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`

Answer

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 can apply Le Chatelier's principle, which states that if a system at equilibrium is subjected to a change in conditions (such as pressure or temperature), the equilibrium will shift in a direction that counteracts the change.

### Step 1: Analyze the Reaction
The given reaction involves 2 moles of gas \(X\) and 1 mole of gas \(Y\) on the reactant side, and 2 moles of gas \(Z\) on the product side.

- Total moles of reactants = 2 (from \(X\)) + 1 (from \(Y\)) = 3 moles
- Total moles of products = 2 (from \(Z\)) = 2 moles

### Step 2: Effect of Pressure
According to Le Chatelier's principle, increasing the pressure will favor the side of the reaction with fewer moles of gas. In this case, since there are 3 moles of gas on the reactant side and 2 moles on the product side, increasing the pressure will shift the equilibrium to the right, favoring the formation of \(Z\).

### Step 3: Effect of Temperature
The reaction is exothermic, as indicated by the release of 80 Kcal. For exothermic reactions, increasing the temperature will favor the endothermic direction (the reverse reaction). Therefore, to maximize the yield of \(Z\), we should lower the temperature.

### Conclusion
To achieve the highest yield of \(Z\) at equilibrium, we should:

- **Increase the pressure** to favor the production of \(Z\).
- **Decrease the temperature** to favor the forward reaction.

### Final Answer
The combination of **high pressure** and **low temperature** gives the highest yield of \(Z\) at equilibrium.

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