Question

the density of a noble gas is 2.71 g/l at 3.00 atm and 0°c. identify the gas.

Explanation:

Step1: Use the ideal gas law in density form

The ideal gas law can be written as \(PV = nRT\). Since \(n=\frac{m}{M}\) (where \(m\) is mass and \(M\) is molar mass), and \(
ho=\frac{m}{V}\) (density), we can rewrite the ideal gas law as \(P=\frac{
ho RT}{M}\), then \(M = \frac{
ho RT}{P}\)

Step2: Substitute the given values

Given \(
ho = 2.71\space g/L\), \(P=3.00\space atm\), \(T = 273\space K\) (since \(0^{\circ}C=273\space K\)), and \(R = 0.0821\space L\cdot atm/(mol\cdot K)\)

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The molar mass of neon (\(\ce{Ne}\)) is approximately \(20.2\space g/mol\)

Answer:

Neon ($\ce{Ne}$)