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), we can follow these steps:

### Step 1: Understand the Law of Definite Proportions
The law of definite proportions states that in a given chemical compound, the elements are always present in fixed proportions by mass, regardless of the source or method of preparation.

### Step 2: Write the Chemical Reaction
The reaction for the formation of silver carbide can be represented as:
\[ 2 \text{Ag} + \text{C} \rightarrow \text{Ag}_2\text{C}_2 \]

### Step 3: Calculate the Moles of Silver
To find out how much carbon is needed, we first need to calculate the number of moles of silver (Ag) present in 2.16 g.

- The atomic weight of silver (Ag) is approximately 107.86 g/mol.
- Moles of Ag can be calculated using the formula:
\[ \text{Moles of Ag} = \frac{\text{mass of Ag}}{\text{molar mass of Ag}} \]
\[ \text{Moles of Ag} = \frac{2.16 \, \text{g}}{107.86 \, \text{g/mol}} \approx 0.0200 \, \text{mol} \]

### Step 4: Determine the Stoichiometric Ratio
From the balanced equation, we see that:
- 2 moles of Ag react with 1 mole of C.

This means that the moles of carbon required will be half the moles of silver:
\[ \text{Moles of C} = \frac{0.0200 \, \text{mol Ag}}{2} = 0.0100 \, \text{mol C} \]

### Step 5: Calculate the Mass of Carbon
Now, we can calculate the mass of carbon needed using its atomic weight, which is approximately 12 g/mol.

- Using the formula:
\[ \text{Mass of C} = \text{moles of C} \times \text{molar mass of C} \]
\[ \text{Mass of C} = 0.0100 \, \text{mol} \times 12 \, \text{g/mol} = 0.12 \, \text{g} \]

### Step 6: Conclusion
Thus, the amount of carbon that must combine with 2.16 g of silver to form silver carbide (Ag₂C₂) is **0.12 g**.

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