Hydrogen chloride gas is held at a fixed pressure of ( )

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric fields in matter · Electric fields in matter

The Boundary-Value Problem, Ch Molecular polarisability, permanent dipoles and the Clausius-Mossotti relation

Problem

Hydrogen chloride gas is held at a fixed pressure of

1.000\,\mathrm{atm}

(

1.013\times10^5\,\mathrm{Pa}

). The measured electric susceptibility is

\chi_e = 2.81\times10^{-3}

T=350\,\mathrm{K}

and

\chi_e = 1.82\times10^{-3}

T=450\,\mathrm{K}

. The gas is dilute enough that the local field equals the macroscopic field. ((a)) Find the number density

N_v

at each temperature, treating the gas as ideal. ((b)) Compute

\varepsilon_0\chi_e/N_v

at each temperature and use the Debye equation

\varepsilon_0\chi_e/N_v = \alpha + \dfrac{p^2}{3k_B}\dfrac{1}{T}

to find the slope and intercept of the line through the two points. ((c)) Read off the permanent dipole moment

p

(in

\mathrm{C\,m}

and in debye,

1\,\mathrm{D}=3.336\times10^{-30}\,\mathrm{C\,m}

) and the electronic polarisability volume

\alpha/4\pi\varepsilon_0