The number of grams of `H_2SO_4` required to dissolve 5 g of `CaCO_(3)` is:

Options

A. 10.24
B. 4.9
C. 5.12
D. 2.56

Answer

To determine the number of grams of `H₂SO₄` required to dissolve 5 g of `CaCO₃`, we can follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between calcium carbonate (CaCO₃) and sulfuric acid (H₂SO₄) can be represented as:
\[ \text{CaCO}_3 + \text{H}_2\text{SO}_4 \rightarrow \text{CaSO}_4 + \text{CO}_2 + \text{H}_2\text{O} \]

### Step 2: Calculate the moles of `CaCO₃`
To find the number of moles of `CaCO₃`, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

The molar mass of `CaCO₃` is calculated as follows:
- Calcium (Ca) = 40 g/mol
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol (3 atoms)

Thus, the molar mass of `CaCO₃` is:
\[ 40 + 12 + (16 \times 3) = 100 \, \text{g/mol} \]

Now, substituting the values:
\[ \text{Number of moles of } CaCO_3 = \frac{5 \, \text{g}}{100 \, \text{g/mol}} = 0.05 \, \text{moles} \]

### Step 3: Determine the moles of `H₂SO₄` required
From the balanced equation, we see that 1 mole of `CaCO₃` reacts with 1 mole of `H₂SO₄`. Therefore, the number of moles of `H₂SO₄` required is the same as the number of moles of `CaCO₃`:
\[ \text{Number of moles of } H_2SO_4 = 0.05 \, \text{moles} \]

### Step 4: Calculate the mass of `H₂SO₄`
To find the mass of `H₂SO₄`, we again use the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]

The molar mass of `H₂SO₄` is calculated as follows:
- Hydrogen (H) = 1 g/mol (2 atoms)
- Sulfur (S) = 32 g/mol
- Oxygen (O) = 16 g/mol (4 atoms)

Thus, the molar mass of `H₂SO₄` is:
\[ (1 \times 2) + 32 + (16 \times 4) = 98 \, \text{g/mol} \]

Now, substituting the values:
\[ \text{Mass of } H_2SO_4 = 0.05 \, \text{moles} \times 98 \, \text{g/mol} = 4.9 \, \text{g} \]

### Conclusion
The number of grams of `H₂SO₄` required to dissolve 5 g of `CaCO₃` is **4.9 g**.