How to Calculate the Density of a Gas

The density of a gas can be determined from its molecular weight using the ideal gas law. It is simple, because it is enough to know the variables that are needed and to carry out a simple calculation.

These are the steps needed to calculate the density of a gas:

• The density of a gas is defined as its mass per unit volume. Therefore, if the mass of the gas in a given volume is known, the calculation is easy. Usually these two parameters are not known directly, so it is necessary to use the ideal gas law to complete the calculation.
• The ideal gas law is expressed as PV = n RT, where P is the pressure of the gas, V is the volume it occupies, n is the number of moles of gas, R is the universal gas constant, and T is its absolute temperature (measured in degrees Kelvin, ^or K). With this equation it is possible to determine any of these parameters knowing the rest.
• The ideal gas law is an approximation to the behavior of real gases, and it is very useful to determine the parameters of gases because it is very simple; however, we must not forget that it is only an approximation.

How Gas Density Is Calculated

What would be the density of a gas of molecular weight 100 g/mol at 0.5 atm and 27 degrees Celsius?

First of all, it must be observed that the units of the parameters are homogeneous, that they correspond to the same system of units and that they are in accordance with the definition of the ideal gas law. Density is defined as mass per unit volume, but the units can be grams per liter, kilograms per cubic meter, or others, so care must be taken to check the consistency of the units when calculating.

Let’s start by defining the ideal gas law.

PV=n RT

where P is the pressure of the gas, V is the volume it occupies, n is the number of moles of gas, R is the universal gas constant (0.0821 L · atm / mol · or K) and T is its absolute temperature (measured in degrees ^Kelvin ; ^or K).

Let’s look at the units in which the universal gas constant R is expressed. This constant can be expressed in various units, but once a value with its corresponding units is chosen, the units of the other parameters must be the same. In this case, the pressure must be expressed in atmospheres and the volume in liters (temperature must always be expressed in degrees Kelvin, regardless of the units of the other variables).

As already mentioned, to determine the density of the gas, it is necessary to know the mass and the volume it occupies. Let’s use the ideal gas law to determine the volume, for which we clear the volume V from the previous equation:

V = n RT / P

Once the volume of the gas has been determined, we must calculate its mass, which can be done from the number of moles, which is defined as the mass of the gas (m) divided by its molecular weight (PM):

n = m / PM

If we substitute this expression of n in the equation of the ideal gas law in which we have cleared the volume V we obtain:

V = m RT /(PM x P)

If we divide both terms of the equation by the mass of the gas (m) we obtain:

V/m = RT /(PM x P)

And by inverting both terms of the equality, the density (ρ=m/V) is obtained in the left term:

m/V = PM x P /(RT)

ρ = PM x P /(RT)

The reformulation of the ideal gas law now allows us to determine the density of the gas from the data we have: the molecular weight, the pressure and the temperature. Substituting these values, expressed in the appropriate units, we will obtain the density of the gas. In this case we only have to convert the temperature from degrees Celsius ( ^or C) to absolute temperature ( ^or K) (the exact conversion to absolute temperature is obtained by adding 273.15 to the temperature in degrees Celsius; in this case we approximate the term of conversion to 273),

27 ^o C + 273 = 300 ^o K

and substitute the values ​​into the equation we got

ρ = (100 g/mol)(0.5 atm) / (0.0821 L atm/mol ^oK )(300 ^oK )

and the value of density ρ that we obtain is:

ρ = 2.03g/l

How do we know if we are working with an ideal gas?

The ideal gas law precisely describes the ideal behavior of gases, and can be applied to real gases in certain situations. When the parameters of a real gas can be described with the ideal gas law, it is said that this gas, under those conditions, behaves like an ideal gas. In general, real gases behave like ideals at low pressure and low temperature. As both the pressure and the temperature increase, the interaction between the gas molecules increases, causing their behavior to deviate from the ideal.

References

• https://www.herramientasingenieria.com/onlinecalc/spa/densidad-gases-ideales/densidad-gases-ideales.html Accessed 03/8/2022. Gas density calculator.
• http://www.valvias.com/prontuario-propiedades-materiales-densidad-gases.php Accessed 03/8/2022. Gas density table.