Answer :
To determine the correctly balanced chemical equation for the reaction between [tex]\( KOH \)[/tex] (potassium hydroxide) and [tex]\( H_2SO_4 \)[/tex] (sulfuric acid), we need to ensure that the number of atoms for each element is the same on both sides of the equation.
The general form of the chemical reaction between potassium hydroxide and sulfuric acid can be given as:
[tex]\[ KOH + H_2SO_4 \rightarrow \text{products} \][/tex]
Step-by-step solution:
1. Identify the products of the reaction:
Potassium hydroxide (a base) reacts with sulfuric acid (an acid) to form potassium sulfate and water. The expected products are potassium sulfate ([tex]\( K_2SO_4 \)[/tex]) and water ([tex]\( H_2O \)[/tex]).
2. Write the unbalanced equation:
[tex]\[ KOH + H_2SO_4 \rightarrow K_2SO_4 + H_2O \][/tex]
3. Balance the potassium (K) atoms:
On the left side, we have 1 potassium (K) atom in [tex]\( KOH \)[/tex], and on the right side, we have 2 potassium atoms in [tex]\( K_2SO_4 \)[/tex]. To balance K, we need 2 moles of [tex]\( KOH \)[/tex]:
[tex]\[ 2KOH + H_2SO_4 \rightarrow K_2SO_4 + H_2O \][/tex]
4. Balance the sulfur (S) atoms:
There is 1 sulfur atom on both sides of the equation, so sulfur is already balanced.
5. Balance the oxygen (O) atoms:
On the left side, there are 4 oxygen atoms from [tex]\( H_2SO_4 \)[/tex] and 2 oxygen atoms from 2 moles of [tex]\( KOH \)[/tex], making a total of 6 oxygen atoms.
On the right side, there are 4 oxygen atoms from [tex]\( K_2SO_4 \)[/tex] and 1 oxygen atom from [tex]\( H_2O \)[/tex]. Since we have 2 moles of water, this gives:
[tex]\[ 2H_2O \rightarrow 2 \times 1 (Oxygen\text{ atom}) = 2 \][/tex]
Adding the oxygen atoms from [tex]\( K_2SO_4 \)[/tex] and [tex]\( H_2O \)[/tex]:
[tex]\[ 4 + 2 = 6 \][/tex]
Both sides have 6 oxygen atoms, so the oxygen is balanced.
6. Balance the hydrogen (H) atoms:
On the left side, there are 2 hydrogen atoms from [tex]\( H_2SO_4 \)[/tex] and 2 hydrogen atoms from each [tex]\( KOH \)[/tex] (since we have 2 moles of [tex]\( KOH \)[/tex], this makes 4 hydrogen atoms):
[tex]\[ 2 (H) from 2KOH + 2 (H) from H_2SO_4 = 4 (H) \][/tex]
On the right side, there are 2 water molecules ([tex]\( 2H_2O \)[/tex]), which means we have:
[tex]\[ 2H_2O \rightarrow 2 \times 2 (Hydrogen\text{ atoms}) = 4\][/tex]
Both sides have 4 hydrogen atoms, so the hydrogen is balanced.
Thus, the correctly balanced equation is:
[tex]\[ 2KOH + H_2SO_4 \rightarrow K_2SO_4 + 2H_2O \][/tex]
The correct choice is the third option:
[tex]\[ \boxed{2 KOH + H_2SO_4 \rightarrow K_2SO_4 + 2 H_2O} \][/tex]
The general form of the chemical reaction between potassium hydroxide and sulfuric acid can be given as:
[tex]\[ KOH + H_2SO_4 \rightarrow \text{products} \][/tex]
Step-by-step solution:
1. Identify the products of the reaction:
Potassium hydroxide (a base) reacts with sulfuric acid (an acid) to form potassium sulfate and water. The expected products are potassium sulfate ([tex]\( K_2SO_4 \)[/tex]) and water ([tex]\( H_2O \)[/tex]).
2. Write the unbalanced equation:
[tex]\[ KOH + H_2SO_4 \rightarrow K_2SO_4 + H_2O \][/tex]
3. Balance the potassium (K) atoms:
On the left side, we have 1 potassium (K) atom in [tex]\( KOH \)[/tex], and on the right side, we have 2 potassium atoms in [tex]\( K_2SO_4 \)[/tex]. To balance K, we need 2 moles of [tex]\( KOH \)[/tex]:
[tex]\[ 2KOH + H_2SO_4 \rightarrow K_2SO_4 + H_2O \][/tex]
4. Balance the sulfur (S) atoms:
There is 1 sulfur atom on both sides of the equation, so sulfur is already balanced.
5. Balance the oxygen (O) atoms:
On the left side, there are 4 oxygen atoms from [tex]\( H_2SO_4 \)[/tex] and 2 oxygen atoms from 2 moles of [tex]\( KOH \)[/tex], making a total of 6 oxygen atoms.
On the right side, there are 4 oxygen atoms from [tex]\( K_2SO_4 \)[/tex] and 1 oxygen atom from [tex]\( H_2O \)[/tex]. Since we have 2 moles of water, this gives:
[tex]\[ 2H_2O \rightarrow 2 \times 1 (Oxygen\text{ atom}) = 2 \][/tex]
Adding the oxygen atoms from [tex]\( K_2SO_4 \)[/tex] and [tex]\( H_2O \)[/tex]:
[tex]\[ 4 + 2 = 6 \][/tex]
Both sides have 6 oxygen atoms, so the oxygen is balanced.
6. Balance the hydrogen (H) atoms:
On the left side, there are 2 hydrogen atoms from [tex]\( H_2SO_4 \)[/tex] and 2 hydrogen atoms from each [tex]\( KOH \)[/tex] (since we have 2 moles of [tex]\( KOH \)[/tex], this makes 4 hydrogen atoms):
[tex]\[ 2 (H) from 2KOH + 2 (H) from H_2SO_4 = 4 (H) \][/tex]
On the right side, there are 2 water molecules ([tex]\( 2H_2O \)[/tex]), which means we have:
[tex]\[ 2H_2O \rightarrow 2 \times 2 (Hydrogen\text{ atoms}) = 4\][/tex]
Both sides have 4 hydrogen atoms, so the hydrogen is balanced.
Thus, the correctly balanced equation is:
[tex]\[ 2KOH + H_2SO_4 \rightarrow K_2SO_4 + 2H_2O \][/tex]
The correct choice is the third option:
[tex]\[ \boxed{2 KOH + H_2SO_4 \rightarrow K_2SO_4 + 2 H_2O} \][/tex]
