If `0.049 g ` of `H_(2)SO_(4)` are present in 10 litre of the solution, the pH of the solution will be

Explanation

To find the pH of a solution containing 0.049 g of H₂SO₄ in 10 liters, we can follow these steps:

### Step 1: Calculate the number of moles of H₂SO₄
To find the number of moles, we need to use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

The molar mass of H₂SO₄ (sulfuric acid) is approximately 98 g/mol.

\[ \text{Number of moles of H₂SO₄} = \frac{0.049 \, \text{g}}{98 \, \text{g/mol}} \approx 5.0 \times 10^{-4} \, \text{moles} \]

### Step 2: Calculate the concentration of H₂SO₄ in the solution
Concentration (C) is calculated using the formula:

\[ C = \frac{\text{Number of moles}}{\text{Volume (L)}} \]

Given that the volume of the solution is 10 L:

\[ C = \frac{5.0 \times 10^{-4} \, \text{moles}}{10 \, \text{L}} = 5.0 \times 10^{-5} \, \text{M} \]

### Step 3: Determine the concentration of H⁺ ions
Since H₂SO₄ is a strong acid, it dissociates completely in solution:

\[ \text{H₂SO₄} \rightarrow 2 \text{H}^+ + \text{SO₄}^{2-} \]

From one mole of H₂SO₄, we get 2 moles of H⁺ ions. Therefore, the concentration of H⁺ ions will be:

\[ [\text{H}^+] = 2 \times [\text{H₂SO₄}] = 2 \times 5.0 \times 10^{-5} \, \text{M} = 1.0 \times 10^{-4} \, \text{M} \]

### Step 4: Calculate the pH of the solution
The pH is calculated using the formula:

\[ \text{pH} = -\log [\text{H}^+] \]

Substituting the concentration of H⁺ ions:

\[ \text{pH} = -\log (1.0 \times 10^{-4}) = 4 \]

### Final Answer:
The pH of the solution is **4**.

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