To determine the correctly balanced chemical equation for the reaction of KOH and [tex]\( H_2SO_4 \)[/tex], we must follow these steps:
1. Identify the reactants and products:
- Reactants: [tex]\( KOH \)[/tex] (potassium hydroxide) and [tex]\( H_2SO_4 \)[/tex] (sulfuric acid).
- Products: [tex]\( K_2SO_4 \)[/tex] (potassium sulfate) and [tex]\( H_2O \)[/tex] (water).
2. Write the unbalanced chemical equation:
[tex]\[
KOH + H_2SO_4 \rightarrow K_2SO_4 + H_2O
\][/tex]
3. Balance the chemical equation:
- Count the number of atoms of each element on both the reactant and product sides.
- Adjust coefficients to balance each type of atom.
4. Step-by-step balancing:
- Initially, the equation is:
[tex]\[
KOH + H_2SO_4 \rightarrow K_2SO_4 + H_2O
\][/tex]
- Balance potassium (K) atoms: There are 2 potassium atoms in [tex]\( K_2SO_4 \)[/tex], so we need 2 [tex]\( KOH \)[/tex]:
[tex]\[
2 KOH + H_2SO_4 \rightarrow K_2SO_4 + H_2O
\][/tex]
- Balance hydrogen (H) and oxygen (O) atoms: On the left side, we have (2 from [tex]\( KOH \)[/tex] and 2 from [tex]\( H_2SO_4 \)[/tex], total = 4 H) and on the right side, we need 4 H, requiring 2 [tex]\( H_2O \)[/tex].
[tex]\[
2 KOH + H_2SO_4 \rightarrow K_2SO_4 + 2 H_2O
\][/tex]
The final balanced chemical equation is:
[tex]\[
2 KOH + H_2SO_4 \rightarrow K_2SO_4 + 2 H_2O
\][/tex]
Thus, the correctly balanced chemical equation for the reaction of KOH and [tex]\( H_2SO_4 \)[/tex] is:
[tex]\[
2 KOH + H_2SO_4 \rightarrow K_2SO_4 + 2 H_2O
\][/tex]
Among the given options, the correct one is option number 3:
[tex]\[
2 KOH + H_2SO_4 \rightarrow K_2SO_4 + 2 H_2O
\][/tex]
