When `2.76 g` of silver carbonate is strongly heated, it yields a residue weighing

Options

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

Answer

To find the mass of silver obtained from the thermal decomposition of silver carbonate (Ag2CO3), we can follow these steps:

### Step 1: Write the decomposition reaction
The decomposition of silver carbonate upon heating can be represented as:
\[ \text{2 Ag}_2\text{CO}_3 \rightarrow \text{4 Ag} + \text{2 CO}_2 + \text{O}_2 \]
This means that when silver carbonate is heated, it decomposes into silver, carbon dioxide, and oxygen.

### Step 2: Calculate the molar mass of silver carbonate (Ag2CO3)
The molar mass of Ag2CO3 can be calculated as follows:
- Molar mass of Ag = 108 g/mol (for silver)
- Molar mass of C = 12 g/mol (for carbon)
- Molar mass of O = 16 g/mol (for oxygen)

Calculating the total molar mass:
\[ \text{Molar mass of Ag}_2\text{CO}_3 = (2 \times 108) + 12 + (3 \times 16) = 216 + 12 + 48 = 276 \text{ g/mol} \]

### Step 3: Determine the mass of silver produced from the given mass of Ag2CO3
From the balanced equation, we see that 276 g of Ag2CO3 produces 216 g of Ag. We need to find out how much silver is produced from 2.76 g of Ag2CO3.

Using the ratio:
\[ \text{Mass of Ag} = \left( \frac{216 \text{ g Ag}}{276 \text{ g Ag}_2\text{CO}_3} \right) \times 2.76 \text{ g Ag}_2\text{CO}_3 \]

### Step 4: Calculate the mass of silver
Now we can calculate:
\[ \text{Mass of Ag} = \left( \frac{216}{276} \right) \times 2.76 \]
Calculating the fraction:
\[ \frac{216}{276} = 0.7826 \quad (\text{approximately}) \]
Now substituting back:
\[ \text{Mass of Ag} = 0.7826 \times 2.76 \approx 2.16 \text{ g} \]

### Conclusion
The mass of silver obtained from the decomposition of 2.76 g of silver carbonate is approximately **2.16 g**.

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