The standard enthalpy of formation of `C_(2)H_(4)(l)`, `CO_(2)(g)` and `H_(2)O(l)` are `52`, `394` and `-286 kJ mol^(-1)` respectively. Then the amount of heat evolved by burning `7g` of `C_(2)H_(4)(g)` is

Options

A. `1412 kJ`
B. `9884 kJ`
C. `353 kJ`
D. `706 kJ`

Explanation

To solve the problem of calculating the amount of heat evolved by burning 7 g of \(C_2H_4(g)\), we will follow these steps:

### Step 1: Write the balanced equation for the combustion of \(C_2H_4\).
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 2: Determine the standard enthalpy change (\(\Delta H\)) for the combustion reaction.
We can calculate the standard enthalpy change using the formula:

\[ \Delta H = \sum (\Delta H \text{ of products}) - \sum (\Delta H \text{ of reactants}) \]

From the problem, we have:
- \(\Delta H_f\) of \(C_2H_4(l) = 52 \, kJ/mol\)
- \(\Delta H_f\) of \(CO_2(g) = -394 \, kJ/mol\)
- \(\Delta H_f\) of \(H_2O(l) = -286 \, kJ/mol\)

Calculating the enthalpy of products:
\[ \Delta H \text{ of products} = 2 \times (-394) + 2 \times (-286) \]
\[ = -788 - 572 = -1360 \, kJ \]

Calculating the enthalpy of reactants:
\[ \Delta H \text{ of reactants} = 52 + 0 = 52 \, kJ \quad (\text{since } O_2 \text{ is in elemental state}) \]

Now substituting into the equation:
\[ \Delta H = (-1360) - (52) = -1412 \, kJ/mol \]

### Step 3: Calculate the number of moles of \(C_2H_4\) in 7 g.
The molar mass of \(C_2H_4\) is:
\[ C: 12 \times 2 = 24 \, g/mol \]
\[ H: 1 \times 4 = 4 \, g/mol \]
\[ \text{Total} = 24 + 4 = 28 \, g/mol \]

Now, calculate the number of moles in 7 g:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{7 \, g}{28 \, g/mol} = \frac{1}{4} \, mol \]

### Step 4: Calculate the heat evolved for burning 7 g of \(C_2H_4\).
Since the enthalpy change is per mole, we need to multiply by the number of moles:
\[ \text{Heat evolved} = \Delta H \times \text{Number of moles} = -1412 \, kJ/mol \times \frac{1}{4} \, mol \]
\[ = -353 \, kJ \]

### Final Answer:
The amount of heat evolved by burning 7 g of \(C_2H_4(g)\) is \(353 \, kJ\).

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