Given :
(i) `C("graphite") + O_(2)(g) rarr CO(g) ,Delta_(r )H^(@) = xkJ mol^(-1)`
(ii) `C("graphite") + 1/2 O_(2)(g) rarr CO_(2)(g), Delta_(r )H^(@) = ykJ mol^(-1)`
(iii) `CO(g) + 1/2 O_(2)(g) rarr CO_(2)(g) , Delta_(r )H = z kJ mol^(-1)`
Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct ?

Options

A. `x = x + y`
B. `y = 2z -x`
C. `x = y - z`
D. `x = y + z`

Explanation

To solve the problem, we need to analyze the given thermochemical equations and derive the relationship between the enthalpy changes (ΔH) for these reactions.

### Step-by-Step Solution:

1. **Identify the Reactions and Their Enthalpy Changes:**
- Reaction (i):
\[ \text{C (graphite)} + \text{O}_2(g) \rightarrow \text{CO}(g), \quad \Delta_r H^{\circ} = x \text{ kJ/mol} \]
- Reaction (ii):
\[ \text{C (graphite)} + \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g), \quad \Delta_r H^{\circ} = y \text{ kJ/mol} \]
- Reaction (iii):
\[ \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g), \quad \Delta_r H = z \text{ kJ/mol} \]

2. **Reverse Reaction (i) to Relate to Reaction (iii):**
- If we reverse Reaction (i), we get:
\[ \text{CO}(g) \rightarrow \text{C (graphite)} + \text{O}_2(g), \quad \Delta_r H = -x \text{ kJ/mol} \]

3. **Combine the Reversed Reaction (i) with Reaction (ii):**
- Now, we can add the reversed Reaction (i) to Reaction (ii):
\[ \text{CO}(g) \rightarrow \text{C (graphite)} + \text{O}_2(g) \quad (-x) \]
\[ \text{C (graphite)} + \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad (y) \]
- Adding these two reactions gives:
\[ \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g) \]

4. **Calculate the Enthalpy Change for the Combined Reaction:**
- The total enthalpy change for this combined reaction is:
\[ \Delta H = (-x) + y = y - x \]
- This is equal to the enthalpy change for Reaction (iii):
\[ z = y - x \]

5. **Rearranging the Equation:**
- From the equation \( z = y - x \), we can rearrange it to find:
\[ x = y - z \]

### Conclusion:
The correct algebraic relationship based on the given reactions is:
\[ x = y - z \]