What volume of 0.34 M KOH is sufficient to react with 20 ml of 0.15M `H_(2)SO_(4)` solution ?

Explanation

To determine the volume of 0.34 M KOH required to react with 20 ml of 0.15 M H₂SO₄, we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced reaction between KOH and H₂SO₄ is:
\[ \text{H}_2\text{SO}_4 + 2 \text{KOH} \rightarrow \text{K}_2\text{SO}_4 + 2 \text{H}_2\text{O} \]

### Step 2: Calculate the moles of H₂SO₄
Using the formula for molarity:
\[ \text{Molarity (M)} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]
We can rearrange this to find the number of moles:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume in liters} \]
Given:
- Molarity of H₂SO₄ = 0.15 M
- Volume of H₂SO₄ = 20 ml = 0.020 L (since 1 L = 1000 ml)

Calculating the moles of H₂SO₄:
\[ \text{Number of moles of H}_2\text{SO}_4 = 0.15 \, \text{mol/L} \times 0.020 \, \text{L} = 0.003 \, \text{moles} \]

### Step 3: Determine the moles of KOH required
From the balanced equation, we see that 1 mole of H₂SO₄ reacts with 2 moles of KOH. Therefore, the moles of KOH required can be calculated as:
\[ \text{Moles of KOH} = 2 \times \text{Moles of H}_2\text{SO}_4 = 2 \times 0.003 \, \text{moles} = 0.006 \, \text{moles} \]

### Step 4: Calculate the volume of KOH solution needed
Using the molarity formula again for KOH:
\[ \text{Molarity of KOH} = \frac{\text{Number of moles of KOH}}{\text{Volume in liters}} \]
Rearranging gives us:
\[ \text{Volume in liters} = \frac{\text{Number of moles of KOH}}{\text{Molarity of KOH}} \]
Substituting the values:
- Moles of KOH = 0.006 moles
- Molarity of KOH = 0.34 M

Calculating the volume:
\[ \text{Volume of KOH} = \frac{0.006 \, \text{moles}}{0.34 \, \text{mol/L}} = 0.01765 \, \text{L} \]

### Step 5: Convert the volume from liters to milliliters
To convert liters to milliliters, multiply by 1000:
\[ \text{Volume in ml} = 0.01765 \, \text{L} \times 1000 = 17.65 \, \text{ml} \]

### Final Answer
The volume of 0.34 M KOH required to react with 20 ml of 0.15 M H₂SO₄ is **17.65 ml**.

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