0.92 g of `Ag_(2)CO_(3)` is heated strongly beyond its melting point . After heating the amount of residue is

Options

A. 0.36 g
B. 0.39 g
C. 0.77 g
D. 0.72 g

Answer

To solve the problem of determining the amount of residue left after heating 0.92 g of silver carbonate (Ag₂CO₃), we will follow these steps:

### Step 1: Write the decomposition reaction
When silver carbonate (Ag₂CO₃) is heated, it decomposes into silver (Ag), carbon dioxide (CO₂), and oxygen (O₂). The balanced chemical equation for this reaction is:

\[ 2 \text{Ag}_2\text{CO}_3 \rightarrow 4 \text{Ag} + 2 \text{CO}_2 + \text{O}_2 \]

### Step 2: Calculate the molar mass of silver carbonate (Ag₂CO₃)
To find the molar mass of Ag₂CO₃, we need the atomic masses of its constituent elements:
- Silver (Ag): 108 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol

The molar mass of Ag₂CO₃ is calculated as follows:
\[ \text{Molar mass of Ag}_2\text{CO}_3 = 2 \times 108 + 12 + 3 \times 16 \]
\[ = 216 + 12 + 48 = 276 \text{ g/mol} \]

### Step 3: Determine the number of moles of Ag₂CO₃ in 0.92 g
Using the molar mass calculated, we can find the number of moles of Ag₂CO₃ in 0.92 g:
\[ \text{Number of moles of Ag}_2\text{CO}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{0.92 \text{ g}}{276 \text{ g/mol}} \approx 0.00333 \text{ moles} \]

### Step 4: Calculate the amount of silver produced
From the balanced equation, 2 moles of Ag₂CO₃ produce 4 moles of Ag. Therefore, the ratio of moles of Ag produced to moles of Ag₂CO₃ is:
\[ \frac{4 \text{ moles Ag}}{2 \text{ moles Ag}_2\text{CO}_3} = 2 \]
Thus, the number of moles of Ag produced from 0.00333 moles of Ag₂CO₃ is:
\[ \text{Moles of Ag} = 0.00333 \times 2 = 0.00666 \text{ moles} \]

### Step 5: Calculate the mass of silver produced
Now, we can calculate the mass of silver produced using its molar mass:
\[ \text{Mass of Ag} = \text{moles} \times \text{molar mass} = 0.00666 \text{ moles} \times 108 \text{ g/mol} \approx 0.72 \text{ g} \]

### Conclusion
The amount of residue left after heating 0.92 g of Ag₂CO₃ is approximately 0.72 g of silver.