How many millilitres of 0.5 M `H_(2)SO_(4)` are needed to dissolve 0.5 g of copper (II) Carbonate ?

Answer

To solve the problem of how many milliliters of 0.5 M H₂SO₄ are needed to dissolve 0.5 g of copper (II) carbonate (CuCO₃), we can follow these steps:

### Step 1: Write the balanced chemical equation
The reaction of copper (II) carbonate with sulfuric acid can be represented as:
\[ \text{CuCO}_3 + \text{H}_2\text{SO}_4 \rightarrow \text{CuSO}_4 + \text{H}_2\text{O} + \text{CO}_2 \]

### Step 2: Calculate the molar mass of CuCO₃
The molar mass of CuCO₃ can be calculated as follows:
- Copper (Cu): 63.5 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol × 3 = 48 g/mol

Adding these together:
\[ \text{Molar mass of CuCO}_3 = 63.5 + 12 + 48 = 123.5 \text{ g/mol} \]

### Step 3: Calculate the number of moles of CuCO₃
Using the mass of CuCO₃ given (0.5 g), we can find the number of moles:
\[ \text{Number of moles of CuCO}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{0.5 \text{ g}}{123.5 \text{ g/mol}} \approx 0.00405 \text{ moles} \]

### Step 4: Determine the number of moles of H₂SO₄ required
From the balanced equation, we see that 1 mole of CuCO₃ reacts with 1 mole of H₂SO₄. Therefore, the number of moles of H₂SO₄ required is the same as the number of moles of CuCO₃:
\[ \text{Number of moles of H}_2\text{SO}_4 = 0.00405 \text{ moles} \]

### Step 5: Calculate the mass of H₂SO₄ needed
Using the molar mass of H₂SO₄:
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Sulfur (S): 32 g/mol
- Oxygen (O): 16 g/mol × 4 = 64 g/mol

Adding these together:
\[ \text{Molar mass of H}_2\text{SO}_4 = 2 + 32 + 64 = 98 \text{ g/mol} \]

Now, we can calculate the mass of H₂SO₄ needed:
\[ \text{Mass of H}_2\text{SO}_4 = \text{Number of moles} \times \text{Molar mass} = 0.00405 \text{ moles} \times 98 \text{ g/mol} \approx 0.397 \text{ g} \]

### Step 6: Calculate the volume of H₂SO₄ solution needed
Using the molarity equation:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]
Rearranging gives us:
\[ \text{Volume in liters} = \frac{\text{Number of moles}}{\text{Molarity}} = \frac{0.00405 \text{ moles}}{0.5 \text{ M}} = 0.0081 \text{ L} \]

### Step 7: Convert the volume to milliliters
To convert liters to milliliters:
\[ \text{Volume in milliliters} = 0.0081 \text{ L} \times 1000 \text{ mL/L} = 8.1 \text{ mL} \]

### Final Answer
Therefore, the volume of 0.5 M H₂SO₄ needed to dissolve 0.5 g of copper (II) carbonate is **8.1 mL**.

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