In a cylinder with a capacity of 50 liters at a temperature of 17 degrees C

In a cylinder with a capacity of 50 liters at a temperature of 17 degrees C there is carbon dioxide under a pressure of 5 MPa. Find the mass of the gas.

Initial data: V (cylinder capacity) = 50 l = 50 * 10 ^ -3 m3; Т (absolute temperature of carbon dioxide) = 17 ºС = 290 К; P (pressure of carbon dioxide in the cylinder) = 5 MPa = 5 * 10 ^ 6 Pa.

Constants: M (molar mass of carbon dioxide) = 44 g / mol = 0.044 kg / mol; R (universal gas constant) = 8.31 J / (mol * K).

The mass of carbon dioxide in the cylinder is determined from the formula: P * V = (m / M) * R * T, whence m = P * V * M / (R * T).

Calculation: m = 5 * 10 ^ 6 * 50 * 10 ^ -3 * 0.044 / (8.31 * 290) = 4.56 kg.