Given reaction is `2X_((gas)) + Y_((gas))hArr2Z_((gas)) + 80` Kcal
Which combination of pressure and temperature gives the highest yield of Z at equilibrium ?

Options

A. 1000 atm and `500^(@)C`
B. 500 atm and `500^(@)C`
C. 1000 atm and `100^(@)C`
D. 500 atm and `100^(@)C`

Explanation

To determine the combination of pressure and temperature that gives the highest yield of Z at equilibrium for the reaction:

\[ 2X_{(gas)} + Y_{(gas)} \rightleftharpoons 2Z_{(gas)} + 80 \text{ Kcal} \]

we will apply Le Chatelier's principle, which states that if an external change is applied to a system at equilibrium, the system will adjust itself to counteract that change.

### Step-by-Step Solution:

1. **Identify the Reaction Type**:
- The given reaction is:
\[ 2X + Y \rightleftharpoons 2Z + 80 \text{ Kcal} \]
- This reaction produces 2 moles of Z from 3 moles of reactants (2 moles of X and 1 mole of Y).

2. **Analyze the Effect of Pressure**:
- According to Le Chatelier's principle, increasing the pressure will shift the equilibrium toward the side with fewer moles of gas.
- In this reaction:
- Reactants: \( 2X + Y \) = 3 moles of gas
- Products: \( 2Z \) = 2 moles of gas
- Since the products side has fewer moles (2 moles) compared to the reactants side (3 moles), increasing the pressure will favor the formation of Z.

3. **Analyze the Effect of Temperature**:
- The reaction releases heat (exothermic) as indicated by the +80 Kcal on the product side.
- For exothermic reactions, lowering the temperature favors the formation of products.
- Therefore, to maximize the yield of Z, a lower temperature is preferred.

4. **Combine the Effects**:
- To achieve the highest yield of Z, we need to apply high pressure and low temperature.
- This combination will shift the equilibrium towards the products (Z) due to the reduction in moles and the exothermic nature of the reaction.

5. **Evaluate Given Options**:
- We need to check the provided options for high pressure and low temperature:
- Option 1: 1000 Atm and 500 °C (High pressure, High temperature)
- Option 2: 500 Atm and 500 °C (Medium pressure, High temperature)
- Option 3: 1000 Atm and 100 °C (High pressure, Low temperature)
- Among these, Option 3 (1000 Atm and 100 °C) has the highest pressure and the lowest temperature, which is ideal for maximizing the yield of Z.

### Conclusion:
The combination of high pressure and low temperature that gives the highest yield of Z at equilibrium is:
**1000 Atm and 100 °C**.