In the preparation of CaO from `CaCO_(3)` using the equilibrium,
`CaCO_(3)(s) hArr CaO(s)+CO_(2)(g)`
`K_(p)` is expressed as
`log K_(p)=7.282-8500/T`
For complete decomposition of `CaCO_(3)`, the temperature in celsius to be used is:

Options

A. `1167`
B. `894`
C. `8500`
D. `850`

Explanation

To solve the problem of finding the temperature in Celsius required for the complete decomposition of calcium carbonate (CaCO₃) into calcium oxide (CaO) and carbon dioxide (CO₂), we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Reaction and Kp**:
The equilibrium reaction is:
\[ \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \]
The expression for \( K_p \) is given as:
\[ \log K_p = 7.282 - \frac{8500}{T} \]

2. **Condition for Complete Decomposition**:
For complete decomposition of CaCO₃, we need \( K_p = 1 \). This is because at complete decomposition, the partial pressures of the products and reactants reach a certain equilibrium where they balance out.

3. **Set Up the Equation**:
Since \( K_p = 1 \), we know:
\[ \log K_p = \log 1 = 0 \]
Therefore, we can set up the equation:
\[ 0 = 7.282 - \frac{8500}{T} \]

4. **Solve for T**:
Rearranging the equation gives:
\[ \frac{8500}{T} = 7.282 \]
Now, solving for \( T \):
\[ T = \frac{8500}{7.282} \]
Calculating this gives:
\[ T \approx 1167.26 \text{ K} \]

5. **Convert Temperature to Celsius**:
To convert the temperature from Kelvin to Celsius, use the formula:
\[ T(°C) = T(K) - 273.15 \]
Substituting the value of \( T \):
\[ T(°C) = 1167.26 - 273.15 \approx 894.11 °C \]

6. **Final Answer**:
The temperature required for the complete decomposition of CaCO₃ into CaO and CO₂ is approximately:
\[ \boxed{894.11 °C} \]