Question

For a given reaction at 400 K (R = 0.082 atm-L/mol-K) \[ xA \longleftrightarrow yB \] Given (i) \(K_f = 0.82\), \(K_c = 25.7\)
(ii) \(K_f = 8.2\), \(K_c = 0.25\)
Then which will be the correct combination of x & y for above set (i) & set (ii) data?

• A. (1, 2)
• B. (2, 1)
• C. (1, 1)
• D. (1, 2)

Hint:

When calculating the relationship between \(K_p\) and \(K_c\), use the ideal gas law and the relationship \(K_p = K_c (RT)^{\Delta n}\) to determine the values of \( \Delta n \).

Answer 1

The Correct Option is B

Step 1: Relating \(K_p\) and \(K_c\).
\[ \frac{K_p}{K_c} = (RT)^{\Delta n} \] Where \(R = 0.082 \, \text{atm-L/mol-K}\) and \(T = 400 \, \text{K}\).
Step 2: Calculate \( \Delta n \).
For \( \Delta n = 1 \): \[ K_p = (RT)^{\Delta n} \cdot K_c = (0.082 \times 400)^{1} \times 25.7 = 32.8 \] For \( \Delta n = -1 \): \[ K_p = (RT)^{\Delta n} \cdot K_c = (0.082 \times 400)^{-1} \times 0.25 = 0.03 \]
Step 3: Analyzing the sets.
- In set (i), with \(K_p = 0.82\) and \(K_c = 25.7\), this corresponds to \( \Delta n = -1 \), so the correct value of x = 1 and y = 2. - In set (ii), with \(K_p = 8.2\) and \(K_c = 0.25\), this corresponds to \( \Delta n = +1 \), so the correct value of x = 2 and y = 1.
Step 4: Conclusion.
The correct combination of x and y is (2), i.e., (2, 1).