Which of the following has no existence?
A.${K_2}S{O_4}.A{l_2}{\left( {S{O_4}} \right)_3}.24{H_2}O$
B.${\left( {N{H_4}} \right)_2}S{O_4}.C{r_2}{\left( {S{O_4}} \right)_3}.24{H_2}O$
C.$L{i_2}S{O_4}.A{l_2}{\left( {S{O_4}} \right)_3}.24{H_2}O$
D.${K_2}S{O_4}.F{e_2}{\left( {S{O_4}} \right)_3}.24{H_2}O$

Hint: To answer this question you must recall the characteristics of the class of double sulphates of aluminium commonly known as alums. The chromium analogs of alums are known as chrome alums. Alums are hydrates of double sulphate salts of aluminium. The size of cation attached to aluminium should be of comparable size.

Complete step by step answer:
Alums are generally the hydrates of a double sulphate salt of aluminium. It is represented by the chemical formula $X.A{l_2}{\left( {S{O_4}} \right)_3}.12{H_2}O$, where $X$ is a monovalent cation.
Option A is potassium alum or potash alums it is known commonly. It is the most widely used alum and thus undoubtedly has existence.
Option B shows ammonium chrome alum which too is an existent crystalline salt
Option C, has the compound $L{i_2}S{O_4}.A{l_2}{\left( {S{O_4}} \right)_3}.24{H_2}O$
The monovalent cation in the alum is given as lithium in this case. In 1902, a rule was stated for alums, which said that alums are formed easily if the alkali metal cation or the monovalent cation $X$ is big in size. We know that lithium ions are very small in size. As a result, it is not able to occupy the lattice positions in the alum lattice which are too big in size for it. Thus, this compound does not exist.
Option D is ferric potassium alum and is obtained by mixing concentrated solutions of ferric and potassium sulphates.

Hence, the correct option is C.

Note:
One of the most common and important alums contains potassium as the monovalent cation and is known as potassium alum. Thus the entire class of these hydrated double sulphates is represented by the same formula and structure. Potassium alum has many vast applications and is used widely in dyeing, water purification, textiles and leather tanning. In some cases, the aluminium ion may be replaced by another trivalent metal cation most commonly chromium.