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How can I balance this equation?
${\text{AlB}}{{\text{r}}_{\text{3}}} + {{\text{K}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} \to \_{\text{KBr}} + \_{\text{A}}{{\text{l}}_2}{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)_3}$

Last updated date: 13th Jun 2024
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Hint: We know that a chemical is called a balanced chemical equation when the number of atoms of all elements is equal in both the product and reactant side of the reaction. While balancing a chemical equation we also need to equate charges if any charge is present.

Complete step by step answer:
The given chemical equation is,
${\text{AlB}}{{\text{r}}_{\text{3}}} + {{\text{K}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} \to {\text{KBr}} + {\text{A}}{{\text{l}}_2}{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)_3}$
To balance the K atoms, we have to add coefficient 6 to KBr and 3 to K2SO4. This action equates the number of K atoms in both sides of the reaction.
${\text{AlB}}{{\text{r}}_{\text{3}}} + 3{{\text{K}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} \to 6{\text{KBr}} + {\text{A}}{{\text{l}}_2}{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)_3}$
Now, to balance the number of aluminium atoms, we have to add coefficient 2 to ${\text{AlB}}{{\text{r}}_{\text{3}}}$.
${\text{2AlB}}{{\text{r}}_{\text{3}}} + 3{{\text{K}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} \to 6{\text{KBr}} + {\text{A}}{{\text{l}}_2}{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)_3}$
Now, in both sides (Product and reactant) of the reaction,
The number of atoms of Al=2
The number of atoms of Br=6
The number of atoms of K=6
The number of atoms of S =3
The number of atoms of O=12
So, the above equation is the balanced chemical equation.

Additional Information:
The given reaction is,
${\text{2AlB}}{{\text{r}}_{\text{3}}} + 3{{\text{K}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} \to 6{\text{KBr}} + {\text{A}}{{\text{l}}_2}{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)_3}$
It is a double displacement reaction. In a double displacement reaction, two ionic compounds in aqueous solution switch anions and produce two new compounds. Here, aluminium forms a compound with sulphate ion and potassium forms a compound with bromine by switching each other’s ions.

Note: It is to be noted that a chemical reaction needs to be balanced to follow the law of conservation of mass. According to this law, the creation or destruction of mass is not possible. So, the number of atoms present before the reaction must be equal to the number of atoms after the reaction.