Calculate the heat required to make 6.4kg of `CaC_2` from `CaO(s) and C(s)` from the reaction that `DeltaH_f^@(CaO) = -151.6 kcal`
`DeltaH_f^@(CaC_2) = -14.2 kcal`
`DeltaH_f^@(CO) = -26.4 kcal`.

Options

A. `5624 kcal`
B. `86.24 xx 10^3 kcal`
C. `1.11 xx 10^4 kcal`
D. `1100 kcal`

Answer

To calculate the heat required to make 6.4 kg of CaC₂ from CaO(s) and C(s) using the given reaction, we will follow these steps:

### Step 1: Write the balanced chemical reaction
The balanced reaction is:
\[ \text{CaO}(s) + 3\text{C}(s) \rightarrow \text{CaC}_2(s) + \text{CO}(g) \]

### Step 2: Write the enthalpy change for the reaction
The enthalpy change (\( \Delta H \)) for the reaction can be calculated using the standard enthalpy of formation values:
\[ \Delta H = \Delta H_f(\text{CaC}_2) + \Delta H_f(\text{CO}) - \Delta H_f(\text{CaO}) - 3 \Delta H_f(\text{C}) \]

Given:
- \( \Delta H_f(\text{CaO}) = -151.6 \, \text{kcal} \)
- \( \Delta H_f(\text{CaC}_2) = -14.2 \, \text{kcal} \)
- \( \Delta H_f(\text{CO}) = -26.4 \, \text{kcal} \)
- \( \Delta H_f(\text{C}) = 0 \, \text{kcal} \) (since carbon in its standard state has an enthalpy of formation of zero)

Substituting the values:
\[ \Delta H = (-14.2) + (-26.4) - (-151.6) - 3(0) \]
\[ \Delta H = -14.2 - 26.4 + 151.6 \]
\[ \Delta H = 111.0 \, \text{kcal} \]

### Step 3: Calculate the moles of CaC₂ produced
To find the moles of CaC₂ in 6.4 kg:
1. Convert kg to grams:
\[ 6.4 \, \text{kg} = 6400 \, \text{g} \]
2. Calculate the molar mass of CaC₂:
- Ca: 40.08 g/mol
- C: 12.01 g/mol
- Molar mass of CaC₂ = 40.08 + (2 × 12.01) = 64.10 g/mol

3. Calculate the number of moles of CaC₂:
\[ \text{moles of CaC}_2 = \frac{6400 \, \text{g}}{64.10 \, \text{g/mol}} \approx 99.84 \, \text{mol} \]

### Step 4: Calculate the total heat required
Using the enthalpy change for the reaction:
\[ \text{Total heat} = \text{moles of CaC}_2 \times \Delta H \]
\[ \text{Total heat} = 99.84 \, \text{mol} \times 111.0 \, \text{kcal/mol} \]
\[ \text{Total heat} \approx 11097.84 \, \text{kcal} \]

### Final Answer
The heat required to make 6.4 kg of CaC₂ is approximately **11097.84 kcal**.

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