Question

The decreasing order of solubility of silver halide is:
A.\[AgI{\text{ }} > {\text{ }}AgBr{\text{ }} > {\text{ }}AgCl{\text{ }} > {\text{ }}AgF\]
B.\[AgF{\text{ }} > {\text{ }}AgCl{\text{ }} > {\text{ }}AgBr{\text{ }} > {\text{ }}AgI\]
C.\[AgCl{\text{ }} > {\text{ }}AgF{\text{ }} > {\text{ }}AgBr{\text{ }} > {\text{ }}AgI\]
D.\[AgBr{\text{ }} > {\text{ }}AgF{\text{ }} > {\text{ }}AgI{\text{ }} > {\text{ }}AgCl\]

Answer 1

Hint:Solubility is dependent on the ionic size and hydration energy of the halides in the salts.

Complete step by step answer:
The Halides in consideration here are AgCl, AgBr, AgI and AgF.
Now the question under discussion is the solubility of the salts. But to better understand this comparison of solubility, we must first understand a few properties of halides. And more importantly, we must understand the trends that these properties follow or obey throughout the periodic table.
Ionic size: To achieve better stability, elements tend to either give or take their valence electrons. This process leads to the formation of charged ions. Depending on whether the element or compound gives or takes electrons, the ionic size of this newly formed ion can be determined correspondingly. Ionic size is nothing but ionic radius.
Now all the halides belong to the same period. Hence their atomic sizes keep on increasing as we move down the period. If we keep this trend in mind, then their ionic sizes also increase as we move down the period.
Hence, the trend in the ionic sizes in halogens is as follows:
${F^ - } < C{l^ - } < B{r^ - } < {I^ - }$
Hydration Energy: Hydration energy is the amount of energy released when one mole of ions undergo hydration. When a compound is dissolved, the solubility depends upon the amount of hydration energy released. If there is a net release of energy, i.e., if more energy is released upon hydration than that is stored in the ionic solid lattice, then solubility is favored. If there is a net gain of energy, i.e., if less energy is released on hydration than that is stored in the ionic solid lattice, then solubility is unfavored.
As we move down the period, Hydration energy decreases. Hence solubility also decreases as we move down a period. Hence, the trend for solubility in halides due to hydration energy can be shown as:
${F^ - } < C{l^ - } < B{r^ - } < {I^ - }$
Hence, from the above explanation, we can conclude that, the decreasing order of solubility of silver halide is:
\[AgF{\text{ }} > {\text{ }}AgCl{\text{ }} > {\text{ }}AgBr{\text{ }} > {\text{ }}AgI\]

Hence, Option B is the correct.

Note:
Hydration energy is the energy liberated when something is dissolved in water. If the hydration energy is greater than lattice energy, the substance will be soluble. Lattice energy is the amount of energy which bound the crystal lattice.