If enthalpies of formation of `C_(2)H_(4)(g)1`,CO_(2) and`H_(2)O(l)` at`25(@)C` and`1`atm pressure be `52,-394`and`-286kJmol^(-1)`respectively ,the enthalpy of combustion of `C_(2)H_(4)(g)`will be

Options

A. `-141.2 KJ//mol`
B. `-1412` KJ/mol
C. `+14.2` KJ/mol
D. `+1412` KJ/mol

Explanation

To find the enthalpy of combustion of \( C_2H_4(g) \), we will use the enthalpy of formation values provided for the reactants and products involved in the combustion reaction. The combustion of ethylene (\( C_2H_4 \)) can be represented by the following balanced chemical equation:

\[ C_2H_4(g) + 3O_2(g) \rightarrow 2CO_2(g) + 2H_2O(l) \]

### Step 1: Write down the enthalpy of formation values.
- Enthalpy of formation of \( C_2H_4(g) \): \( \Delta H_f = +52 \, \text{kJ/mol} \)
- Enthalpy of formation of \( CO_2(g) \): \( \Delta H_f = -394 \, \text{kJ/mol} \)
- Enthalpy of formation of \( H_2O(l) \): \( \Delta H_f = -286 \, \text{kJ/mol} \)
- Enthalpy of formation of \( O_2(g) \): \( \Delta H_f = 0 \, \text{kJ/mol} \) (as it is in its standard state)

### Step 2: Calculate the total enthalpy of formation for the products.
The products of the reaction are \( 2CO_2 \) and \( 2H_2O \). Therefore, we calculate the total enthalpy of formation for the products:

\[ \Delta H_{products} = 2 \times \Delta H_f(CO_2) + 2 \times \Delta H_f(H_2O) \]
\[ = 2 \times (-394) + 2 \times (-286) \]
\[ = -788 - 572 \]
\[ = -1360 \, \text{kJ} \]

### Step 3: Calculate the total enthalpy of formation for the reactants.
The reactants are \( C_2H_4 \) and \( 3O_2 \):

\[ \Delta H_{reactants} = \Delta H_f(C_2H_4) + 3 \times \Delta H_f(O_2) \]
\[ = 52 + 3 \times 0 \]
\[ = 52 \, \text{kJ} \]

### Step 4: Calculate the enthalpy of combustion.
The enthalpy of combustion (\( \Delta H_{combustion} \)) can be calculated using the formula:

\[ \Delta H_{combustion} = \Delta H_{products} - \Delta H_{reactants} \]
\[ = -1360 - 52 \]
\[ = -1412 \, \text{kJ/mol} \]

### Final Answer:
The enthalpy of combustion of \( C_2H_4(g) \) is \( -1412 \, \text{kJ/mol} \).

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