Question

smDetermine the heat of formation of CO from the following equations:
C +O= CO2; heat of formation= -393kj
CO + 1/2O2 = CO2; heat of formation= -285 and explain step by step

Answer 1

To find the heat of formation of carbon monoxide (CO), we can utilize Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps.

We are given two reactions with their associated heats of formation:

1. \( C + O_2 \rightarrow CO_2 \)
- Heat of formation (\( \Delta H_f \)) = -393 kJ

2. \( CO + \frac{1}{2} O_2 \rightarrow CO_2 \)
- Heat of formation (\( \Delta H_f \)) = -285 kJ

### Step 1: Write the reaction for CO formation
First, we need to find the reaction for the formation of carbon monoxide (CO):

\[
C + \frac{1}{2} O_2 \rightarrow CO
\]

### Step 2: Apply Hess’s Law
We will manipulate the given reactions to find the enthalpy change for the formation of CO.

1. The first reaction can be reversed to represent the formation of CO from CO2:
\[
CO_2 \rightarrow C + O_2
\]
Since we reversed this reaction, the sign of its enthalpy will change:
- Therefore, \( \Delta H = +393 \) kJ (since reversing reverses the sign).

2. The second reaction can be used directly:
\[
CO + \frac{1}{2} O_2 \rightarrow CO_2
\]
And its enthalpy change is:
- Therefore, \( \Delta H = -285 \) kJ.

### Step 3: Add the reactions
Now we can add these reactions together to find the desired reaction:

1. Reversed reaction (formation of CO2):
\[
CO_2 \rightarrow C + O_2 \quad \Delta H = +393 \, \text{kJ}
\]

2. Second reaction (formation of CO):
\[
CO + \frac{1}{2} O_2 \rightarrow CO_2 \quad \Delta H = -285 \, \text{kJ}
\]

Now, adding these two reactions together cancels out the CO2 and gives us the reaction for the formation of CO:
\[
CO_2 \rightarrow C + O_2 + CO + \frac{1}{2} O_2 \rightarrow CO_2
\]

It simplifies to:
\[
C + \frac{1}{2} O_2 \rightarrow CO
\]

### Step 4: Calculate the total enthalpy change
Now, add the enthalpy changes together:
\[
\Delta H = +393 \, \text{kJ} - 285 \, \text{kJ}
\]
\[
\Delta H = +108 \, \text{kJ}
\]

### Conclusion
Thus, the heat of formation\( \Delta H_f \) of carbon monoxide (CO) is:
\[
\Delta H_f = +108 \, \text{kJ/mol}
\]

This indicates that the formation of CO from its elements (carbon and oxygen) is an endothermic process.