Question:
\(\dfrac{K_p}{K_c}\) for the reaction at \(T(K)\) is
\[
CO(g)+\frac{1}{2}O_2(g)\rightleftharpoons CO_2(g)
\]
\(\dfrac{K_p}{K_c}\) for the reaction at \(T(K)\) is
\[
CO(g)+\frac{1}{2}O_2(g)\rightleftharpoons CO_2(g)
\]
Show Hint
Always use
\[
K_p=K_c(RT)^{\Delta n}
\]
where
\[
\Delta n=(\text{gaseous product moles})-(\text{gaseous reactant moles})
\]
Only gaseous species are considered while calculating \(\Delta n\).
Updated On: Jul 18, 2026
- \(\sqrt{RT}\)
- \(2RT\)
- \(RT\)
- \(\dfrac{1}{\sqrt{RT}}\)
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Use the relation between \(K_p\) and \(K_c\).
For a gaseous equilibrium, \[ K_p=K_c(RT)^{\Delta n} \] where \[ \Delta n = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants}) \]
Step 2: Calculate \(\Delta n\) for the given reaction.
Given reaction: \[ CO(g)+\frac{1}{2}O_2(g)\rightleftharpoons CO_2(g) \] Number of moles of gaseous products: \[ n_p=1 \] Number of moles of gaseous reactants: \[ n_r=1+\frac{1}{2} = \frac{3}{2} \] Therefore, \[ \Delta n = 1-\frac{3}{2} = -\frac{1}{2} \]
Step 3: Substitute \(\Delta n\) into the formula.
\[ K_p = K_c(RT)^{-1/2} \] Therefore, \[ \frac{K_p}{K_c} = (RT)^{-1/2} \]
Step 4: Simplify the expression.
Using the property \[ a^{-1/2} = \frac{1}{\sqrt{a}} \] we get \[ \frac{K_p}{K_c} = \frac{1}{\sqrt{RT}} \]
Step 5: Final conclusion.
Hence, \[ \boxed{\frac{K_p}{K_c}=\frac{1}{\sqrt{RT}}} \] Therefore, option (4) is correct.
For a gaseous equilibrium, \[ K_p=K_c(RT)^{\Delta n} \] where \[ \Delta n = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants}) \]
Step 2: Calculate \(\Delta n\) for the given reaction.
Given reaction: \[ CO(g)+\frac{1}{2}O_2(g)\rightleftharpoons CO_2(g) \] Number of moles of gaseous products: \[ n_p=1 \] Number of moles of gaseous reactants: \[ n_r=1+\frac{1}{2} = \frac{3}{2} \] Therefore, \[ \Delta n = 1-\frac{3}{2} = -\frac{1}{2} \]
Step 3: Substitute \(\Delta n\) into the formula.
\[ K_p = K_c(RT)^{-1/2} \] Therefore, \[ \frac{K_p}{K_c} = (RT)^{-1/2} \]
Step 4: Simplify the expression.
Using the property \[ a^{-1/2} = \frac{1}{\sqrt{a}} \] we get \[ \frac{K_p}{K_c} = \frac{1}{\sqrt{RT}} \]
Step 5: Final conclusion.
Hence, \[ \boxed{\frac{K_p}{K_c}=\frac{1}{\sqrt{RT}}} \] Therefore, option (4) is correct.
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