 \ \text{kg/m³}
  4. That's it. If you search for air density on Google, you'll get this answer.

🔎 We also have a dedicated air density calculator that, besides temperature and pressure, takes into account air moisture properties.

Aspects to consider when using ideal gas law to find the density

Consider these points when using the ideal gas law:

  • If you want to find density using the ideal gas law, you need to provide the absolute pressure of the gas, not its manometric pressure.
  • The ideal gas law is an idealization, and real gases deviate from it. The nearer temperature and pressure to the critical point, the more our gas will differ from this idealization.
  • We can quantify the deviation from ideal-gas behavior using a correction factor called the "compressibility factor" (you can learn more about it in our compressibility factor calculator).

Other tools similar to our ideal gas density calculator

Now that you know how to calculate density with the ideal gas law, you can take a look at these tools related to our gas density calculator:

FAQ

Is steam an ideal gas?

At atmospheric pressures below 10 kPa, steam is an ideal gas (or behaves like that), no matter its temperature. The error increases at higher pressures, like the atmospheric pressure, especially near the critical point where it reaches about 100% error.

Is CO2 an ideal gas?

Yes, we can consider CO2 an ideal gas as long as it keeps far away from its critical pressure (7.39 MPa) or, failing that, far below its critical temperature (31.05 °C). The reduced pressure and temperature quantify how far away it is from those values.

How to determine which gas behaves most ideally?

To determine which gas behaves most ideally:

  1. Determine the reduced temperature (TR) and reduced pressure (PR) of each gas.
  2. With TR and PR, determine the compressibility factor (Z) using a compressibility chart.
  3. The gas with the Z nearer to 1 is the one that behaves most ideally.

Is the density of all ideal gases the same?

No, the density of all ideal gases is not the same. Every substance has a different molar mass that translates into a different density. You can use our gas density calculator and check how different they are!

Luis Fernando
Substance
Custom ▾
Absolute presure (P)
Pa
Gas constant (R)
J/kg⋅K
Temperature (T)
K
Density (ρ)
kg/m³
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