A can for the preparation of sparkling water has a volume of 5 cm ^ 2 and contains carbon dioxide under

| June 20, 2021 | education

A can for the preparation of sparkling water has a volume of 5 cm ^ 2 and contains carbon dioxide under a pressure of 1.6 MPa at a temperature of 30C. What is the mass of the gas in the can?

To find the value of the mass of the carbon dioxide used in the cartridge, we use the Mendeleev-Clapeyron equation: P * V = m * R * T / MCO2, from where we express: m = P * V * MCO2 / (R * T).

Constants and variables: P – pressure of the used carbon dioxide (P = 1.6 MPa = 1.6 * 10 ^ 6 Pa); V is the volume of the can (V = 5 cm3 = 5 * 10 ^ -6 m3); MСO2 – molar mass (MСO2 = 0.044 kg / mol); R – universal gas constant (R = 8.31 J / (K * mol)); T – abs. gas temperature (Т = 303 К = 30 ºС).

Calculation: m = P * V * MSO2 / (R * T) = 1.6 * 10 ^ 6 * 5 * 10 ^ -6 * 0.044 / (8.31 * 303) = 1.4 * 10 ^ -4 kg = 0.14 g.

Answer: The can contains 0.14 g of carbon dioxide.



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