To balance the chemical equation for the reaction [tex]\( H_2SO_4 + KOH \rightarrow H_2O + K_2SO_4 \)[/tex], we need to ensure that the number of atoms of each element is equal on both sides of the equation. Here is a step-by-step guide to achieving a balanced equation:
1. Write down the unbalanced equation:
[tex]\[
H_2SO_4 + KOH \rightarrow H_2O + K_2SO_4
\][/tex]
2. List the number of atoms of each element on both the reactant and product sides:
- Reactants:
- [tex]\( H_2SO_4 \)[/tex]: 2 H, 1 S, and 4 O
- [tex]\( KOH \)[/tex]: 1 K, 1 O, 1 H
- Products:
- [tex]\( H_2O \)[/tex]: 2 H, 1 O
- [tex]\( K_2SO_4 \)[/tex]: 2 K, 1 S, 4 O
3. Balance the elements that appear in only one compound on each side first:
- Sulfur appears only in H_2SO_4 and K_2SO_4, so it is already balanced with 1 sulfur atom on both sides.
4. Balance the potassium (K) atoms:
- There are 2 potassium atoms in K_2SO_4, so we need 2 molecules of KOH:
[tex]\[
H_2SO_4 + 2KOH \rightarrow H_2O + K_2SO_4
\][/tex]
- Now, the number of potassium atoms is balanced.
5. Balance the hydrogen (H) atoms next:
- Reactants: From the updated reactants, we have [tex]\( H_2SO_4 \)[/tex] (2 H atoms) + 2[tex]\( KOH \)[/tex] (each contributing 1 H atom) = 2 + 2 = 4 H atoms.
- Products: To balance the 4 H atoms, we need 2 molecules of [tex]\( H_2O \)[/tex], since each [tex]\( H_2O \)[/tex] contains 2 H atoms:
[tex]\[
H_2SO_4 + 2KOH \rightarrow 2H_2O + K_2SO_4
\][/tex]
6. Balance the oxygen (O) atoms:
- Reactants: [tex]\( H_2SO_4 \)[/tex] (4 O atoms) + 2[tex]\( KOH \)[/tex] (each contributing 1 O atom) = 4 + 2 = 6 O atoms.
- Products: [tex]\( 2H_2O \)[/tex] (each contributing 1 O atom) + [tex]\( K_2SO_4 \)[/tex] (4 O atoms) = 2 + 4 = 6 O atoms.
Now all the atoms balance out, and we have the balanced equation:
[tex]\[
H_2SO_4 + 2KOH \rightarrow 2H_2O + K_2SO_4
\][/tex]
The coefficients for [tex]\( a, b, c, \)[/tex] and [tex]\( d \)[/tex] are:
[tex]\[
a = 1, \, b = 2, \, c = 2, \, d = 1
\][/tex]
So, the final answer is:
[tex]\[
\begin{array}{l}
a = 1 \\
b = 2 \\
c = 2 \\
d = 1 \\
\end{array}
\][/tex]
