In accordance with law of definite proportions, `2.16g` of Ag must combine with how much amount of carbon to form silver carbide `(Ag_(2)C_(2))`?

Options

A. 12g
B. 0.24g
C. 0.12g
D. 2.4g

Answer

To solve the problem of how much carbon combines with 2.16 g of silver (Ag) to form silver carbide (Ag₂C₂) according to the law of definite proportions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Law of Definite Proportions**:
- The law states that a chemical compound always contains its component elements in fixed ratio by mass.

2. **Write the Chemical Reaction**:
- The formation of silver carbide can be represented as:
\[ 2 \text{Ag} + 2 \text{C} \rightarrow \text{Ag}_2\text{C}_2 \]
- This indicates that 2 moles of silver react with 2 moles of carbon to form 1 mole of silver carbide.

3. **Calculate the Molar Mass of Silver (Ag)**:
- The molar mass of silver (Ag) is approximately 108 g/mol.

4. **Calculate the Number of Moles of Silver (Ag)**:
- Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
- For 2.16 g of Ag:
\[ \text{Number of moles of Ag} = \frac{2.16 \text{ g}}{108 \text{ g/mol}} = 0.02 \text{ moles} \]

5. **Determine the Moles of Carbon Required**:
- From the balanced equation, 2 moles of Ag react with 2 moles of C. Therefore, 0.02 moles of Ag will react with 0.02 moles of C.

6. **Calculate the Molar Mass of Carbon (C)**:
- The molar mass of carbon (C) is approximately 12 g/mol.

7. **Calculate the Mass of Carbon Required**:
- Using the number of moles of carbon:
\[ \text{Mass of C} = \text{Number of moles of C} \times \text{Molar mass of C} \]
- For 0.02 moles of C:
\[ \text{Mass of C} = 0.02 \text{ moles} \times 12 \text{ g/mol} = 0.24 \text{ g} \]

8. **Conclusion**:
- Therefore, 2.16 g of silver must combine with 0.24 g of carbon to form silver carbide (Ag₂C₂).

### Final Answer:
The amount of carbon that must combine with 2.16 g of silver is **0.24 g**.