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Ideal Gas Density Calculator

Created by Luis Hoyos
Reviewed by Steven Wooding
Last updated: Jan 18, 2024


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 use the ideal gas to calculate density. Even so, knowing the equations is essential 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 of 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.

Remembering that the specific gas constant equals the universal gas constant divided by the molar mass, we can calculate the density of an ideal gas this other way:

ρ=Mp/RˉT\rho = Mp/\bar{R}T

, where:

  • MM — Molar mass, in kg/mol or g/mol; and
  • Rˉ\bar{R} — Universal gas constant, which equals 8.3144626 J/(mol K).

Example: Air ideal gas density calculation

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 the ideal gas 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 formula, 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" (learn more about in our compressibility factor calculator).

Now that you know the most important aspects when calculating density with the ideal gas law let's look at some FAQs.

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 Hoyos
Substance
Custom ▾
Absolute presure (P)
Pa
Temperature (T)
K
Specific gas constant (Rₛ)
J/(kg·K)
Molar mass (M)
kg
/mol
Density (ρ)
kg/m³
Check out 45 similar thermodynamics and heat calculators 🌡️
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