Respuesta :
The molar mass of the gas 49.0 g/mol.
Given:
Unknown gas with a density of 2.00 g/L at 1.00 atm and 25.0 °C.
To find:
The molar mass of an unknown gas.
Solution:
The mass of gas = m
The volume of the gas =V
The molar mass of the gas = M
The density of the gas = d = 2.00 g/L
[tex]d=\frac{m}{V}[/tex]
The pressure of the gas = P
The temperature of the gas T = 25.0 °C = 25.0+273.15 K=298.15 K
The ideal gas equation:
[tex]PV=nRT\\\\PV=\frac{\text{Mass of gas(m)}}{\text{Molar mass of gas(M)}}RT\\\\PM=\frac{m}{V}RT \\\\PM=dRT\\\\1 atm\times M=2.00 g/L\times 0.0821 atm L/molK\times 298.15 K\\\\M=\frac{2.00 g/L\times 0.0821 atm L/molK\times 298.15 K}{1 atm}\\\\M=48.96 g/mol \approx 49.0 g/mol[/tex]
The molar mass of the gas 49.0 g/mol.
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