Understanding Kp vs Kc and the Δng Rule: Why most students overcomplicate this

Concept Breakdown

1. TITLE

Understanding $K_p$ vs $K_c$ and the $\Delta n_g$ Rule: Why most students overcomplicate this

2. CONCEPT EXPLANATION

When dealing with reversible reactions, we express the equilibrium constant using molar concentrations ($K_c$) or partial pressures ($K_p$). The bridge connecting these two constants is the Ideal Gas Law ($p = cRT$). By substituting molar concentration ($c$) with $p/RT$, we derive the ultimate linking formula: $K_p = K_c(RT)^{\Delta n}$.

Here, $R$ is the gas constant, $T$ is the temperature in Kelvin, and the absolute star of the formula is $\Delta n$. The underlying principle is that $\Delta n$ represents the difference between the number of moles of gaseous products and gaseous reactants ($\Delta n = c + d - a - b$).

The most common misconception to avoid is counting every molecule in the balanced equation. Because partial pressure is a property of gases, pure solids and pure liquids are completely ignored in this calculation because their molar concentrations remain constant. Just like in a busy market, only the actively moving crowds (gases) contribute to the pressure, not the fixed stalls (solids)!

3. MCQ

For the purification of nickel, the following heterogeneous equilibrium is established:
$Ni(s) + 4CO(g) \rightleftharpoons Ni(CO)_4(g)$

What is the correct relationship between $K_p$ and $K_c$ for this reaction?
(a) $K_p = K_c(RT)^{-3}$
(b) $K_p = K_c(RT)^{-4}$
(c) $K_p = K_c(RT)^{3}$
(d) $K_p = K_c$

4. ANSWER + EXPLANATION

Correct Answer: (a) $K_p = K_c(RT)^{-3}$

In the equilibrium formula $K_p = K_c(RT)^{\Delta n}$, the exponent $\Delta n$ stands strictly for the difference in the number of gaseous moles (moles of gaseous products minus moles of gaseous reactants). In this specific reaction, there is 1 mole of gaseous product ($Ni(CO)_4$) and 4 moles of gaseous reactant ($CO$). Therefore, $\Delta n = 1 - 4 = -3$.

Option (b) is a trap based on a common misconception: it incorrectly counts the solid Nickel ($Ni$) as a reactant, which would give $1 - 5 = -4$. Because the molar concentration of a pure solid is constant, it does not exert partial pressure and must be omitted from both the equilibrium expression and the $\Delta n$ count.

5. KEY TAKEAWAY BOX

Remember:
When calculating $\Delta n$ for the $K_p = K_c(RT)^{\Delta n}$ formula, only count the moles of gases; completely ignore all solids and liquids!

6. NCERT REFERENCE

NCERT Class 11, Chapter 6, Page 178
"NCERT defines this as: '$\Delta n =$ (number of moles of gaseous products) – (number of moles of gaseous reactants) in the balanced chemical equation.'"

7. CTA

Full chapter explanation → Equilibrium Complete Guide