The Question is from neet-chemistry the-solid-state stoichiometric-defects-non-stoichiometric-defects, and it was created by the author Mr. S M HUSSAIN

Question

A crystal of NaCl is doped with $10^{-5}$ mol% of $SrCl_2$. What is the concentration of cation vacancies?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Defects in crystals, specifically cation vacancies due to doping.
 **Related Topics**:  Solid state chemistry, stoichiometry, doping of ionic crystals.
 **Prerequisites**: Understanding of ionic crystals, mole fraction, and the concept of charge neutrality.
## SOLUTION PATHWAY
**Given Information**:
  Doping concentration of $SrCl_2$ = $10^{-5}$ mol% = $10^{-5} / 100 = 10^{-7}$ mol/mol of NaCl
  $SrCl_2$ replaces $NaCl$ in the crystal lattice.
**Method & Steps**:
 1. Determine the effect of $SrCl_2$ doping on the crystal lattice.
  Reasoning: Each $Sr^{2+}$ ion replaces one $Na^+$ ion. To maintain charge neutrality, one cation vacancy is created for every $Sr^{2+}$ ion added.
  Formula/Rule: None explicitly, but the principle of charge neutrality is crucial.
 2. Calculate the concentration of cation vacancies.
  Working: Since one cation vacancy is created for each $Sr^{2+}$ ion, the concentration of cation vacancies is equal to the concentration of $SrCl_2$ added.
  Key Point: The concentration of $SrCl_2$ is given as $10^{-7}$ mol/mol of NaCl.
 3. State the final answer.
  Result: The concentration of cation vacancies is $10^{-7}$ mol/mol of NaCl.
  Verification: The answer is consistent with the principle of charge neutrality in ionic crystals.
 ## OPTION ANALYSIS
A ✓: $10^{-7}$ mol/mol of NaCl: Correct.  This directly reflects the mol% of $SrCl_2$ added, considering that one vacancy is created per $Sr^{2+}$ ion.
B :x: $10^{-5}$ mol/mol of NaCl: Incorrect. This is the mol% of $SrCl_2$ without accounting for the creation of cation vacancies.
C :x: $2 	imes 10^{-5}$ mol/mol of NaCl: Incorrect. This incorrectly doubles the concentration, ignoring the 1:1 ratio of SrCl2 to vacancies.
D :x: $10^{-9}$ mol/mol of NaCl: Incorrect. This is not a justified value based on the given information.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Ignoring the creation of cation vacancies to maintain charge neutrality: Remember that doping with a higher valence cation will create vacancies to balance the charge.
  2.Misinterpreting the mol%:  Make sure to convert the mol% to mol/mol of NaCl before calculating the concentration of vacancies.
 **Quick Tips**:
  1.For every $n+$ charged dopant replacing an $m+$ charged ion, $(n-m)$ cation vacancies are created.
  2.Always consider charge neutrality when dealing with ionic crystals and doping.

Mr. S M HUSSAIN · Answer

The correct Option is "$10^{-7}$ mol/mol of NaCl"

Mr. S M HUSSAIN · Answer

$10^{-5}$ mol/mol of NaCl

Mr. S M HUSSAIN · Answer

$2 	imes 10^{-5}$ mol/mol of NaCl

Mr. S M HUSSAIN · Answer

$10^{-9}$ mol/mol of NaCl

NEET Chemistry The Solid State Stoichiometric Defects, Non-Stoichiometric Defects MCQs

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