A solid has a structure in which `X` atoms are located at cubic corners of unit cell, `O` atom are at the edge centres and `Y` atoms at cube centre.
Then the formula of compound is `X_(a)Y_(b)O_(c)`
If two atoms of `O` missing from any of two edge centres per unit cell, then the molecular formula is `X_(a)Y_(b)O_(z)`. Then, find the value of `(x + y + z) - (a + b+ c)`.

Explanation

To solve the problem step by step, we will analyze the structure of the solid and calculate the number of atoms of each type in the unit cell.

### Step 1: Determine the number of X atoms in the unit cell.
- X atoms are located at the corners of the cubic unit cell.
- There are 8 corners in a cube, and each corner contributes \( \frac{1}{8} \) of an atom to the unit cell.

\[ \text{Number of X atoms} = 8 \times \frac{1}{8} = 1 \]

### Step 2: Determine the number of O atoms in the unit cell.
- O atoms are located at the edge centers of the cubic unit cell.
- There are 12 edges in a cube, and each edge contributes \( \frac{1}{4} \) of an atom to the unit cell.

\[ \text{Number of O atoms} = 12 \times \frac{1}{4} = 3 \]

### Step 3: Determine the number of Y atoms in the unit cell.
- Y atoms are located at the body center of the cubic unit cell.
- There is 1 body center in a cube, and it contributes 1 atom to the unit cell.

\[ \text{Number of Y atoms} = 1 \]

### Step 4: Write the initial formula of the compound.
From the calculations:
- Number of X atoms = 1
- Number of Y atoms = 1
- Number of O atoms = 3

Thus, the initial formula is:
\[ X_a Y_b O_c = X_1 Y_1 O_3 \]

### Step 5: Adjust the number of O atoms due to missing atoms.
- It is given that 2 O atoms are missing from the edge centers.
- After removing 2 O atoms from the edge centers, the number of O atoms becomes:
\[ \text{Remaining O atoms} = 3 - 2 = 1 \]

### Step 6: Calculate the new number of O atoms in terms of contributions.
Since there are 10 edge centers remaining (12 - 2), the contribution from these edge centers is:
\[ \text{Number of O atoms} = 10 \times \frac{1}{4} = 2.5 \]

### Step 7: Write the revised formula of the compound.
With the new counts:
- Number of X atoms = 1
- Number of Y atoms = 1
- Number of O atoms = 2.5

The revised formula is:
\[ X_1 Y_1 O_{2.5} \]

### Step 8: Express the revised formula in terms of integers.
To express the formula in whole numbers, we can multiply all subscripts by 2:
\[ X_2 Y_2 O_5 \]

### Step 9: Identify values of x, y, z, a, b, c.
From the formulas:
- \( x = 2 \)
- \( y = 2 \)
- \( z = 5 \)
- \( a = 1 \)
- \( b = 1 \)
- \( c = 3 \)

### Step 10: Calculate \( (x + y + z) - (a + b + c) \).
\[ (x + y + z) = (2 + 2 + 5) = 9 \]
\[ (a + b + c) = (1 + 1 + 3) = 5 \]
\[ (x + y + z) - (a + b + c) = 9 - 5 = 4 \]

### Final Answer:
The value of \( (x + y + z) - (a + b + c) \) is \( 4 \).

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