Question

(a) Explain the Pauling method to determine ionic radii?
(b) Describe how noble gases are isolated from air by the Ramsay-Rayleigh method?

Answer 1

Hint: The ionic radius is the radius of an atom’s ion and it is the value assigned to the radius of an ion in a crystalline solid, assuming that the ions are spherical with a definite size. The ionic radii are the plural form of the ionic radius.
Ramsay-Rayleigh method: The vaporous blend that is liberated from oxygen and nitrogen is utilized for isolating the respectable gases.

Complete step-by-step answer:
(A) In a crystal lattice, the ionic radius is a proportion of the size of the ion’s particle. When formed, ionic molecules change in size as for their original ion. Cation radii will diminish and the anion radii will increment in size contrasted with their neutral particles.
Pauling has determined the radii of the particles based on the observed internuclear separation in four crystals to be specific.
NaF, KCl, CsI, and RbCl.
1) In every ionic crystal, the cations and anions are isoelectronic with inert gas setup.
${ K }^{ + }{ =2,8,8 }$
${ Cl }^{ - }{ =2,8,8 }$
These show inert gas (Ar) type configuration.
2) The cations and anions of an ionic crystal are thought to be in contact with one another and thus the total of their radii will be equivalent to the internuclear separation between them.
${ r\left( K \right) }^{ + }{ +r\left( Cl \right) }^{ - }{ =d\left( { K }^{ + }-{ Cl }^{ - } \right) }$ ……….(1)
where ${ r\left( K \right) }^{ + }$ = radius of potassium cation
${ r\left( Cl \right) }^{ - }$ = radius of chloride anion
${ d\left( { K }^{ + }-{ Cl }^{ - } \right) }$ = internuclear distance between them.
3) For a given noble gas setup the span of a particle is conversely corresponding to its effective atomic charge.
${ r\left( K^{ + } \right) }\infty \frac { 1 }{ Z\times \left( { K }^{ + } \right) } $…….(2)
${ r\left( { Cl }^{ - } \right) }\infty \frac { 1 }{ Z\times \left( { Cl }^{ - } \right) } $.......(3)
where, ${ Z(K) }^{ + }$ = effective nuclear charge of potassium cation
${ Z(Cl) }^{ - }$= effective nuclear charge of chloride anion
Now, when we combine equation (2) and (3), we get
$\frac { r\left( { K }^{ + } \right) }{ r\left( { Cl }^{ - } \right) } { = }\frac { { Z(K) }^{ + } }{ Z{ (Cl }^{ - }{ ) } } $ …..(4)
As we can see equations (1) and (4) are used to calculate the ionic radii.

(b) Isolation of noble gases from air by Ramsay-Rayleigh method:
This is finished utilizing coconut charcoal which adsorbs various gases at various temperatures. The property of adsorption to coconut charcoal increments with a nuclear load of the honorable gases. In this manner, helium which has the least nuclear weight absorbs the least while xenon with most extreme nuclear weight adsorbs firmly. The temperature at which the adsorption happens increments with the expansion in the nuclear weight.
The vaporous blend is passed into a twofold walled bulb containing coconut charcoal. The blend is held in the bulb for about ${ 60 }$ minutes. During this period the gases argon, krypton, and xenon get adsorbed while the helium and neon remain unadsorbed and are siphoned out. The blend of helium and neon are held independently in another bulb that is kept up at a temperature of ${ 93 K }$. At this temperature neon totally adsorbs to the coconut charcoal abandoning helium. Neon can be recuperated from the charcoal by warming.
Presently, the charcoal containing argon, krypton, and xenon are acquired in contact with another charcoal held at room temperature of ${ 80 K }$. Argon gets adsorbed onto the charcoal that is held at room temperature.
At last, the partition of xenon and krypton is accomplished by warming the charcoal to a temperature of ${ 183 K }$. At this temperature, krypton is liberated while xenon remains adsorbed to the charcoal.

Note: The possibility to make a mistake is that Pauling has observed ionic radii on the basis of internuclear distance, not the intermolecular distance. As internuclear distance is the distance between two nuclei in a molecule while the intermolecular distance is the distance between two metals.