What is the amount of heat to be supplied to prepare `128g` of `CaC_(2)` by using `CaCO_(3)` and followed by reduction with carbon, Reactions are
`CaCO_(3)(s)=CaO(s)+CO_(2)(g),DeltaH^(@)=42.8Kcal`
`CaO(s)+3C(s)=CaC_(2)+CO(g),DeltaH^(@)=111Kcal`

Options

A. 102.6 kcals
B. 221.78 kcals
C. 307.6 kcals
D. 453.46 kcals

Explanation

To solve the problem of calculating the amount of heat required to prepare 128 g of calcium carbide (CaC₂) from calcium carbonate (CaCO₃) followed by reduction with carbon, we can follow these steps:

### Step 1: Calculate the number of moles of CaC₂ needed
The molar mass of CaC₂ is calculated as follows:
- Molar mass of Ca = 40 g/mol
- Molar mass of C = 12 g/mol
- Therefore, molar mass of CaC₂ = 40 + (2 × 12) = 40 + 24 = 64 g/mol

Now, we can calculate the number of moles of CaC₂:
\[ \text{Number of moles of CaC₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{128 \text{ g}}{64 \text{ g/mol}} = 2 \text{ moles} \]

### Step 2: Write down the reactions and their enthalpy changes
1. The first reaction:
\[ \text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g) \quad \Delta H_1 = 42.8 \text{ kcal} \]

2. The second reaction:
\[ \text{CaO}(s) + 3\text{C}(s) \rightarrow \text{CaC}_2 + \text{CO}(g) \quad \Delta H_2 = 111 \text{ kcal} \]

### Step 3: Combine the reactions
To find the overall reaction for the preparation of CaC₂ from CaCO₃, we can add the two reactions together:
\[ \text{CaCO}_3 + 3\text{C} \rightarrow \text{CaC}_2 + \text{CO}_2 + \text{CaO} \]

### Step 4: Calculate the total enthalpy change for the combined reaction
The total enthalpy change for the combined reaction is:
\[ \Delta H_{\text{total}} = \Delta H_1 + \Delta H_2 = 42.8 \text{ kcal} + 111 \text{ kcal} = 153.8 \text{ kcal} \]

### Step 5: Adjust for the number of moles
Since the calculated enthalpy change is for 1 mole of CaC₂, and we need to prepare 2 moles, we multiply by 2:
\[ \Delta H_{\text{required}} = 2 \times 153.8 \text{ kcal} = 307.6 \text{ kcal} \]

### Final Answer
The amount of heat to be supplied to prepare 128 g of CaC₂ is **307.6 kcal**.

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