Question

The set of numerical coefficients that balances the equation
\[{{K}_{2}}Cr{{O}_{4}}+HCl\to {{K}_{2}}C{{r}_{2}}{{O}_{7}}+KCl+{{H}_{2}}O\]
(A) 1,1,2,2,1
(B) 2,2,1,1,1
(C) 2,1,1,2,1
(D) 2,2,1,2,1

Answer 1

Hint: To solve this question, we first need to balance this equation. A reaction in which the number of atoms involved in a reaction is equal for each element on both the reactant side and the product side is known as a balanced chemical equation. A chemical reaction satisfies the law of conservation of matter.

Complete answer:
In a chemical equation, there are two types of numbers that determine the number of atoms and molecules. These are coefficients and subscripts.
Coefficients indicate the number of molecules of a substance that is used or produced or produced in a chemical reaction.
Subscripts are a part of the chemical formulas that shows the ratio of atoms of a molecule and determines its chemical identity. They are not changed while balancing an equation.
A chemical equation can be balanced by using these simple steps.
- First, we write the unbalanced equation of the reaction.
\[{{K}_{2}}Cr{{O}_{4}}+HCl\to {{K}_{2}}C{{r}_{2}}{{O}_{7}}+KCl+{{H}_{2}}O\]
- Now we compare the number of atoms of each element on the product and the reactant side.

Atom	Reactant	Product
K	2	3
Cr	1	2
O	4	8
H	1	2
Cl	1	1

- Now we add stoichiometric coefficient to the molecules containing elements that have a different number of atoms on the reactant and product side. The most complex molecule is balanced first. Oxygen and hydrogen are balanced last.
Since there are 2 Cr atoms on the product side, so there must be 2 Cr atoms on the reactant side
\[2{{K}_{2}}Cr{{O}_{4}}+HCl\to {{K}_{2}}C{{r}_{2}}{{O}_{7}}+KCl+{{H}_{2}}O\]

Atom	Reactant	Product
K	4	3
Cr	2	2
O	8	8
H	1	2
Cl	1	1

Now, to balance K atoms,
\[2{{K}_{2}}Cr{{O}_{4}}+HCl\to {{K}_{2}}C{{r}_{2}}{{O}_{7}}+2KCl+{{H}_{2}}O\]

Atom	Reactant	Product
K	4	4
Cr	2	2
O	8	8
H	1	2
Cl	1	2

Now, to balance Cl atoms,
\[2{{K}_{2}}Cr{{O}_{4}}+2HCl\to {{K}_{2}}C{{r}_{2}}{{O}_{7}}+2KCl+{{H}_{2}}O\]

Atom	Reactant	Product
K	4	4
Cr	2	2
O	8	8
H	2	2
Cl	2	2

- The equation is now balanced, as the number of atoms of each molecule is equal on both the product side as well as the reactant side.

So, the set of numerical coefficients that balance the equation are option (D) 2, 2, 1, 2, 1.

Note:
The addition of hydrochloric acid (HCl) to potassium chromate (${{K}_{2}}Cr{{O}_{4}}$) is a neutralization reaction and forms two salts ${{K}_{2}}C{{r}_{2}}{{O}_{7}}$ and KCl along with a water molecule. Here HCl acts as an acid and ${{K}_{2}}Cr{{O}_{4}}$ acts as a base.