When V ml of `2.2 M H_(2)SO_(4)` solution is mixed with 10 V ml of water, the volume contraction of 2% take place. Calculate the molarity of diluted solution ?

Answer

To solve the problem step by step, we will calculate the molarity of the diluted sulfuric acid solution after mixing it with water and accounting for the volume contraction.

### Step 1: Calculate the number of moles of H₂SO₄ in the original solution

The number of moles of H₂SO₄ can be calculated using the formula:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume (in liters)} \]
Given:
- Molarity (M) = 2.2 M
- Volume (V ml) = \(\frac{V}{1000}\) L

Thus, the number of moles of H₂SO₄ is:
\[ \text{Number of moles} = 2.2 \times \frac{V}{1000} = \frac{2.2V}{1000} \]

### Step 2: Calculate the total volume of the solution after mixing

When V ml of the H₂SO₄ solution is mixed with 10V ml of water, the total initial volume before accounting for contraction is:
\[ \text{Total Volume} = V + 10V = 11V \text{ ml} \]

### Step 3: Account for the volume contraction

A volume contraction of 2% means that the final volume is 98% of the initial volume. Therefore, the final volume after contraction is:
\[ \text{Final Volume} = 11V \times \left(1 - \frac{2}{100}\right) = 11V \times 0.98 = 10.78V \text{ ml} \]

### Step 4: Convert the final volume to liters

To convert the final volume from ml to liters:
\[ \text{Final Volume (in liters)} = \frac{10.78V}{1000} \]

### Step 5: Calculate the molarity of the diluted solution

Molarity (M) is defined as the number of moles of solute divided by the volume of solution in liters. Thus, the molarity of the diluted solution is:
\[ \text{Molarity of diluted solution} = \frac{\text{Number of moles of H₂SO₄}}{\text{Final Volume (in liters)}} \]
Substituting the values we have:
\[ \text{Molarity of diluted solution} = \frac{\frac{2.2V}{1000}}{\frac{10.78V}{1000}} = \frac{2.2V}{10.78V} = \frac{2.2}{10.78} \]

Calculating this gives:
\[ \text{Molarity of diluted solution} \approx 0.204 \text{ M} \]

### Final Answer
The molarity of the diluted solution is approximately **0.204 M**.

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