What is the estimated density of air at 300 K and 101,325 Pa using the ideal gas law?

To calculate the estimated density of air at a temperature of 300 K and a pressure of 101,325 Pa using the ideal gas law, the formula applied is:

[

PV = nRT

]

where:

• P is the pressure (Pa),

• V is the volume (m³),

• n is the number of moles of gas,

• R is the ideal gas constant (approximately 8.314 J/(mol·K)),

• T is the temperature (K).

Rearranging this equation to find the density (ρ) involves recognizing that density is mass (m) divided by volume (V). The number of moles can be expressed as:

[

n = \frac{m}{M}

]

where M is the molar mass of air, approximately 0.029 kg/mol.

Substituting for n in the ideal gas equation, we can write:

[

P = \left(\frac{m}{M}\right)RT/V

]

Rearranging gives us:

[

\rho = \frac{m}{V} = \frac{PM}{RT}

]

Now, substituting the known values:

• P = 101,325 Pa,