1.245 g of `CuSO_(4). xH_(2)O` was dissolved in water and `H_(2)S` gas was passed through it will till CuS was completely precipitated . The `H_(2)SO_(4)` produced in the filtrate required 100 ml of 0.1 M NaOH solution . Calculate x (approximately)

Options

A. 5
B. 6
C. 7
D. 8

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the moles of NaOH used
Given that 100 mL of 0.1 M NaOH solution was used, we can calculate the moles of NaOH.

\[ \text{Moles of NaOH} = \text{Volume (L)} \times \text{Molarity (mol/L)} = 0.1 \, \text{L} \times 0.1 \, \text{mol/L} = 0.01 \, \text{mol} \]

### Step 2: Relate moles of NaOH to moles of H2SO4
From the reaction, we know that:

\[ \text{H}_2\text{SO}_4 + 2 \text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O} \]

This shows that 1 mole of H2SO4 reacts with 2 moles of NaOH. Therefore, the moles of H2SO4 produced can be calculated as follows:

\[ \text{Moles of H}_2\text{SO}_4 = \frac{\text{Moles of NaOH}}{2} = \frac{0.01 \, \text{mol}}{2} = 0.005 \, \text{mol} \]

### Step 3: Relate moles of H2SO4 to moles of CuSO4
From the reaction of CuSO4 with H2S, we know that:

\[ \text{CuSO}_4 + \text{H}_2\text{S} \rightarrow \text{CuS} + \text{H}_2\text{SO}_4 \]

This indicates that 1 mole of CuSO4 produces 1 mole of H2SO4. Therefore, the moles of CuSO4 are equal to the moles of H2SO4 produced:

\[ \text{Moles of CuSO}_4 = 0.005 \, \text{mol} \]

### Step 4: Calculate the mass of CuSO4
The molar mass of CuSO4 is approximately 159.5 g/mol. The mass of CuSO4 can be calculated using the number of moles:

\[ \text{Mass of CuSO}_4 = \text{Moles} \times \text{Molar mass} = 0.005 \, \text{mol} \times 159.5 \, \text{g/mol} = 0.7975 \, \text{g} \]

### Step 5: Calculate the mass of water in CuSO4·xH2O
The total mass of CuSO4·xH2O is given as 1.245 g. Therefore, the mass of water can be calculated as follows:

\[ \text{Mass of water} = \text{Total mass} - \text{Mass of CuSO}_4 = 1.245 \, \text{g} - 0.7975 \, \text{g} = 0.4475 \, \text{g} \]

### Step 6: Calculate the number of moles of water
The molar mass of water (H2O) is approximately 18 g/mol. The number of moles of water can be calculated as:

\[ \text{Moles of water} = \frac{\text{Mass of water}}{\text{Molar mass of water}} = \frac{0.4475 \, \text{g}}{18 \, \text{g/mol}} \approx 0.0249 \, \text{mol} \]

### Step 7: Relate moles of water to x
The number of moles of water in CuSO4·xH2O is equal to x. Therefore, we can conclude that:

\[ x \approx 0.0249 \, \text{mol} \]

### Step 8: Calculate x
To find the value of x, we need to find the total mass of CuSO4·xH2O:

\[ \text{Molar mass of CuSO}_4 \cdot x\text{H}_2\text{O} = 159.5 + 18x \]

Using the total mass:

\[ 1.245 = 0.7975 + 18x \]

Solving for x:

\[ 1.245 - 0.7975 = 18x \\ 0.4475 = 18x \\ x \approx \frac{0.4475}{18} \approx 0.0249 \, \text{mol} \]

Calculating x gives us:

\[ x \approx 5 \]

### Final Result
Thus, the approximate value of x is 5.

---