Question

The ratio \( \frac{K_p}{K_c} \) for the reaction \[ {CO}(g) + \frac{1}{2} {O}_2(g) \rightleftharpoons {CO}_2(g) \] is:

• A. \( (RT)^{1/2} \)
• B. \( RT \)
• C. 1
• D. \( \frac{1}{\sqrt{RT}} \)

Hint:

The ratio \( \frac{K_p}{K_c} \) depends on the change in the number of moles of gas between the products and reactants, and it is governed by the equation \( K_p = K_c (RT)^{\Delta n} \).

Answer 1

The Correct Option is D

Step 1: {Relationship Between \( K_p \) and \( K_c \)}
The equilibrium constants \( K_p \) and \( K_c \) are linked by the equation: \[ K_p = K_c (RT)^{\Delta n} \] where \( \Delta n \) represents the difference in the number of moles of gaseous products and reactants. 
Step 2: {Determine \( \Delta n \)} 
For the specified reaction: \[ \Delta n = {moles of products} - {moles of reactants} = 1 - \left( 1 + \frac{1}{2} \right) = -\frac{1}{2} \] 
Step 3: {Insert \( \Delta n \)} 
Substitute \( \Delta n = -\frac{1}{2} \) into the relationship: \[ K_p = K_c (RT)^{-\frac{1}{2}} \] The correct option is (D).