Chapter Six: Equilibrium - PDF

## Chapter Six: Equilibrium Chemical equilibria are important in numerous **biological** and **environmental processes**. - For example, the equilibrium involving **oxygen molecules** and **hemoglobin** is crucial for the transport and delivery of oxygen from the lungs to the muscles. - Similarl...

## Chapter Six: Equilibrium Chemical equilibria are important in numerous **biological** and **environmental processes**. - For example, the equilibrium involving **oxygen molecules** and **hemoglobin** is crucial for the transport and delivery of oxygen from the lungs to the muscles. - Similarly, the equilibrium involving **carbon monoxide molecules** and **hemoglobin** accounts for the toxicity of CO. ### The concept of Equilibrium - When a liquid evaporates in a closed container, molecules with **relatively higher kinetic energy** escape from the liquid surface into the **vapor phase**. - Molecules from the vapor phase strike the liquid surface and **remain** in the liquid phase. - Equilibrium establishes when the **number of molecules leaving the liquid phase** is equal to the **number of molecules returning to the liquid phase**. - At this **equilibrium stage**, the system reaches a **constant vapor pressure**. - However, this is not a **static equilibrium**. There is constant activity at the boundary between the liquid and the vapor phases. - The **rate of evaporation** is equal to the **rate of condensation** at equilibrium. - This is represented as follows: ``` H2O(l) ⇌ H2O(g) ``` - The **double half arrows** indicate that the process occurs in both directions simultaneously. - The **mixture of reactants and products** at equilibrium is called the **equilibrium mixture**. - Equilibrium can be established for both **physical processes** and **chemical reactions**. ### Factors Affecting Equilibrium - The **rate of a reaction** (fast or slow) depends on the **experimental conditions and the nature of the reactants**. - For a given reaction, the **extent of the reaction** is determined by the following factors: - **Temperature** - **Concentration of reactants** - **Pressure** - **Catalyst** ### Equilibrium in Physical Processes The characteristics of equilibrium can be better understood by examining **familiar physical processes**. - **Phase transformation processes** are prominent examples: ``` Solid ⇌ Liquid Liquid ⇌ Gas Solid ⇌ Gas ``` - **Solid-Liquid Equilibrium:** - At **273 K** and **atmospheric pressure**, a perfectly insulated **thermos flask containing ice and water** is at equilibrium. - There is no exchange of heat between the contents and the surrounding. - The mass of ice and water remains **constant**. - This is a dynamic equilibrium, with constant activity at the boundary between ice and water. - The rate of **molecules transferring from ice to water** is equal to the rate of **molecules transferring from water to ice**. - At the melting point (or freezing point), the solid and liquid phases of a pure substance are **in equilibrium**. - **Liquid-Vapor Equilibrium:** - Consider a **transparent box** containing a U-tube with mercury (a manometer) and a drying agent (anhydrous calcium chloride or phosphorus pentaoxide). - After removing the drying agent, a **dish of water** is placed in the box. - The mercury level in the manometer's **right limb** slowly increases, indicating an increase in **pressure inside the box**. - The **volume of water** in the dish decreases. - Initially, the box contains very **little water vapor**. - As water evaporates, the pressure inside the box **increases**. - The **rate of evaporation** is constant, but the rate of **condensation** increases as pressure increases. - Ultimately, **equilibrium is attained** when there is no net evaporation, and the **number of molecules leaving the liquid phase** equals the **number of molecules entering the liquid phase.** - The **pressure exerted by the water molecules** at equilibrium is called the **equilibrium vapor pressure of water**, or simply the **vapor pressure of water**. - Vapor pressure **increases with temperature**. - Substances with **higher vapor pressures** are more **volatile** and have **lower boiling points**. - The rate of evaporation depends on the **nature of the liquid**, its **amount**, and the **temperature**. - If the watch glass is open to the air, the rate of evaporation is constant, but the rate of condensation is much less. - Equilibrium is not possible in **open systems**. - At **1.013 bar pressure** and **100°C**, water and water vapor are **in equilibrium in a closed vessel**. This is the **normal boiling point of water**. - The boiling point of a pure liquid is **dependent on pressure**. - Boiling point is **lower at higher altitudes**. - **Solid-Vapor Equilibrium:** - Consider a **closed vessel** containing **solid iodine**. - The vessel soon fills with **violet vapors**. - The **intensity of the color** increases with time, attaining a **constant value** at equilibrium. - Solid iodine sublimes to form iodine vapor, and iodine vapor **condenses** to form solid iodine. - This is represented as follows: ``` I_2(s) ⇌ I_2(g) ``` - **Other examples** of solid-vapor equilibrium are: - **Camphor (s) ⇌ Camphor (g)** - **NH₄Cl(s) ⇌ NH₄Cl(g)** - **Equilibrium involving the Dissolution of Solids or Gases in Liquids:** - A **saturated solution** is formed when no more solute can dissolve at a given temperature. - In a saturated solution, there is a **dynamic equilibrium** between the dissolved solute and the undissolved solid: ``` Sugar (solution) ⇌ Sugar (solid) ``` - The rate of dissolution equals the rate of crystallization. - This can be confirmed using **radioactive sugar**. - Radioactive sugar is added to a saturated solution of non-radioactive sugar. - Over time, both the dissolved and undissolved sugar become radioactive. - This indicates that exchange of molecules between the two phases is occurring, demonstrating the dynamic nature of equilibrium. - **Gases in Liquids:** - When a **bottle of soda water** is opened, dissolved CO₂ escapes **rapidly**. - This is because the solubility of a gas in a liquid is **dependent on pressure**. - For **gaseous CO₂** in **liquid water** at equilibrium, the following applies: ``` CO₂(g) ⇌ CO₂ (aq) ``` - This equilibrium is governed by **Henry's law**. - Henry's law states that "at a given temperature, the mass of a gas dissolved in a given mass of solvent is proportional to the partial pressure of the gas above the solvent." - The solubility of a gas **decreases with increasing temperature**. - When a bottle of soda water is sealed under high pressure, the solubility of CO₂ is high. - When the bottle is opened, dissolved CO₂ escapes to achieve a new equilibrium with a lower partial pressure. - This causes the soda water to go "flat". - **Key points for equilibrium in physical processes:** - Physical systems are in equilibrium at a **given temperature** and **atmospheric pressure (1.013 bar)**. - **Masses of the phases** remain constant. - **Heat is not exchanged** between the system and its surroundings. - **Vapor pressure** is constant at a given temperature. - **Solubility** is constant at a given temperature. ### Equilibrium in Chemical Reactions - Chemical reactions can also attain a **state of equilibrium**. - In a chemical reaction, reactants are converted to products, and products can be converted back to reactants: ``` A + B ⇌ C + D ``` - The **rate of the forward reaction** (reactants to products) decreases with time, while the **rate of the reverse reaction** (products to reactants) increases. - When the **rates of the forward and reverse reactions** are equal, the system reaches **chemical equilibrium**. - The **concentrations of the reactants and products** are constant at equilibrium. - Chemical Equilibrium is **dynamic**, with both the forward and reverse reactions occurring constantly. - This is demonstrated by the **Haber process**, where hydrogen and nitrogen react to form ammonia. - The concentration of ammonia remains constant after a certain time, even though both hydrogen and nitrogen are still present. - This is a dynamic equilibrium because the **composition of the mixture** does not change, even though the **exchange of atoms** is occurring. - **Key characteristics of chemical equilibrium:** - Equilibrium is achieved for a **closed system** at a given temperature. - Forward and reverse reactions occur at the **same rate**. - All **measurable properties of the system** are constant. - Chemical reactions are **characterized by specific constant values** at a given temperature. - These values are dependent on the extent to which the reaction has progressed. - Chemical reactions are reversible, meaning the **direction of the reaction can be reversed by changing the conditions**. - **Equilibrium constant**: - The equilibrium constant, Kc, for a general reversible reaction is defined by the following equation: ``` aA + bB ⇌ cC + dD Kc = [C]c[D]d / [A]a[B]b ``` - where: - a, b, c, and d are the **stoichiometric coefficients** in the balanced equation. - [A], [B], [C], and [D] are the **equilibrium concentrations** of the reactants and products. - **Law of mass action**: - The equilibrium constant, Kc, represents the **law of mass action**. - This law states that the equilibrium constant is **proportional to the product of the concentrations of the products, each raised to the power of its stoichiometric coefficient**, divided by the **product of the concentrations of the reactants, each raised to the power of its stoichiometric coefficient**. - **Applications of Kc**: - Kc can be used to: - Predict the **extent of the reaction**. - Predict the **direction of the reaction**. - Calculate the **equilibrium concentrations**. - **Predicting the extent of the reaction**: - The value of Kc indicates the **extent of the reaction**. - **Large values of Kc** indicate that the reaction proceeds almost completely. - **Small values of Kc** indicate that the reaction proceeds very little. - Examples: - The reaction of H₂ and O₂ to form H₂O at 500 K has a very large Kc (~24 × 10⁴⁷), indicating that the reaction goes almost to completion. - Most reactions have Kc values within the range of 10⁻³ - 10³, indicating that both reactants and products are present in significant amounts at equilibrium. - **Predicting the direction of the reaction:** - The **reaction quotient, Qc**, is calculated using the same expression as Kc, but instead of equilibrium concentrations, the **current concentrations** of the reactants and products are used. - By comparing Qc to Kc, we can predict the direction of the reaction: - **Qc < Kc**: The reaction proceeds **forward** to reach equilibrium. - **Qc > Kc**: The reaction proceeds **reverse** to reach equilibrium. - **Qc = Kc**: The system is at **equilibrium**. - **Calculating equilibrium concentrations**: - If you know the initial concentrations of reactants and the value of the equilibrium constant, you can calculate the equilibrium concentrations of all reactants and products. - **Heterogeneous Equilibria**: - Heterogeneous equilibria involve reactants and products in **different phases**. - The **concentrations of pure solids and liquids** are **considered constant** because they are independent of the amount present. - Therefore, these concentrations do not appear in the equilibrium constant expression. - **Examples of heterogeneous equilibria**: - CaCO₃ (s) ⇌ CaO (s) + CO₂ (g) - Ni(s) + 4CO (g) ⇌ Ni(CO)₄ (g) - Ag₂O (s) + 2HNO₃ (aq) ⇌ 2AgNO₃ (aq) + H₂O (l) - **Units of equilibrium constants**: - The units of the equilibrium constant depend on the **expression used for the equilibrium constant** (mole fractions, pressure, molarity) and the **balanced chemical equation**. - For example, the equilibrium constant Kc is dimensionless if the concentrations of the products and reactants are expressed in **mole fractions**. - The equilibrium constant Kc is dimensionless if the concentrations of the products and reactants are expressed in partial pressures in **bars**. **Important Note:** When quoting the equilibrium constant, always specify the: - **Temperature** - **Balanced chemical equation** - **Units of concentration** The following table summarizes the relationship between Kc and Kp: **Table**: Equilibrium Constant Relationship | Chemical equation | Equilibrium constant | |----------------|--------------------| | aA + bB ⇌ cC + dD | Kc = [C]c[D]d/[A]a[B]b | | aA + bB ⇌ cC + dD | Kp = (Pc)c(Pd)d/(Pa)a(Pb)b | | aA + bB ⇌ cC + dD | Kp = Kc(RT)Δn | where Δn is the **change in the number of moles of gas** (moles of gaseous products - moles of gaseous reactants). - **Applications of equilibrium constants**: - Equilibrium constants help us understand the **extent to which reactions proceed**. - They can also be used to **predict the direction of a reaction** and to **calculate equilibrium concentrations**. - They are important tools for **designing and optimizing chemical processes**.