Question

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.

Answer 1

Answer:

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