For the following reactions, occurring at 500 K, arrange them in order of increasing tendency to proceed to completion (least `rarr` greatest tendency)
1. `2NOCl hArr 2NO + Cl_2 , K_p = 1.7 xx10^(-2)`
2. `2SO_3 hArr 2SO_2 + O_2 , K_p = 1.3 xx10^(-5)`
3. `2NO_2hArr 2NO+ O_2, K_p = 5.9 xx10^(-5)`

Options

A. `2 lt 1 lt 3`
B. `1 lt 2 lt 3`
C. `2 lt 3 lt 1`
D. ` 3 lt 2 lt 1 `

Answer

To solve the problem of arranging the given reactions in order of increasing tendency to proceed to completion, we will analyze the equilibrium constants (Kp) for each reaction. The larger the Kp value, the greater the tendency for the reaction to proceed to completion.

### Step-by-Step Solution:

1. **Identify the Kp values for each reaction:**
- Reaction 1: \( 2NOCl \rightleftharpoons 2NO + Cl_2 \), \( K_p = 1.7 \times 10^{-2} \)
- Reaction 2: \( 2SO_3 \rightleftharpoons 2SO_2 + O_2 \), \( K_p = 1.3 \times 10^{-5} \)
- Reaction 3: \( 2NO_2 \rightleftharpoons 2NO + O_2 \), \( K_p = 5.9 \times 10^{-5} \)

2. **Compare the Kp values:**
- \( K_p \) for Reaction 1: \( 1.7 \times 10^{-2} \) (highest)
- \( K_p \) for Reaction 2: \( 1.3 \times 10^{-5} \) (lowest)
- \( K_p \) for Reaction 3: \( 5.9 \times 10^{-5} \) (intermediate)

3. **Determine the order of tendency to proceed to completion:**
- Since the Kp value indicates the extent of the reaction, we can arrange the reactions based on their Kp values:
- Reaction 2 has the lowest Kp value, indicating the least tendency to proceed to completion.
- Reaction 3 has a higher Kp value than Reaction 2 but lower than Reaction 1, indicating a moderate tendency.
- Reaction 1 has the highest Kp value, indicating the greatest tendency to proceed to completion.

4. **Final Arrangement:**
- Least tendency to proceed to completion: Reaction 2
- Moderate tendency: Reaction 3
- Greatest tendency to proceed to completion: Reaction 1

Thus, the order from least to greatest tendency to proceed to completion is:
**Reaction 2 < Reaction 3 < Reaction 1**