The heat of combustion of carbon and monoxide are -394 and -285 KJ `mol^(-1)` respectively. The heat of formation of CO in KJ `mol^(-1)` is :-

Options

A. `+109`
B. `-109`
C. `+218`
D. `-218`

Answer

To determine the heat of formation of carbon monoxide (CO) using the given heats of combustion, we can follow these steps:

### Step 1: Write the combustion reactions
1. The combustion of carbon (C) to form carbon dioxide (CO₂):
\[ C + O_2 \rightarrow CO_2 \quad \Delta H_1 = -394 \, \text{kJ/mol} \]

2. The combustion of carbon monoxide (CO) to form carbon dioxide (CO₂):
\[ 2CO + O_2 \rightarrow 2CO_2 \quad \Delta H_2 = -285 \, \text{kJ/mol} \]

### Step 2: Write the formation reaction of CO
The formation of carbon monoxide (CO) from its elements is represented as:
\[ C + \frac{1}{2} O_2 \rightarrow CO \quad \Delta H_f = ? \]

### Step 3: Use Hess's Law
According to Hess's Law, the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps. We can manipulate the combustion reactions to find the heat of formation of CO.

1. From the first combustion reaction, we have:
\[ C + O_2 \rightarrow CO_2 \quad \Delta H_1 = -394 \, \text{kJ/mol} \]

2. From the second combustion reaction, we need to reverse it to express the formation of CO:
\[ CO_2 \rightarrow 2CO + O_2 \quad \Delta H_2 = +285 \, \text{kJ/mol} \]
(Note: Reversing the reaction changes the sign of ΔH)

### Step 4: Combine the reactions
Now, we can add these two reactions:
- The first reaction (combustion of C) produces CO₂.
- The second reaction (reversed combustion of CO) consumes CO₂.

Adding these gives:
\[ C + O_2 \rightarrow CO_2 \quad (-394 \, \text{kJ/mol}) \\ CO_2 \rightarrow 2CO + O_2 \quad (+285 \, \text{kJ/mol}) \]

When we add these, we can cancel out CO₂ and O₂:
\[ C + \frac{1}{2} O_2 \rightarrow CO \]

### Step 5: Calculate the heat of formation
Now we can calculate the heat of formation of CO:
\[ \Delta H_f = \Delta H_1 + \Delta H_2 = -394 + 285 \]
\[ \Delta H_f = -109 \, \text{kJ/mol} \]

### Final Answer
The heat of formation of carbon monoxide (CO) is:
\[ \Delta H_f = -109 \, \text{kJ/mol} \]