To balance the chemical equation for the reaction between a weak base (potassium nitrite, [tex]\( \text{KNO}_2 \)[/tex]) and a strong acid (sulfuric acid, [tex]\( \text{H}_2\text{SO}_4 \)[/tex]), we can write both the reactants and the products. The products of this reaction are potassium sulfate ([tex]\( \text{K}_2\text{SO}_4 \)[/tex]) and nitrous acid ([tex]\( \text{HNO}_2 \)[/tex]).
Starting with the unbalanced equation:
[tex]\[ \text{KNO}_2 (aq) + \text{H}_2\text{SO}_4 (aq) \rightarrow \text{K}_2\text{SO}_4 (aq) + \text{HNO}_2 (aq) \][/tex]
Let us ensure that there are equal numbers of each type of atom on both sides of the equation:
- Potassium (K): On the left, we have 1 atom from [tex]\( \text{KNO}_2 \)[/tex]. On the right, [tex]\( \text{K}_2\text{SO}_4 \)[/tex] provides 2 potassium atoms, so we need 2 [tex]\( \text{KNO}_2 \)[/tex] molecules on the left.
- Nitrogen (N): By adjusting the potassium, we now have 2 nitrogen atoms from 2 [tex]\( \text{KNO}_2 \)[/tex] molecules on the left. On the right, each [tex]\( \text{HNO}_2 \)[/tex] provides 1 nitrogen atom. Thus, we need 2 [tex]\( \text{HNO}_2 \)[/tex] molecules on the right.
- Sulfur (S): The sulfur content from [tex]\( \text{H}_2\text{SO}_4 \)[/tex] and [tex]\( \text{K}_2\text{SO}_4 \)[/tex] is already balanced with 1 sulfur atom on each side.
- Oxygen (O): On the left, we have 2 oxygen atoms from each [tex]\( \text{KNO}_2 \)[/tex] (total 4) plus 4 from [tex]\( \text{H}_2\text{SO}_4 \)[/tex] (total 8). On the right, [tex]\( \text{K}_2\text{SO}_4 \)[/tex] has 4 oxygen atoms, and each [tex]\( \text{HNO}_2 \)[/tex] has 2 (total 4), summing up to 8, which is balanced.
- Hydrogen (H): On the left, 2 hydrogen atoms from [tex]\( \text{H}_2\text{SO}_4 \)[/tex]. On the right, we have 2 molecules of [tex]\( \text{HNO}_2 \)[/tex], each contributing 1 hydrogen atom (total 4), which is balanced.
Following these corrections, the fully balanced equation is:
[tex]\[ 2 \text{KNO}_2 (aq) + \text{H}_2\text{SO}_4 (aq) \rightarrow \text{K}_2\text{SO}_4 (aq) + 2 \text{HNO}_2 (aq) \][/tex]
This balanced equation reflects the reaction's stoichiometry, ensuring every atom is accounted for and conserved.
