Chemical Equilibria And Dissociation

To solve this problem, we need to find the correct relationship between the degree of dissociation of and its equilibrium constant . Let's analyze the given reaction:

1. Let the initial pressure of be .
2. At equilibrium, let the degree of dissociation of be . Thus, the pressures at equilibrium are:
   • For :
   • For :
   • For :
3. Using these expressions, the total pressure at equilibrium is:
4. The equilibrium constant, , is defined as:
   • Substitute the equilibrium pressures:
5. Rearranging for gives:
   • Assuming is small, .
   • Solving for , we get:
6. Hence, the correct relationship between and is:

The solution confirms that the correct answer is the equation .

To solve this problem, we need to find the degree of dissociation, , in terms of the equilibrium constant and the total pressure for the given reaction.

1. Understanding the Equilibrium:
The reaction is: . We will use an ICE table to relate the initial pressure, the change in pressure due to dissociation, and the equilibrium pressures.

2. Setting Up the ICE Table:
Assume initial pressure of is .

| | | | | | :---------- | :---------- | :-------- | :---------------- | | Initial | | | | | Change | | | | | Equilibrium | | | |

3. Total Pressure at Equilibrium:
The total pressure is the sum of the partial pressures at equilibrium:
Since , .

4. Expressing in Terms of Partial Pressures:

5. Simplifying the Expression:
Since , we can approximate :
Since , .

6. Solving for :

Final Answer:
The degree of dissociation is .