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Which of the following cannot be explained on the basis of Fajan’s rules?
A. $A{g_2}S$ is much less soluble than $A{g_2}O$
B. $Fe{(OH)_3}$ is much less soluble than $Fe{(OH)_2}$
C. $BaC{O_3}$ is much less soluble than $MgC{O_3}$
D. Melting point of $AlC{l_3}$ is much less than that of $NaCl$

Answer
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Hint: The elements that occur in nature are classified in the periodic table based on their atomic number. The elements in the atomic table are categorised in blocks that make them easier to correlate and thus make the comparison easier. The periodic table shows the trends in which various properties change based on the atomic number.

Complete answer:
Fajan’s rules in inorganic chemistry are the set of rules which tell whether a bond is ionic or covalent. All this prediction is made based on the size of the cations and the anions that participate in the bonding process.
If the ion has a low positive charge and the size of the cation is large along with the small size of the anion will make for an ionic bond. While high positive charge with small cation and large anion will make up a covalent bond.
According to the second rule which describes the polarizability of the anion, the effective nuclear charge in case of a large anion that usually holds the valence ion in its place is less. All this makes it more likely to be polarized by a cation.
The size of the $B{a^{2 + }}$ ion is larger so according to the Fajan’s rules it should be more soluble in the $MgC{O_3}$ solution but the compound containing barium ions is less soluble in the solution. This phenomenon is not able to be explained through the Fajan’s Rules.

So, the correct answer is Option C.

Note: The capability of the cation to distort the power and tendency of the anion is called the polarizing power while the tendency of the anion to become polarized by the effect of a cation is termed as polarizability.