MCQ Detailed View

The relationship between density, molar mass, and the ideal gas law is a key concept in physical chemistry. The given problem provides the density of a gas as 1.964 g dm⁻³ at 273 K and 76 cm Hg. At standard conditions, the ideal gas equation can be applied to determine the identity of the gas.

The ideal gas law is written as $PV=nRT$. Rearranging in terms of molar mass gives the formula:

M=dRTPM = \frac{dRT}{P}M=PdRT

Here, $M$ is the molar mass of the gas, $d$ is the density in g dm⁻³, $R$ is the gas constant (0.0821 dm³ atm mol⁻¹ K⁻¹), $T$ is the absolute temperature in Kelvin, and $P$ is the pressure in atm.

Substituting the values:

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  $d=1.964$ g dm⁻³

  
  


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  $R=0.0821$

  
  


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  $T=273$ K

  
  


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  $P=1$ atm (since 76 cm Hg = 1 atm)

  
  

M=1.964×0.0821×2731M = \frac{1.964 \times 0.0821 \times 273}{1}M=11.964×0.0821×273 $$M\approx 44g/mol$$

The calculated molar mass is approximately 44 g/mol. Comparing with the given options:

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  Methane (CH₄) = 16 g/mol

  
  


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  Carbon dioxide (CO₂) = 44 g/mol

  
  


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  Ethene (C₂H₄) = 28 g/mol

  
  


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  Xenon (Xe) = 131 g/mol

  
  

Only carbon dioxide has a molar mass of 44 g/mol, which matches the calculation. Therefore, the gas is CO₂.

This example demonstrates how gas density measurements can be used to determine molar mass and identify an unknown gas. It highlights the practical use of the ideal gas equation in analytical chemistry and physical chemistry for connecting measurable properties like density and pressure to molecular identity.