Question

Alum is found to contain hydrated monovalent cation ${{\left[ M{{({{H}_{2}}O)}_{6}} \right]}^{+}}$, trivalent cation \[{{\left[ {M}'{{({{H}_{2}}O)}_{6}} \right]}^{3+}}\] and $SO_{4}^{2-}$ in the ratio of:
(A)- $1:1:1$
(B)- $1:2:3$
(C)- $1:3:2$
(D)- $1:1:2$

Answer 1

Hint: Alums refers to the class of hydrated double salts of aluminum sulphate with sulphate of monovalent cation of sodium ($N{{a}^{+}}$), potassium (${{K}^{+}}$), ammonium ($NH_{4}^{+}$).
The general formula for alums is \[{{M}_{2}}S{{O}_{4}}\cdot {{{M}'}_{2}}{{(S{{O}_{4}})}_{3}}\cdot 24{{H}_{2}}O\], where M is a monovalent cation and ${M}'$ is a trivalent cation.

Complete answer:
Alums consist of sulphate of a monovalent and a trivalent cation.
Trivalent cation is generally aluminum ($A{{l}^{3+}}$), thus we also define alums as double sulphate salts of aluminum.
Monovalent cation is generally potassium (${{K}^{+}}$), sodium ($N{{a}^{+}}$) or ammonium ($NH_{4}^{+}$) thus, depending on the type of monovalent cation, they are named as potash alum, sodium alum, etc.
Molecular formulas of some of the important alums are:
Potassium aluminum sulphate of potash alum: ${{K}_{2}}S{{O}_{4}}\cdot A{{l}_{2}}{{(S{{O}_{4}})}_{3}}\cdot 24{{H}_{2}}O$
Sodium aluminum sulphate or sodium alum: $N{{a}_{2}}S{{O}_{4}}\cdot A{{l}_{2}}{{(S{{O}_{4}})}_{3}}\cdot 24{{H}_{2}}O$
Ammonium aluminum sulphate :${{(N{{H}_{4}})}_{2}}S{{O}_{4}}\cdot A{{l}_{2}}{{(S{{O}_{4}})}_{3}}\cdot 24{{H}_{2}}O$
Let us take potash alum and proceed to find the ratio of monovalent, trivalent and sulphate ions.
We know that the molecular formula for potash alum is
     ${{K}_{2}}S{{O}_{4}}\cdot A{{l}_{2}}{{(S{{O}_{4}})}_{3}}\cdot 24{{H}_{2}}O$
We can see that there are 2 ${{K}^{+}}$ , 2$A{{l}^{3+}}$ and 4 $SO_{4}^{2-}$ ions in potash alum, i.e.
     \[\begin{align}
  & 2{{K}^{+}}:2A{{l}^{3+}}:4SO_{4}^{2-} \\
 & \Rightarrow 1{{K}^{+}}:1A{{l}^{3+}}:2SO_{4}^{2-} \\
\end{align}\]
Therefore, the ratio of ${{K}^{+}}$, $A{{l}^{3+}}$ and $SO_{4}^{2-}$ ions in potash alum is $1:1:2$.
These ions are hydrated by six water molecules each in alums, i.e. ${{\left[ K{{({{H}_{2}}O)}_{6}} \right]}^{+}}$and \[{{\left[ Al{{({{H}_{2}}O)}_{6}} \right]}^{3+}}\].
In general, alums have the ratio of hydrated monovalent cation ${{\left[ M{{({{H}_{2}}O)}_{6}} \right]}^{+}}$, trivalent cation \[{{\left[ {M}'{{({{H}_{2}}O)}_{6}} \right]}^{3+}}\] and $SO_{4}^{2-}$ as $1:1:2$.

Hence, the correct option is (D).

Note:
Note that monovalent and trivalent cations are hydrated by water due to their small sizes. Six molecules of water surround each cation to form hydrated cations. So do not get confused about why the six molecules of water are written with the monovalent and trivalent ions. These water molecules are represented in the formula as water of crystallization.