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, we need to follow these steps:

### Step 1: Calculate the number of moles of H₂SO₄ in V ml of the 2.2 M solution.

The formula to calculate the number of moles (n) is:
\[ n = M \times V \]
where:
- \( M \) is the molarity (2.2 M)
- \( V \) is the volume in liters (V ml = V/1000 L)

So, the number of moles of H₂SO₄ is:
\[ n = 2.2 \, \text{mol/L} \times \frac{V}{1000} \, \text{L} = \frac{2.2V}{1000} \, \text{mol} \]

### Step 2: Determine the total volume after dilution.

Initially, we have V ml of H₂SO₄ solution and we add 10 V ml of water. The total volume before considering contraction is:
\[ \text{Total Volume} = V + 10V = 11V \, \text{ml} \]

### Step 3: Account for the volume contraction.

The problem states that there is a volume contraction of 2%. Therefore, the effective volume after contraction is:
\[ \text{Effective Volume} = 11V - 0.02 \times 11V = 11V \times (1 - 0.02) = 11V \times 0.98 = 10.78V \, \text{ml} \]

### Step 4: Convert the effective volume to liters.

To convert the effective volume from ml to liters:
\[ \text{Effective Volume in Liters} = \frac{10.78V}{1000} \, \text{L} \]

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

Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ M = \frac{\text{Number of moles}}{\text{Volume in Liters}} \]

Substituting the values we have:
\[ M = \frac{\frac{2.2V}{1000}}{\frac{10.78V}{1000}} \]

The \( V \) cancels out:
\[ M = \frac{2.2}{10.78} \]

### Step 6: Calculate the final value.

Now, we can compute the value:
\[ M \approx 0.204 \, \text{M} \]

Thus, the molarity of the diluted solution is approximately **0.204 M**.

---