Question

The value of x in $KAl{\left( {S{O_4}} \right)_x} \cdot 12{H_2}O$ is:
A. 1
B. 2
C. 3
D. 4

Answer 1

Hint: We have to know that x in the given compound represents the number the number of atoms of sulfate. We can determine the number of atoms of sulfate using the charges of potassium, aluminum, and sulfate. We have to calculate the total charges of the cations and then compare with the charges of the anion to get the value of x..

Complete step by step answer:
The given compound is $KAl{\left( {S{O_4}} \right)_x} \cdot 12{H_2}O$.
We know that the charge of potassium ion is $ + 1$ and the charge on aluminum ion present would be $ + 3$. Let us calculate the total charges of the cation by adding the charges of potassium ion and aluminum ion.
The total charges present in the cation=${\text{Charge of potassium}} + {\text{Charge of aluminium}}$
The total charges present in the cation = $1 + 3$
The total charges present in the cation = $4$
The total charges present in the cation are four.
We know that the charges present on sulfate ions are \[ - 2\]. We know that the total number of charges present in the cation is equal to the total number of charges present in the anion. Each sulfate ion has charge of\[ - 2\]. In order to balance the charge of \[ + 4\]on cations, we need two sulfate ions to balance the charges. The completed chemical formula is $KAl{\left( {S{O_4}} \right)_2} \cdot 12{H_2}O$

Therefore, the correct option is B. .

Note: We have to know the name of $KAl{\left( {S{O_4}} \right)_2}$ is potassium alum/potash alum/potassium aluminum sulfate. Potassium alum is the double salt of sulfate of potassium and aluminum. The chemical name of $KAl{\left( {S{O_4}} \right)_2} \cdot 12{H_2}O$ is potassium aluminum sulfate dodecahydrate. We can use potassium alum in purification of water, tanning of leather, dyeing, baking powder, and fireproof textiles.