From the mixture of 4 moles `Ca_(3)(PO_(4))_(2)` and 5 moles of `P_(4) O_(10)` and 6 moles of `H_(3)PO_(3)` all the phosphorus atoms are removed then moles of `P_(4)` molecule formed from all these atoms is

Options

A. `8.5`
B. 17
C. 34
D. 10

Explanation

To solve the problem, we will calculate the total number of phosphorus atoms from the given compounds and then determine how many moles of \( P_4 \) can be formed from those atoms.

### Step-by-Step Solution:

1. **Calculate Phosphorus Atoms from Calcium Phosphate (\( Ca_3(PO_4)_2 \))**:
- Each mole of \( Ca_3(PO_4)_2 \) contains 2 moles of phosphorus atoms.
- Given: 4 moles of \( Ca_3(PO_4)_2 \).
- Calculation:
\[ \text{Phosphorus from } Ca_3(PO_4)_2 = 4 \text{ moles} \times 2 = 8 \text{ moles of phosphorus} \]

2. **Calculate Phosphorus Atoms from \( P_4O_{10} \)**:
- Each mole of \( P_4O_{10} \) contains 4 moles of phosphorus atoms.
- Given: 5 moles of \( P_4O_{10} \).
- Calculation:
\[ \text{Phosphorus from } P_4O_{10} = 5 \text{ moles} \times 4 = 20 \text{ moles of phosphorus} \]

3. **Calculate Phosphorus Atoms from \( H_3PO_3 \)**:
- Each mole of \( H_3PO_3 \) contains 1 mole of phosphorus atom.
- Given: 6 moles of \( H_3PO_3 \).
- Calculation:
\[ \text{Phosphorus from } H_3PO_3 = 6 \text{ moles} \times 1 = 6 \text{ moles of phosphorus} \]

4. **Total Phosphorus Atoms**:
- Now, we will sum all the phosphorus atoms obtained from each compound.
- Calculation:
\[ \text{Total phosphorus} = 8 + 20 + 6 = 34 \text{ moles of phosphorus} \]

5. **Calculate Moles of \( P_4 \) Formed**:
- Each molecule of \( P_4 \) is formed from 4 phosphorus atoms.
- To find the number of \( P_4 \) molecules formed from 34 phosphorus atoms:
- Calculation:
\[ \text{Moles of } P_4 = \frac{34 \text{ moles of phosphorus}}{4} = 8.5 \text{ moles of } P_4 \]

### Final Answer:
The moles of \( P_4 \) molecules formed from all the phosphorus atoms is **8.5 moles**.