Consider the following reactions,
`A_(x)+yB_(2) underset("supply of air")overset("limited")to"Compound"'P' underset("excess air")overset(+zB_(2))to`Compound 'Q'
If atomic number of elements A and B are 15 and 8 respectively, then according to the given information the correct statement(s) is/are:

Options

A. (B-A-B) bond angle in compound 'Q'gt(B-A-B) bond angle in compound 'P'
B. (A-B) bond length in compound 'Q'`lt`(A-B) bond length in compound 'P'
C. Value of `x+y+z` is 9
D. Compound 'P' is `P_(2)O_(5)` and compound 'Q' is `P_(4)O_(10)`

Explanation

To solve the problem, we need to analyze the given reactions and identify the compounds formed based on the atomic numbers of elements A and B.

### Step-by-Step Solution:

1. **Identify Elements A and B:**
- The atomic number of element A is 15, which corresponds to phosphorus (P).
- The atomic number of element B is 8, which corresponds to oxygen (O).

2. **Write the Initial Reaction:**
- The reaction given is \( A_x + yB_2 \) in limited air to form compound P.
- Substituting the identified elements, we have \( P_x + yO_2 \) in limited air.

3. **Determine the Compound P:**
- In limited air, phosphorus reacts with oxygen to form phosphorus oxides. The most common oxides are \( P_4O_6 \) and \( P_4O_{10} \).
- For the reaction \( P_4 + 3O_2 \) in limited air, we get \( P_4O_6 \) as compound P.
- Here, \( x = 4 \) and \( y = 3 \).

4. **Write the Second Reaction:**
- The second reaction involves treating compound P with excess oxygen: \( P + zB_2 \) in excess air to form compound Q.
- Substituting the identified compound, we have \( P_4O_6 + zO_2 \) in excess air.

5. **Determine the Compound Q:**
- In excess air, \( P_4O_6 \) reacts to form \( P_4O_{10} \).
- The balanced reaction is \( P_4O_6 + 2O_2 \rightarrow P_4O_{10} \), thus \( z = 2 \).

6. **Summarize the Values:**
- From the reactions, we have:
- \( x = 4 \)
- \( y = 3 \)
- \( z = 2 \)

7. **Check the Statements:**
- **Statement A:** The \( O-P-O \) bond angle in Q is greater than in P.
- Correct, as \( P_4O_{10} \) has double bonds which increase bond angles compared to \( P_4O_6 \).
- **Statement B:** The \( P-O \) bond length in Q is less than in P.
- Correct, as increased bond order (due to double bonds in \( P_4O_{10} \)) leads to shorter bond lengths.
- **Statement C:** \( x + y + z = 9 \).
- Correct, \( 4 + 3 + 2 = 9 \).
- **Statement D:** Compound P is \( P_2O_5 \) and compound Q is \( P_4O_{10} \).
- Incorrect, as compound P is \( P_4O_6 \).

8. **Final Conclusion:**
- The correct statements are A, B, and C.