A vessel with a volume of 0.5 m3 contains 20 mol of nitrogen. determine the nitrogen pressure at a temperature of 27 degrees.

To find the required nitrogen pressure in the vessel, we apply the Mendeleev-Clapeyron law: P * V = m / M * R * T = ν * R * T, whence we express: P = ν * R * T / V.

Constants and variables: ν – amount of substance (ν = 20 mol); R – universal gas constant (R = 8.31 J / (mol * K)); T – temperature (Т = 27 ºС = 300 К); V is the volume of the vessel (V = 0.5 m3).

Let’s calculate: P = ν * R * T / V = 20 * 8.31 * 300 / 0.5 = 99 720 Pa ≈ 100 kPa.

Answer: The taken nitrogen is in a vessel under a pressure of 100 kPa.