The heats of combustion of carbon,hydrogen and acetylene are `-394kJ, -286kJ and -1301kJ` respectively. Calculate heat of formation of `C_(2)H_(2)`

Options

A. 621 kJ
B. 454 kJ
C. `-227 kJ`
D. 227 kJ

Answer

To calculate the heat of formation of acetylene (C₂H₂) using the heats of combustion of carbon, hydrogen, and acetylene, we can use Hess's law. Here’s a step-by-step solution:

### Step 1: Write the combustion reactions and their enthalpy changes.

1. **Combustion of Carbon:**
\[ C + O_2 \rightarrow CO_2 \quad \Delta H = -394 \text{ kJ} \]

2. **Combustion of Hydrogen:**
\[ H_2 + \frac{1}{2} O_2 \rightarrow H_2O \quad \Delta H = -286 \text{ kJ} \]

3. **Combustion of Acetylene:**
\[ C_2H_2 + \frac{5}{2} O_2 \rightarrow 2 CO_2 + H_2O \quad \Delta H = -1301 \text{ kJ} \]

### Step 2: Write the formation reaction for acetylene.

The formation reaction for acetylene from its elements is:
\[ 2 C (s) + H_2 (g) \rightarrow C_2H_2 (g) \quad \Delta H_f = ? \]

### Step 3: Manipulate the combustion reactions to derive the formation reaction.

To find the heat of formation of acetylene, we need to manipulate the combustion reactions. We will reverse the combustion reactions of acetylene, carbon, and hydrogen to match the formation reaction.

1. **Reverse the combustion of acetylene:**
\[ 2 CO_2 + H_2O \rightarrow C_2H_2 + \frac{5}{2} O_2 \quad \Delta H = +1301 \text{ kJ} \]

2. **Use the combustion of carbon (2 moles):**
\[ 2 C + O_2 \rightarrow 2 CO_2 \quad \Delta H = -788 \text{ kJ} \quad (\text{since } 2 \times -394 \text{ kJ}) \]

3. **Use the combustion of hydrogen:**
\[ H_2 + \frac{1}{2} O_2 \rightarrow H_2O \quad \Delta H = -286 \text{ kJ} \]

### Step 4: Combine the reactions.

Now, we combine the reactions:
- From the reverse combustion of acetylene: \( +1301 \text{ kJ} \)
- From the combustion of carbon: \( -788 \text{ kJ} \)
- From the combustion of hydrogen: \( -286 \text{ kJ} \)

### Step 5: Calculate the overall enthalpy change.

Now we can add the enthalpy changes:
\[ \Delta H_f = (+1301) + (-788) + (-286) \]

Calculating this gives:
\[ \Delta H_f = 1301 - 788 - 286 = 227 \text{ kJ} \]

### Conclusion

The heat of formation of acetylene (C₂H₂) is \( +227 \text{ kJ} \).