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14 October, 17:44

A closed vessel having a volume of 1 liter holds 2.5 * 1022 molecules of carbon dioxide gas. Determine the mass of CO2 present, in kg and the number of moles, in kmol. Determine the specific volume of the CO2, in m3/kg, and the molar specific volume, in m3/kmol.

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  1. 14 October, 18:52
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    mass = 1.8x10⁻³ kg; number of moles = 4.1x10⁻⁵ kmol; specific volume = 0.55 m³/kg; molar specific volume = 24.4 m³/kmol

    Explanation:

    By the Avogadro's number, 1 mol of the matter has 6.02x10²³ molecules, thus, the number of moles (n) is the number of molecules presented divided by Avogadro's number:

    n = 2.5x10²²/6.02x10²³

    n = 0.041 mol

    n = 4.1x10⁻⁵ kmol

    The molar mass of CO₂ is 44 g/mol (12 g/mol of C + 2*16g/mol of O), and the mass is the number of moles multiplied by the molar mass:

    m = 0.041 mol * 44 g/mol

    m = 1.804 g

    m = 1.8x10⁻³ kg

    The specific volume (v) is the volume (1L = 0.001 m³) divided by the mass, and it represents how much volume is presented in each part of the mass:

    v = 0.001/1.8x10⁻³

    v = 0.55 m³/kg

    The molar specific volume (nv) is the volume divided by the number of moles, and it represents how much volume is presented in each part of the mol:

    nv = 0.001/4.1x10⁻⁵

    nv = 24.4 m³/kmol
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