2.76 g of `Ag_2CO_3` on being heated yields a residue weighing

Options

A. A)2.16 g
B. B)2.32 g
C. C)2.48 g
D. D)2.64 g

Explanation

To find the residue obtained from heating 2.76 g of silver carbonate (Ag₂CO₃), we will follow these steps:

### Step 1: Write the balanced chemical equation
The decomposition of silver carbonate can be represented by the following balanced equation:

\[ 2 \, \text{Ag}_2\text{CO}_3 \, \text{(s)} \rightarrow 4 \, \text{Ag (s)} + 2 \, \text{CO}_2 \, \text{(g)} + \text{O}_2 \, \text{(g)} \]

### Step 2: Calculate the molar mass of Ag₂CO₃
To find the molar mass of silver carbonate (Ag₂CO₃), we sum the atomic masses of its constituent elements:

- Silver (Ag): 107.87 g/mol (2 atoms)
- Carbon (C): 12.01 g/mol (1 atom)
- Oxygen (O): 16.00 g/mol (3 atoms)

Calculating the molar mass:

\[ \text{Molar mass of Ag}_2\text{CO}_3 = (2 \times 107.87) + (1 \times 12.01) + (3 \times 16.00) = 215.74 + 12.01 + 48.00 = 275.75 \, \text{g/mol} \]

### Step 3: Calculate the number of moles of Ag₂CO₃
Using the formula for the number of moles:

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

Substituting the values:

\[ \text{Number of moles of Ag}_2\text{CO}_3 = \frac{2.76 \, \text{g}}{275.75 \, \text{g/mol}} \approx 0.01 \, \text{mol} \]

### Step 4: Determine the number of moles of silver produced
From the balanced equation, we see that 2 moles of Ag₂CO₃ produce 4 moles of Ag. Therefore, the number of moles of silver produced is:

\[ \text{Number of moles of Ag} = 0.01 \, \text{mol Ag}_2\text{CO}_3 \times \frac{4 \, \text{mol Ag}}{2 \, \text{mol Ag}_2\text{CO}_3} = 0.02 \, \text{mol Ag} \]

### Step 5: Calculate the mass of silver produced
Now, we can find the mass of silver produced using its molar mass (Ag = 107.87 g/mol):

\[ \text{Mass of Ag} = \text{Number of moles} \times \text{molar mass} = 0.02 \, \text{mol} \times 107.87 \, \text{g/mol} \approx 2.16 \, \text{g} \]

### Conclusion
The residue obtained from heating 2.76 g of silver carbonate is approximately **2.16 g of silver**.

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