Question

Given below are the reactions. Identify the reaction for which \(K_p<K_c\):

• A. \(\ce{N2(g)+O2(g)<=>2NO(g)}\)
• B. \(\ce{H2O(g)+CO(g)<=>H2(g)+CO2(g)}\)
• C. \(\ce{H2(g)+I2(g)<=>2HI(g)}\)
• D. \(\ce{N2(g)+3H2(g)<=>2NH3(g)}\)

Hint:

If \(\Delta n_g=0\), then \(K_p=K_c\). If \(\Delta n_g<0\), then \(K_p<K_c\).

Answer 1

The Correct Option is D

Step 1: Recall relation between \(K_p\) and \(K_c\).
For gaseous reactions: \[ K_p=K_c(RT)^{\Delta n_g} \] where: \[ \Delta n_g=\text{moles of gaseous products}-\text{moles of gaseous reactants}. \]

Step 2: Condition for \(K_p<K_c\).
If: \[ \Delta n_g<0, \] then: \[ (RT)^{\Delta n_g}<1 \] and hence: \[ K_p<K_c. \]

Step 3: Check option (A).
\[ \ce{N2(g)+O2(g)2NO(g)} \] \[ \Delta n_g=2-(1+1)=0. \] So: \[ K_p=K_c. \]

Step 4: Check option (B).
\[ \ce{H2O(g)+CO(g)H2(g)+CO2(g)} \] \[ \Delta n_g=2-2=0. \] So: \[ K_p=K_c. \]

Step 5: Check option (C).
\[ \ce{H2(g)+I2(g)2HI(g)} \] \[ \Delta n_g=2-2=0. \] So: \[ K_p=K_c. \]

Step 6: Check option (D).
\[ \ce{N2(g)+3H2(g)2NH3(g)} \] Moles of gaseous products: \[ 2 \] Moles of gaseous reactants: \[ 1+3=4. \] \[ \Delta n_g=2-4=-2. \] Since: \[ \Delta n_g<0, \] therefore: \[ K_p<K_c. \] Hence, the correct answer is: \[ \ce{N2(g)+3H2(g)2NH3(g)}. \]