What will be the heat of formation of ethane, if the heat of combustion of carbon is `-x kJ` ,heat of formation of water is -ykJ and heat liberated during complete combustion of ethane is zkJ

Options

A. `(-2x-2y+z)kJ`
B. `(-2x-3y+z)kJ`
C. `(-2x+3y+z)kJ`
D. `(-2x-3y-z)kJ`

Answer

To find the heat of formation of ethane (C2H6), we can use the given information about the heat of combustion of carbon, the heat of formation of water, and the heat liberated during the complete combustion of ethane.

### Step-by-Step Solution:

1. **Write the combustion reaction for ethane (C2H6):**
\[ C_2H_6 + O_2 \rightarrow 2CO_2 + 3H_2O \]

2. **Balance the combustion reaction:**
The balanced equation shows that 1 mole of ethane reacts with oxygen to produce 2 moles of carbon dioxide and 3 moles of water.

3. **Identify the heat of combustion of ethane:**
The heat liberated during the complete combustion of ethane is given as \( z \, \text{kJ} \).

4. **Use the enthalpy of formation for products:**
The enthalpy change for the combustion of ethane can be expressed using the enthalpies of formation of the products:
\[ \Delta H_{combustion} = \Delta H_f (products) - \Delta H_f (reactants) \]
For our reaction:
\[ z = [2 \Delta H_f (CO_2) + 3 \Delta H_f (H_2O)] - \Delta H_f (C_2H_6) \]

5. **Substitute the known values:**
We know:
- The heat of combustion of carbon (for forming CO2) is \( -x \, \text{kJ} \), so:
\[ \Delta H_f (CO_2) = -x \, \text{kJ} \]
- The heat of formation of water is \( -y \, \text{kJ} \), so:
\[ \Delta H_f (H_2O) = -y \, \text{kJ} \]

6. **Substituting these values into the equation:**
\[ z = [2(-x) + 3(-y)] - \Delta H_f (C_2H_6) \]
Simplifying this gives:
\[ z = -2x - 3y - \Delta H_f (C_2H_6) \]

7. **Rearranging to find the heat of formation of ethane:**
\[ \Delta H_f (C_2H_6) = -2x - 3y - z \]

### Final Result:
The heat of formation of ethane (C2H6) is:
\[ \Delta H_f (C_2H_6) = -2x - 3y - z \, \text{kJ} \]