Equilibrium Constant — Revision Notes

⚡ 30-Second Revision

$K_c$ expression: — $K_c = \frac{[Products]^{coefficients}}{[Reactants]^{coefficients}}$ (for aqueous/gaseous species)
$K_p$ expression: — $K_p = \frac{(P_{Products})^{coefficients}}{(P_{Reactants})^{coefficients}}$ (for gaseous species)
Relationship: — $K_p = K_c(RT)^{Delta n_g}$

- $Delta n_g = (\text{moles gaseous products}) - (\text{moles gaseous reactants})$ - $R = 0.0821 \text{ L atm mol}^{-1}\text{ K}^{-1}$ (for $P$ in atm)

Factors affecting K: — Only temperature changes K.
Solids/Liquids: — Pure solids and liquids are excluded from K expressions.
Reaction Quotient (Q): — Same expression as K, but for non-equilibrium conditions.

- If $Q < K$: Reaction shifts forward. - If $Q > K$: Reaction shifts backward. - If $Q = K$: At equilibrium.

Effect of K value:

- Large K ($>10^3$): Products favored. - Small K ($<10^{-3}$): Reactants favored. - K $approx 1$: Comparable amounts of reactants/products.

2-Minute Revision

The equilibrium constant ($K$) quantifies the extent of a reversible reaction at equilibrium. For concentrations, it's $K_c = \frac{[Products]^{coeff}}{[Reactants]^{coeff}}$, and for partial pressures of gases, $K_p = \frac{(P_{Products})^{coeff}}{(P_{Reactants})^{coeff}}$.

Remember to exclude pure solids and liquids from these expressions. The relationship between $K_p$ and $K_c$ is $K_p = K_c(RT)^{Delta n_g}$, where $Delta n_g$ is the change in moles of gaseous species.

Crucially, only temperature affects the value of $K$; catalysts, initial concentrations, or pressure changes (at constant T) do not. A large $K$ means products are favored at equilibrium, while a small $K$ means reactants are favored.

The reaction quotient ($Q$) is calculated like $K$ but for non-equilibrium conditions. Comparing $Q$ with $K$ predicts the reaction direction: $Q < K$ (forward), $Q > K$ (reverse), $Q = K$ (equilibrium).

5-Minute Revision

The equilibrium constant ($K$) is a dimensionless value that describes the ratio of product concentrations (or partial pressures) to reactant concentrations (or partial pressures) at chemical equilibrium. It's a fundamental measure of the extent to which a reversible reaction proceeds. We primarily use two forms: $K_c$ for molar concentrations and $K_p$ for partial pressures of gases.

For a general reaction $aA + bB \rightleftharpoons cC + dD$:

$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ — (where $[X]$ denotes molar concentration at equilibrium)
$K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$ — (where $P_X$ denotes partial pressure at equilibrium)

Key Rules for Writing K Expressions:

1
Only include gaseous and aqueous species. Pure solids and liquids are omitted because their concentrations are constant.
2
Coefficients in the balanced equation become exponents in the K expression.

Relationship between $K_c$ and $K_p$:

For gaseous reactions, $K_p = K_c(RT)^{Delta n_g}$, where:

$R$ is the ideal gas constant ($0.0821 \text{ L atm mol}^{-1}\text{ K}^{-1}$ if $P$ in atm; $8.314 \text{ J mol}^{-1}\text{ K}^{-1}$ if $P$ in Pa).
$T$ is the absolute temperature in Kelvin.
$Delta n_g = (\text{sum of moles of gaseous products}) - (\text{sum of moles of gaseous reactants})$.

Interpreting K Value:

If $K gg 1$ (e.g., $K > 10^3$): Products are highly favored; reaction goes almost to completion.
If $K ll 1$ (e.g., $K < 10^{-3}$): Reactants are highly favored; very little product is formed.
If $K approx 1$: Significant amounts of both reactants and products are present at equilibrium.

Factors Affecting K:

Temperature: — The only factor that changes the numerical value of $K$. For endothermic reactions, $K$ increases with $T$; for exothermic reactions, $K$ decreases with $T$.
Other factors (concentration, pressure, catalyst): — Do NOT change the value of $K$. They only shift the equilibrium position to re-establish the same $K$ value.

Reaction Quotient (Q):

$Q$ has the same mathematical form as $K$ but is calculated using non-equilibrium concentrations/pressures. It helps predict the direction of reaction:

If $Q < K$: Reaction proceeds forward (towards products).
If $Q > K$: Reaction proceeds backward (towards reactants).
If $Q = K$: System is at equilibrium.

Example: For $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, if $K_c = 0.061,\text{M}^{-2}$ at $500,\text{K}$. $Delta n_g = 2 - (1+3) = -2$. $K_p = K_c(RT)^{Delta n_g} = 0.061 \times (0.0821 \times 500)^{-2} = 3.6 \times 10^{-5},\text{atm}^{-2}$.

Prelims Revision Notes

The equilibrium constant, $K$, is a crucial concept in chemical equilibrium, quantifying the ratio of products to reactants at a state of dynamic balance. For NEET, understanding its definition, calculation, and factors affecting it is paramount.

1. Definition and Expressions:

$K_c$ (Concentration): — For $aA + bB \rightleftharpoons cC + dD$, $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$. Concentrations are in mol/L.
$K_p$ (Partial Pressure): — For gaseous reactions, $K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$. Pressures are typically in atm or Pa.
Heterogeneous Equilibria: — Pure solids and pure liquids are excluded from $K$ expressions as their concentrations are constant. Example: $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$, $K_p = P_{CO_2}$, $K_c = [CO_2]$.

2. Relationship between $K_c$ and $K_p$:

$K_p = K_c(RT)^{Delta n_g}$
$Delta n_g = (\text{sum of stoichiometric coefficients of gaseous products}) - (\text{sum of stoichiometric coefficients of gaseous reactants})$.
$R = 0.0821 \text{ L atm mol}^{-1}\text{ K}^{-1}$ when pressure is in atm.
$T$ must be in Kelvin.
If $Delta n_g = 0$, then $K_p = K_c$.

3. Significance of K:

Extent of Reaction:

* $K gg 1$ (e.g., $K > 10^3$): Products are highly favored at equilibrium. * $K ll 1$ (e.g., $K < 10^{-3}$): Reactants are highly favored at equilibrium. * $K approx 1$: Significant amounts of both reactants and products exist at equilibrium.

4. Factors Affecting K:

Temperature: — The ONLY factor that changes the value of $K$.

* For endothermic reactions ($Delta H > 0$), increasing $T$ increases $K$. * For exothermic reactions ($Delta H < 0$), increasing $T$ decreases $K$.

Other factors (Concentration, Pressure/Volume, Catalyst): — Do NOT change the value of $K$. They only shift the equilibrium position according to Le Chatelier's principle to re-establish the same $K$.

5. Reaction Quotient (Q):

Calculated using the same expression as $K$, but with non-equilibrium concentrations/pressures.
Prediction of Reaction Direction:

* If $Q < K$: Reaction proceeds forward (towards products). * If $Q > K$: Reaction proceeds backward (towards reactants). * If $Q = K$: System is at equilibrium.

6. Manipulating K:

Reversing a reaction: — New $K' = 1/K$.
Multiplying coefficients by 'n': — New $K' = K^n$.
Adding reactions: — New $K' = K_1 \times K_2 \times K_3 dots$

Key for NEET: Practice ICE table calculations extensively. Be careful with exponents and units. Always check for gaseous species when calculating $Delta n_g$ and for solids/liquids when writing expressions.

Vyyuha Quick Recall

King Plays Chess Really Tough, Doing Numbers Greatly!

King Plays: $K_p$
Chess: $K_c$
Really Tough: $(RT)$
Doing Numbers Greatly: $Delta n_g$

This helps remember the formula: $K_p = K_c(RT)^{Delta n_g}$