The mass of carbon present in 0.5 mole of `K_(4)[Fe(CN)_(6)]` is -

Options

A. 1.8 gm
B. 18 gm
C. 3.6 gm
D. 36 gm

Answer

To find the mass of carbon present in 0.5 moles of \( K_4[Fe(CN)_6] \), we can follow these steps:

### Step 1: Determine the number of moles of carbon in 1 mole of \( K_4[Fe(CN)_6] \)
The formula \( K_4[Fe(CN)_6] \) indicates that there are 6 cyanide ions (CN) in the compound. Each cyanide ion contains 1 carbon atom. Therefore, in 1 mole of \( K_4[Fe(CN)_6] \), there are:

\[ \text{Moles of carbon in 1 mole of } K_4[Fe(CN)_6] = 6 \text{ moles of carbon} \]

### Step 2: Calculate the number of moles of carbon in 0.5 moles of \( K_4[Fe(CN)_6] \)
Since we are interested in 0.5 moles of \( K_4[Fe(CN)_6] \), we can find the number of moles of carbon by multiplying the moles of carbon in 1 mole of the compound by 0.5:

\[ \text{Moles of carbon in 0.5 moles} = 6 \text{ moles} \times 0.5 = 3 \text{ moles of carbon} \]

### Step 3: Calculate the mass of carbon
The molar mass of carbon (C) is approximately 12 grams/mole. To find the mass of carbon in 3 moles, we multiply the number of moles by the molar mass:

\[ \text{Mass of carbon} = \text{Moles of carbon} \times \text{Molar mass of carbon} = 3 \text{ moles} \times 12 \text{ g/mole} = 36 \text{ grams} \]

### Conclusion
The mass of carbon present in 0.5 moles of \( K_4[Fe(CN)_6] \) is **36 grams**.

---