Question

The concentration of cation vacancies when \[NaCl\] is doped with \[{{10}^{-3}}\] mole percent of \[SrC{{l}_{2}}\] is:
A) \[6.023\times {{10}^{20}}\]
B) \[6.023\times {{10}^{23}}\]
C) \[6.023\times {{10}^{21}}\]
D) \[6.023\times {{10}^{18}}\]

Answer 1

Hint: Find out the no. of moles of \[SrC{{l}_{2}}\] present in 100 moles of \[NaCl\]as mole percent of \[SrC{{l}_{2}}\]is given. Then find the doping of I mole of \[NaCl\]and correspondingly we will find the no. of cation vacancies. For concentration multiply the cation vacancies with Avogadro number.

Complete Step By Step Solution: Given:\[NaCl\] is doped with \[{{10}^{-3}}\] mole percent of \[SrC{{l}_{2}}\]

 It means 100 moles of \[NaCl\] are doped with \[0.001~\] moles of \[SrC{{l}_{2}}\]

1 mole of \[NaCl\] is doped with \[\dfrac{0.001}{100}\] moles of \[SrC{{l}_{2}}\] ​ =\[{{10}^{-5}}\] moles of \[S{{r}^{2+}}\] cations.
 And one \[S{{r}^{2+}}\] ion creates one cation vacancy.

 So, \[{{10}^{-5}}\] moles of \[S{{r}^{2+}}\]ion will create \[{{10}^{-5}}\] moles of cation vacancies which corresponds to \[{{10}^{-5}}\times 6.023\times {{10}^{23}}\]= \[6.023\times {{10}^{18}}\]cation vacancies for one mole of \[NaCl\].

So, the correct option is D.

Additional Information: Defect due to the cation vacancy is Fresnel defect or dislocation defect. It is a type of point defect in crystalline solids named after its discoverer Yaakov Fresnel. The defect forms when an atom or smaller ion (usually cation) leaves its place in the lattice, creating a vacancy, and becomes an interstitial by lodging in a nearby location. In elemental systems, they are primarily generated during particle irradiation as their formation enthalpy is typically much higher than for other point defects. In ionic crystals, which usually possess low coordination numbers or a considerable disparity in the sizes of the ions, this defect can be generated also spontaneously, where the smaller ion (usually the cation) is dislocated.
Fresnel defects are exhibited in ionic solids with a large size difference between the anion and cation (with the cation usually smaller)

Some examples of solids which exhibit Fresnel defects:
a)zinc sulfide
b)silver(I) chloride
c)silver(I) bromide
These are due to the comparatively smaller size of zinc and silver ions.

\[SrC{{l}_{2}}\]: It is a salt of strontium and chloride. It is a typical salt, forming neutral aqueous solutions. Like all compounds of \[Sr\], this salt emits a bright red color in a flame. Its molar mass is \[158.53~\] g/mol. The coordinate geometry of Strontium chloride is Octahedral. It is odorless white crystalline solid.

Note: Study the types of doping and its effect. The reason for the creation of vacancies and the defects it can lead to. Study the various types of Defects, the reason behind the occurrence of such defects, compounds exhibiting them, examples of cation vacancies and anion vacancies, concept of moles and the relation with Avogadro number.