Consider the following transformation:
`Cr(CO)_(x) to Cr(CO)_(y)(NO)_(x)`
If both reactant and product follow EAN rule, then calculate value of `x+z-y` (where x,y and z are natural numbers).

Answer

To solve the problem, we need to analyze the transformation of the coordination compound from Cr(CO)_(x) to Cr(CO)_(y)(NO)_(z) and ensure both follow the Effective Atomic Number (EAN) rule.

### Step 1: Identify the EAN for Cr(CO)_(x)
The atomic number of chromium (Cr) is 24. Each carbonyl (CO) ligand donates 2 electrons. Therefore, the EAN for Cr(CO)_(x) can be calculated as follows:

\[ \text{EAN} = \text{Atomic Number of Cr} + 2 \times x \]
\[ \text{EAN} = 24 + 2x \]

### Step 2: Determine the EAN for Cr(CO)_(y)(NO)_(z)
In the product Cr(CO)_(y)(NO)_(z), carbonyl (CO) still donates 2 electrons, while nitrosyl (NO) donates 3 electrons. The EAN can be expressed as:

\[ \text{EAN} = \text{Atomic Number of Cr} + 2 \times y + 3 \times z \]
\[ \text{EAN} = 24 + 2y + 3z \]

### Step 3: Apply the EAN Rule
According to the problem, both reactant and product must satisfy the EAN rule, which means:

\[ 24 + 2x = 24 + 2y + 3z \]

### Step 4: Simplify the Equation
By simplifying the equation, we can eliminate the common terms:

\[ 2x = 2y + 3z \]

### Step 5: Rearrange the Equation
Rearranging gives us:

\[ 2x - 2y = 3z \]
\[ 2(x - y) = 3z \]

### Step 6: Solve for Natural Numbers
Since x, y, and z are natural numbers, we can express z in terms of x and y:

\[ z = \frac{2(x - y)}{3} \]

To ensure z is a natural number, \(2(x - y)\) must be divisible by 3. This implies that \(x - y\) must be a multiple of 3.

### Step 7: Assign Values to x, y, and z
To find suitable values for x, y, and z, we can try different values for x and y.

Let’s assume:
- If \(x = 6\) (which corresponds to 3 CO ligands),
- Then \(y = 3\) (which corresponds to 1 CO ligand),
- We can substitute these values into the equation to find z:

\[ z = \frac{2(6 - 3)}{3} = \frac{2 \times 3}{3} = 2 \]

### Step 8: Calculate x + z - y
Now we can calculate \(x + z - y\):

\[ x + z - y = 6 + 2 - 3 = 5 \]

### Final Answer
Thus, the value of \(x + z - y\) is:

**5**