Given :
(i) `C("graphite") +O_2(g)toCO_2(g)DeltarH^(Theta)="x kj "mol^(-1)`
(ii)`C("graphite") +(1)/(2)O_2(g)toCO(g),DeltarH^(Theta)="y kj "mol^(-1)`
(iii) `CO(g) +(1)/(2)O_2(g) toCO_2(g),DeltarH^(theta)="zkj" mol^(-1)`
Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct ?

Options

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

Explanation

To solve the problem, we will analyze the given thermochemical equations step by step and derive the correct algebraic relationship between the enthalpy changes.

### Step-by-Step Solution:

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

2. **Combine Reactions**:
- We will add Reaction (ii) and Reaction (iii):
- From Reaction (ii):
\[ \text{C (graphite)} + \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}(g) \quad \text{(enthalpy = y)} \]
- From Reaction (iii):
\[ \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \text{(enthalpy = z)} \]

3. **Add the Enthalpy Changes**:
- When we add these two reactions, the CO produced in Reaction (ii) cancels out with the CO consumed in Reaction (iii):
\[ \text{C (graphite)} + \frac{1}{2} \text{O}_2(g) + \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}(g) + \text{CO}_2(g) \]
- This simplifies to:
\[ \text{C (graphite)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) \]

4. **Calculate the Total Enthalpy**:
- The total enthalpy change for this combined reaction is:
\[ \Delta_r H^\Theta = y + z \]

5. **Relate to Reaction (i)**:
- From Reaction (i), we know:
\[ \Delta_r H^\Theta = x \]
- Therefore, we can equate:
\[ x = y + z \]

### Conclusion:
The correct algebraic relationship based on the given thermochemical equations is:
\[ \boxed{x = y + z} \]