Questions: A 0.437 g sample of an unknown pure noble gas occupies a volume of 0.335 L at a pressure of 1.00 atm and a temperature of 100.0°C. The unknown gas is most likely krypton, xenon, helium, argon, neon.

Solution Steps

To use the ideal gas law, we need the temperature in Kelvin. Convert from Celsius to Kelvin:

\[ T = 100.0 + 273.15 = 373.15 \, \text{K} \]

The ideal gas law is given by:

\[ PV = nRT \]

where:

• \( P = 1.00 \, \text{atm} \)
• \( V = 0.335 \, \text{L} \)
• \( R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \)
• \( T = 373.15 \, \text{K} \)

Solve for \( n \) (moles of gas):

\[ n = \frac{PV}{RT} = \frac{1.00 \times 0.335}{0.0821 \times 373.15} \]

\[ n \approx 0.0109 \, \text{mol} \]

The molar mass \( M \) is calculated using the mass of the gas and the number of moles:

\[ M = \frac{\text{mass}}{n} = \frac{0.437 \, \text{g}}{0.0109 \, \text{mol}} \]

\[ M \approx 40.0927 \, \text{g/mol} \]

Compare the calculated molar mass to the known molar masses of noble gases:

• Helium: 4.0026 g/mol
• Neon: 20.1797 g/mol
• Argon: 39.948 g/mol
• Krypton: 83.798 g/mol
• Xenon: 131.293 g/mol

The calculated molar mass is closest to that of argon.

Final Answer