The concentration of cation vacancies in NaCl crystal doped with CdCl2 is found to be 6.02x1016 mol-1. What is the concentration of CdCl2 added to it?

To determine the concentration of CdCl2 added to the NaCl crystal, we need to understand the relationship between the cation vacancies created and the amount of CdCl2 doped into the NaCl. When CdCl2 is introduced into the NaCl lattice, it replaces some of the sodium ions (Na+) and creates vacancies in the cation sublattice. This process is essential for understanding how doping affects the properties of ionic crystals.

Understanding Cation Vacancies

In a pure NaCl crystal, sodium ions and chloride ions are arranged in a face-centered cubic structure. When CdCl2 is added, cadmium ions (Cd²⁺) can substitute for sodium ions. Each time a Cd²⁺ ion replaces a Na⁺ ion, it creates a cation vacancy because the charge balance must be maintained. This means that for every Cd²⁺ ion introduced, one Na⁺ ion is removed, leading to the formation of a vacancy.

Calculating the Concentration of CdCl2

The concentration of cation vacancies is given as 6.02 x 10¹⁶ mol^-1. Since each Cd²⁺ ion creates one cation vacancy, the concentration of Cd²⁺ ions in the crystal will be equal to the concentration of cation vacancies. Therefore, the concentration of Cd²⁺ ions is also 6.02 x 10¹⁶ mol^-1.

Relating CdCl2 to Cd²⁺ Concentration

CdCl2 dissociates in solution to produce one Cd²⁺ ion and two Cl⁻ ions. Thus, for every mole of CdCl2 that dissolves, it contributes one mole of Cd²⁺ ions. Therefore, the concentration of CdCl2 added to the NaCl crystal is directly equal to the concentration of Cd²⁺ ions, which we have already established as 6.02 x 10¹⁶ mol^-1.

Final Answer

In summary, the concentration of CdCl2 added to the NaCl crystal is also 6.02 x 10¹⁶ mol^-1. This relationship highlights the direct connection between the dopant concentration and the resulting cation vacancies in the crystal structure.