Given that:
`2C(s)+O_(2)(g)to2CO_(2)(g)" "(DeltaH=-787kJ)` . . . (i)
`H_(2)(g)+1//2O_(2)(g)toH_(2)O(l)" "(DeltaH=-286kJ)` . . . (ii)
`C_(2)H_(2)+2(1)/(2)O_(2)(g)to2CO_(2)(g)+H_(2)O(l)" "(DeltaH=-1310kJ)` . . .(iii)
The heat of formation of acetylene is:

Options

A. `+1802 kJ`
B. `-1802 kJ`
C. `-800 kJ`
D. `+237 kJ`

Answer

To find the heat of formation of acetylene (C₂H₂), we can use Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps. We will rearrange the given reactions to find the desired reaction for the formation of acetylene.

### Step-by-Step Solution:

1. **Identify the target reaction for the formation of acetylene:**
The formation reaction for acetylene (C₂H₂) can be written as:
\[ 2C(s) + H_2(g) \rightarrow C_2H_2(g) \]

2. **List the given reactions and their enthalpy changes:**
- Reaction (i):
\[ 2C(s) + O_2(g) \rightarrow 2CO_2(g) \quad (\Delta H = -787 \text{ kJ}) \]
- Reaction (ii):
\[ H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l) \quad (\Delta H = -286 \text{ kJ}) \]
- Reaction (iii):
\[ C_2H_2(g) + 2\frac{1}{2}O_2(g) \rightarrow 2CO_2(g) + H_2O(l) \quad (\Delta H = -1310 \text{ kJ}) \]

3. **Rearrange the reactions to form the target reaction:**
- For Reaction (i), we keep it as is since we need 2C on the left.
- For Reaction (ii), we also keep it as is since we need H₂ on the left.
- For Reaction (iii), we need to reverse it to get C₂H₂ on the left:
\[ 2CO_2(g) + H_2O(l) \rightarrow C_2H_2(g) + 2\frac{1}{2}O_2(g) \quad (\Delta H = +1310 \text{ kJ}) \]

4. **Combine the reactions:**
Now we will add the enthalpy changes:
- From Reaction (i): \(-787 \text{ kJ}\)
- From Reaction (ii): \(-286 \text{ kJ}\)
- From reversed Reaction (iii): \(+1310 \text{ kJ}\)

Therefore, the total enthalpy change (\(\Delta H\)) for the formation of acetylene is:
\[ \Delta H = -787 + (-286) + 1310 \]
\[ \Delta H = -787 - 286 + 1310 = 237 \text{ kJ} \]

5. **Final Result:**
The heat of formation of acetylene (C₂H₂) is:
\[ \Delta H_f = +237 \text{ kJ/mol} \]