How many air molecules are in a room with a volume of 120 cubic meters at a temperature of 15 degrees

How many air molecules are in a room with a volume of 120 cubic meters at a temperature of 15 degrees and a pressure of 105 Pa.

To find the number of molecules in the room under consideration, we will use the formula: P * V = (m / M) * R * T = (N / Na) * R * T, whence we express: N = P * V * Na / (R * T).

Constants and variables: P – pressure (P = 10 ^ 5 Pa); V is the volume of the room (V = 120 m3); R – universal gas constant (R = 8.31 J / (mol * K)); Na – Avogadro’s number (Na = 6.02 * 10 ^ 23 mol-1); T – air temperature (T = 15 ºС = 288 K).

Calculation: N = P * V * Na / (R * T) = 10 ^ 5 * 120 * 6.02 * 10 ^ 23 / (8.31 * 288) = 3.02 * 10 ^ 27 molecules.