A 20L bottle contains 4kg of carbon dioxide at a temperature of 15 degrees Celsius.

univerkov | September 30, 2021 | education

A 20L bottle contains 4kg of carbon dioxide at a temperature of 15 degrees Celsius. Find the gas pressure in the cylinder.

Data: V (volume of a carbon dioxide cylinder) = 20 l = 20 * 10 ^ -3 m3; m (mass of carbon dioxide in the cylinder) = 4 kg; Т (absolute temperature of carbon dioxide) = 15 ºС = 288 K.

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

We express the pressure of carbon dioxide in the cylinder from the formula: P * V = (m / M) * R * T, whence P = m * R * T / (V * M).

Calculation: P = 4 * 8.31 * 288 / (0.44 * 20 * 10 ^ -3) ≈ 1 * 10 ^ 6 Pa = 1 MPa.

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