Equilibrium in Physical and Chemical Processes — Revision Notes

⚡ 30-Second Revision

Equilibrium: — Dynamic state where Rate$_{\text{forward}}$ = Rate$_{\text{reverse}}$.
Macroscopic properties: — Constant at equilibrium.
Microscopic properties: — Continuous activity.
Reversible reactions: — Essential for equilibrium ($ightleftharpoons$).
Closed system: — Required for chemical equilibrium.
Catalyst: — Speeds up attainment of equilibrium, *does not* change K or equilibrium position.
Physical Equilibrium: — Phase changes (melting, boiling, sublimation, dissolution).

- $ext{H}_2\text{O}(s) \rightleftharpoons \text{H}_2\text{O}(l)$ at $0^circ\text{C}$.

Chemical Equilibrium: — Reactants $ightleftharpoons$ Products.

- Homogeneous: All species in same phase. - Heterogeneous: Species in different phases (pure solids/liquids excluded from K).

Equilibrium Constant ($K_c$): — For $aA + bB \rightleftharpoons cC + dD$, $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$.
Equilibrium Constant ($K_p$): — For gaseous reactions, $K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$.
Relationship: — $K_p = K_c (RT)^{Delta n_g}$.

- $Delta n_g = (sum n_{\text{gaseous products}}) - (sum n_{\text{gaseous reactants}})$. - $T$ in Kelvin, $R = 0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$.

Magnitude of K:

- Large K ($>10^3$): Products favored. - Small K ($<10^{-3}$): Reactants favored. - K $approx 1$: Significant amounts of both.

2-Minute Revision

Equilibrium is a dynamic state where the rates of forward and reverse processes are equal, leading to constant macroscopic properties but continuous molecular activity. It's crucial to remember that equilibrium does not mean the reaction has stopped or that reactant and product concentrations are equal; rather, they become constant.

Equilibrium can be physical (like melting or evaporation, where chemical identity doesn't change) or chemical (where reactants transform into products). Chemical equilibrium requires a reversible reaction in a closed system.

For chemical reactions, the equilibrium constant ($K_c$ for concentrations, $K_p$ for partial pressures) quantifies the relative amounts of products to reactants at equilibrium. Pure solids and liquids are excluded from these expressions because their concentrations are constant.

A key relationship for gaseous reactions is $K_p = K_c (RT)^{Delta n_g}$, where $Delta n_g$ is the change in moles of gaseous species. Catalysts only speed up the attainment of equilibrium; they do not alter the equilibrium position or the value of K.

The magnitude of K indicates the extent of the reaction: large K means products are favored, small K means reactants are favored.

5-Minute Revision

Let's consolidate the core concepts of equilibrium. Equilibrium is a dynamic state, not a static one. This means that at the molecular level, both the forward and reverse reactions (or physical processes) are continuously occurring, but at precisely equal rates.

Consequently, the observable macroscopic properties of the system, such as concentrations, pressures, and temperature, remain constant over time. This dynamic balance is a hallmark of all equilibrium systems, whether physical or chemical.

Physical Equilibrium involves changes in the physical state or phase of a substance without altering its chemical composition. Common examples include solid-liquid equilibrium (e.g., ice and water at $0^circ\text{C}$), liquid-gas equilibrium (e.g., water and its vapor in a closed container), and the dissolution of a solid in a liquid to form a saturated solution. In each case, the rate of the forward physical change equals the rate of the reverse physical change.

Chemical Equilibrium pertains to reversible chemical reactions where reactants convert to products, and products simultaneously convert back to reactants. For a generic reaction $aA + bB \rightleftharpoons cC + dD$, equilibrium is established when the rate of the forward reaction ($A+B \to C+D$) equals the rate of the reverse reaction ($C+D \to A+B$). The system must be closed to prevent loss or gain of matter.

**Equilibrium Constant ($K_c$ and $K_p$):** This constant quantifies the position of equilibrium. For concentrations, $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$. For gaseous reactions, $K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$.

A crucial point for heterogeneous equilibria is that the concentrations (or partial pressures) of pure solids and pure liquids are considered constant and are therefore omitted from the K expression. For example, for $ext{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g)$, $K_c = [\text{CO}_2]$ and $K_p = P_{\text{CO}_2}$.

**Relationship between $K_c$ and $K_p$:** For gaseous reactions, $K_p = K_c (RT)^{Delta n_g}$, where $Delta n_g = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants})$. Remember to use $T$ in Kelvin and the appropriate $R$ value ($0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$). If $Delta n_g = 0$, then $K_p = K_c$.

Effect of Catalyst: A catalyst accelerates both the forward and reverse reactions equally, thereby speeding up the attainment of equilibrium. However, it does not change the equilibrium constant ($K$) or the final equilibrium concentrations of reactants and products. It simply helps the system reach the same equilibrium state faster.

Magnitude of K: A large K value (e.g., $>10^3$) indicates that products are highly favored at equilibrium, meaning the reaction proceeds extensively. A small K value (e.g., $<10^{-3}$) suggests that reactants are favored, and the reaction proceeds minimally. If K is around 1, significant amounts of both reactants and products are present.

Prelims Revision Notes

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Definition of Equilibrium: — A dynamic state where the rate of the forward process equals the rate of the reverse process. Macroscopic properties (concentration, pressure, temperature, color) remain constant, but microscopic activity continues.
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Reversible Reactions: — Essential for equilibrium. Represented by $ightleftharpoons$.
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Conditions for Equilibrium: — Must occur in a closed system (for chemical equilibrium) and at a constant temperature.
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Catalyst Effect: — Catalysts speed up the attainment of equilibrium by lowering activation energy for both forward and reverse reactions equally. They *do not* change the equilibrium constant ($K$) or the equilibrium position.
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Types of Equilibrium:

* Physical Equilibrium: Involves physical changes (phase transitions, dissolution) without chemical identity change. Examples: $ext{H}_2\text{O}(s) \rightleftharpoons \text{H}_2\text{O}(l)$, $ext{H}_2\text{O}(l) \rightleftharpoons \text{H}_2\text{O}(g)$, $ext{Sugar}(s) \rightleftharpoons \text{Sugar}(aq)$.

* Chemical Equilibrium: Involves chemical reactions where reactants form products and vice-versa. * Homogeneous Equilibrium: All reactants and products are in the same phase (e.g., all gases, all aqueous solutions).

* Heterogeneous Equilibrium: Reactants and products are in different phases (e.g., solid and gas). Pure solids and pure liquids are *excluded* from the equilibrium constant expression as their concentrations are constant.

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Equilibrium Constant Expressions:

* For $aA + bB \rightleftharpoons cC + dD$: * $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ (in terms of molar concentrations) * $K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$ (in terms of partial pressures for gases)

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**Relationship between $K_p$ and $K_c$:**

* $K_p = K_c (RT)^{Delta n_g}$ * $Delta n_g = (\text{sum of stoichiometric coefficients of gaseous products}) - (\text{sum of stoichiometric coefficients of gaseous reactants})$. * $T$ must be in Kelvin ($T(\text{K}) = T(^circ\text{C}) + 273$). * $R = 0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$ (if pressure in atm) or $8.314,\text{J mol}^{-1}\text{K}^{-1}$ (if pressure in Pa). * If $Delta n_g = 0$, then $K_p = K_c$.

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Significance of K:

* $K > 10^3$: Products highly favored (reaction goes almost to completion). * $K < 10^{-3}$: Reactants highly favored (reaction proceeds very little). * $10^{-3} < K < 10^3$: Significant amounts of both reactants and products present at equilibrium.

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Common Misconceptions to Avoid: — Equilibrium does NOT mean reactions stop, nor does it mean concentrations of reactants and products are equal. Catalysts do NOT change K or equilibrium position.

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Dynamic: Equilibrium is dynamic.
Constant Concentrations: Macroscopic properties are constant.
Pure Solids/Liquids: Excluded from K expressions.
Kp = Kc (RT)$^{Delta n_g}$: The key relationship.
Catalyst: No effect on K or equilibrium position.