How can gas density be calculated using the ideal gas law?

The ideal gas law, represented by the equation PV = nRT, relates the pressure, volume, number of moles, and temperature of an ideal gas. To derive a formula for gas density, it's important to recall that density (d) is defined as mass (m) per unit volume (V).

For a gas, we can express the number of moles (n) in terms of mass and molar mass (M). The number of moles is given by the relationship n = m/M. By substituting this into the ideal gas law, we can rearrange the equation.

Starting with the ideal gas law:

PV = nRT

Substituting n with m/M:

PV = (m/M)RT

Now, rearranging this to isolate the mass (m):

m = (PV * M) / R*T

To find density d, we recognize that d = m/V. Substituting for m in the density equation gives:

d = (PV * M) / (RTV)

This simplifies to:

d = (PM) / (RT)

Thus, the formula density (d) = (PM) / (RT) accurately describes how to calculate gas density using the ideal gas