Given the enthalpy of formation of `CO_(2)(g)` is -94.0 KJ, of CaO(s)
is -152 KJ, and the enthalpy of the reaction `CaCO_(3)(s) rarr CaO(s)+CO_(2)(g)` is 42KJ, the enthalpy of
formation of `CaCO_(3) (s)` is

Options

A. `-288` kJ
B. `+202` kJ
C. `-202` kJ
D. `-42 ` kJ

Explanation

To find the enthalpy of formation of calcium carbonate (CaCO₃), we can use the given information and apply Hess's law. Here’s the step-by-step solution:

### Step 1: Write the reaction and identify the given data
The reaction we are considering is:
\[ \text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g) \]

Given data:
- Enthalpy of formation of CO₂(g), \( \Delta H_f^\circ (\text{CO}_2) = -94.0 \, \text{kJ} \)
- Enthalpy of formation of CaO(s), \( \Delta H_f^\circ (\text{CaO}) = -152.0 \, \text{kJ} \)
- Enthalpy change for the reaction, \( \Delta H = 42.0 \, \text{kJ} \)

### Step 2: Write the equation for the enthalpy change of the reaction
According to Hess's law:
\[ \Delta H = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants}) \]

For our reaction:
\[ \Delta H = \Delta H_f^\circ (\text{CaO}) + \Delta H_f^\circ (\text{CO}_2) - \Delta H_f^\circ (\text{CaCO}_3) \]

### Step 3: Substitute the known values into the equation
We can substitute the known values into the equation:
\[ 42.0 \, \text{kJ} = (-152.0 \, \text{kJ}) + (-94.0 \, \text{kJ}) - \Delta H_f^\circ (\text{CaCO}_3) \]

### Step 4: Simplify the equation
Combine the values on the right side:
\[ 42.0 \, \text{kJ} = -246.0 \, \text{kJ} - \Delta H_f^\circ (\text{CaCO}_3) \]

### Step 5: Solve for \( \Delta H_f^\circ (\text{CaCO}_3) \)
Rearranging the equation to solve for \( \Delta H_f^\circ (\text{CaCO}_3) \):
\[ \Delta H_f^\circ (\text{CaCO}_3) = -246.0 \, \text{kJ} - 42.0 \, \text{kJ} \]
\[ \Delta H_f^\circ (\text{CaCO}_3) = -288.0 \, \text{kJ} \]

### Conclusion
The enthalpy of formation of calcium carbonate (CaCO₃) is:
\[ \Delta H_f^\circ (\text{CaCO}_3) = -288.0 \, \text{kJ} \]

### Final Answer
The correct option is: **Option 1: -288 kJ**

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