Calculate the enthalpy of reaction for`CO(g) + (1)/(2) O_(2)(g) rarr CO_(2)(g)`
Given `C(s) + O_(2) (g) rarr CO_(2)(g) , DeltaH = -393.5 kJ mol^(-1)`
`C(s) + (1)/(2) O_(2)(g) rarr CO(g) Delta H = - 110 .5 kJ mol^(-1)`

Answer

To calculate the enthalpy of the reaction for the equation:

\[ \text{CO(g) + } \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g) \]

we can use Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction.

We are given the following reactions and their enthalpy changes:

1. \( \text{C(s) + O}_2(g) \rightarrow \text{CO}_2(g) \), \( \Delta H = -393.5 \, \text{kJ/mol} \) (Equation 1)
2. \( \text{C(s) + } \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO(g)} \), \( \Delta H = -110.5 \, \text{kJ/mol} \) (Equation 2)

### Step 1: Write down the reactions we have

We have two reactions:
- Reaction 1: Produces CO2 from C and O2.
- Reaction 2: Produces CO from C and half O2.

### Step 2: Reverse Equation 2

To find the enthalpy change for the formation of CO from C and O2, we need to reverse Equation 2:

\[ \text{CO(g)} \rightarrow \text{C(s) + } \frac{1}{2} \text{O}_2(g) \]

When we reverse a reaction, the sign of the enthalpy change also reverses:

\[ \Delta H = +110.5 \, \text{kJ/mol} \]

### Step 3: Add the reactions

Now we can add the reversed Equation 2 to Equation 1:

1. \( \text{C(s) + O}_2(g) \rightarrow \text{CO}_2(g) \), \( \Delta H = -393.5 \, \text{kJ/mol} \)
2. \( \text{CO(g)} \rightarrow \text{C(s) + } \frac{1}{2} \text{O}_2(g) \), \( \Delta H = +110.5 \, \text{kJ/mol} \)

Adding these two reactions together:

\[ \text{CO(g) + } \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g) \]

### Step 4: Calculate the total enthalpy change

Now, we can calculate the total enthalpy change for the reaction:

\[ \Delta H = (-393.5 \, \text{kJ/mol}) + (+110.5 \, \text{kJ/mol}) = -283.0 \, \text{kJ/mol} \]

### Final Answer

The enthalpy of reaction for:

\[ \text{CO(g) + } \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g) \]

is:

\[ \Delta H = -283.0 \, \text{kJ/mol} \]