Question

At a given temperature T, gases Ne, Ar, Xe and Kr are found to deviate from ideal gas behavior. Their equation of state is given as \(p = \frac{{{\rm{RT}}}}{{{\rm{V}} - {\rm{b}}}}\) at T.

Here, b is the van der Waals constant. Which gas will exhibit steepest increase in the plot of Z (compression factor) vs p?
1. Xe
2. Kr
3. Ne
4. Ar

Answer 1

Correct Answer - Option 1 : Xe

Concept:

The equation of state is given as

\(p = \frac{{RT}}{{V - b}}\)

P(V-b) = RT

Where, b is the van der Waal’s constant

P is pressure

T is temperature

V is Volume

R is Constant.

⇒ pV- pb = RT

\(\frac{{{\rm{pV}}}}{{{\rm{RT}}}}{\rm{\;}} - \frac{{{\rm{pb}}}}{{{\rm{RT}}}}{\rm{\;}} = 1\)

\(\frac{{{\rm{PV}}}}{{{\rm{RT}}}} = {\rm{Z}}\) (Compressibility factor)

\(\Rightarrow {\rm{Z\;}} = {\rm{\;}}1 + \frac{{{\rm{pb}}}}{{{\rm{RT}}}}{\rm{\;}}\)

Z > 1

Z ∝ b

Slope of Z vs P curve (straight line) = \(\frac{{\rm{b}}}{{{\rm{RT}}}}\)

 Higher the value of b, steeper will be the curve, constant ‘b’ value depends on size of atom or molecule.

Xenon is a chemical element with the symbol Xe and atomic number 54. It is a colorless, dense, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, xenon can undergo a few chemical reactions such as the formation of xenon hexafluoroplatinate, the first noble gas compound to be synthesized.