Questions given below are based on the given diagram for extractive metallurgy.
(iii) The make the following process spontaneous, temperature should be :
`ZnO + C rarr Zn + CO`.

Options

A. ` lt 1000^@ C`
B. `gt 1100^@ C`
C. `lt 500^@ C`
D. `gt 500^@ C " but" lt 1000^@ C`

Explanation

To determine the temperature required to make the reaction \( \text{ZnO} + \text{C} \rightarrow \text{Zn} + \text{CO} \) spontaneous, we can analyze the thermodynamic principles involved, particularly focusing on the Gibbs free energy change (\( \Delta G \)) for the reaction.

### Step-by-Step Solution:

1. **Understand the Reaction**:
The reaction involves zinc oxide (\( \text{ZnO} \)) being reduced by carbon (\( \text{C} \)) to produce zinc (\( \text{Zn} \)) and carbon monoxide (\( \text{CO} \)).

2. **Identify the Conditions for Spontaneity**:
A reaction is spontaneous when the change in Gibbs free energy (\( \Delta G \)) is negative. The relationship can be expressed as:
\[ \Delta G = \Delta H - T \Delta S \]
where \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.

3. **Analyze the Reaction**:
- **Enthalpy Change (\( \Delta H \))**: The reaction is endothermic, meaning it requires heat to proceed. Therefore, \( \Delta H \) is positive.
- **Entropy Change (\( \Delta S \))**: The reaction produces more gaseous products (1 mole of \( \text{CO} \) and 1 mole of \( \text{Zn} \)) from solid reactants, which increases disorder. Thus, \( \Delta S \) is positive.

4. **Determine the Temperature Condition**:
Since \( \Delta H \) is positive and \( \Delta S \) is also positive, for \( \Delta G \) to be negative (indicating spontaneity), the term \( -T \Delta S \) must be greater than \( \Delta H \). This leads to the condition:
\[ T > \frac{\Delta H}{\Delta S} \]
This indicates that at higher temperatures, the negative contribution of \( -T \Delta S \) can outweigh the positive \( \Delta H \).

5. **Refer to the Graph**:
According to the provided information, the critical temperature is around 1000 °C. Above this temperature, the free energy of the products (zinc and carbon monoxide) becomes lower than that of the reactants (zinc oxide and carbon), making the reaction spontaneous.

6. **Conclusion**:
Therefore, to make the reaction \( \text{ZnO} + \text{C} \rightarrow \text{Zn} + \text{CO} \) spontaneous, the temperature should be above 1000 °C.

### Final Answer:
The temperature should be above 1000 °C.

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