For a pressure of 1.00 atm and a temperature of 24.0 ∘C, use the ideal-gas law to estimate the number of air molecules in the room. Assume all the air is N2. Express your answer to three significant figures and include the appropriate units

mass of air = 324 kg

Explanation:

mass of air = moles of air * molecular weight (N₂)

moles of air = PV / RT

Given that

P = 1 atm

Volume of room = 282 m³

R = 0.082L atm mol⁻¹k⁻¹

= (1 * 282 * 10³) / (0.0821 * 297)

= 11.565 * 10³mol

molecular weight of N₂ = 28g/mol

mass of air = (11.565 * 10³) mol * 0.028kg/mol

= 323.8kg

to three significant figures = 324 kg