How many air molecules are there in a room with a volume of 240 m ^ 3 at a temperature of 15 ° C and a pressure of 100 kPa.

To calculate the number of molecules contained in a given room, we will use the formula: P * V = (N / Na) * R * T, from where we express: N = P * V * Na / (R * T).

Constants and variables: P – air pressure (P = 100 kPa or 10 ^ 5 Pa); V is the volume of the room (V = 240 m3); R – gas constant (R = 8.31 J / (mol * K)); Na – Avogadro’s number (Na = 6.02 * 10 ^ 23 mol-1); T – room air temperature (T = 15 ºС or 288 K).

Calculation: N = 10 ^ 5 * 240 * 6.02 * 10 ^ 23 / (8.31 * 288) = 6.04 * 10 ^ 27 molecules.