Ever wondered how temperature and pressure mess with chemical reactions? It's all about balance. When you heat things up or crank up the pressure, reactions can go haywire, shifting towards products or reactants.
Le Chatelier's principle explains it all. It's like a game of tug-of-war between reactants and products. Temperature and pressure changes can tip the scales, affecting equilibrium constants and reaction rates. Understanding this is key to controlling chemical processes.
Temperature Effects on Equilibrium
Le Chatelier's Principle and Temperature Changes
- Le Chatelier's principle states when a system at equilibrium is subjected to a stress or change in conditions, the system shifts its equilibrium position to counteract the change and establish a new equilibrium
- For an endothermic reaction (ΔH > 0), increasing the temperature shifts the equilibrium to the right (towards the products), while decreasing the temperature shifts the equilibrium to the left (towards the reactants)
- For an exothermic reaction (ΔH < 0), increasing the temperature shifts the equilibrium to the left (towards the reactants), while decreasing the temperature shifts the equilibrium to the right (towards the products)
- The magnitude of the equilibrium shift depends on the magnitude of the temperature change and the enthalpy change of the reaction
- The equilibrium constant (K) changes with temperature, increasing for endothermic reactions and decreasing for exothermic reactions as temperature increases
Examples of Temperature Effects on Equilibrium
- In the endothermic reaction N₂(g) + O₂(g) ⇌ 2NO(g), increasing the temperature increases the equilibrium constant and shifts the equilibrium towards the products (NO)
- In the exothermic reaction 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), decreasing the temperature increases the equilibrium constant and shifts the equilibrium towards the products (SO₃)
- For the endothermic decomposition of calcium carbonate, CaCO₃(s) ⇌ CaO(s) + CO₂(g), heating the system shifts the equilibrium to the right, producing more CaO and CO₂
- In the exothermic formation of ammonia, N₂(g) + 3H₂(g) ⇌ 2NH₃(g), cooling the system shifts the equilibrium to the right, producing more NH₃
Pressure Effects on Equilibrium
Le Chatelier's Principle and Pressure Changes in Gaseous Reactions
- For gaseous reactions, the equilibrium position can be affected by changes in pressure or volume, as these factors influence the partial pressures of the reactants and products
- According to Le Chatelier's principle, when the pressure of a gaseous system at equilibrium is increased (volume decreased), the equilibrium shifts to the side with fewer moles of gas to counteract the pressure increase
- Conversely, when the pressure of a gaseous system at equilibrium is decreased (volume increased), the equilibrium shifts to the side with more moles of gas to counteract the pressure decrease
- If the number of moles of gaseous reactants and products is equal, pressure changes do not affect the equilibrium position
- The magnitude of the equilibrium shift depends on the difference in the number of moles of gaseous reactants and products and the magnitude of the pressure change
Examples of Pressure Effects on Equilibrium
- In the synthesis of ammonia, N₂(g) + 3H₂(g) ⇌ 2NH₃(g), increasing the pressure shifts the equilibrium to the right (towards NH₃) because there are 4 moles of gaseous reactants and 2 moles of gaseous products
- For the decomposition of dinitrogen tetroxide, N₂O₄(g) ⇌ 2NO₂(g), decreasing the pressure shifts the equilibrium to the right (towards NO₂) because there are more moles of gaseous products than reactants
- In the water-gas shift reaction, CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g), pressure changes do not affect the equilibrium position because the number of moles of gaseous reactants and products is equal
- For the formation of hydrogen iodide, H₂(g) + I₂(g) ⇌ 2HI(g), increasing the pressure shifts the equilibrium to the right (towards HI) because there are fewer moles of gaseous products than reactants
Enthalpy Change and Equilibrium Constant
Relationship between Enthalpy Change and Temperature Dependence of Equilibrium Constant
- The van 't Hoff equation describes the relationship between the equilibrium constant (K) and temperature (T) for a reaction: $dlnK/dT = ΔH°/(RT²)$, where ΔH° is the standard enthalpy change of the reaction and R is the gas constant
- For endothermic reactions (ΔH° > 0), the equilibrium constant (K) increases with increasing temperature, as the reaction shifts towards the products to absorb the added heat
- For exothermic reactions (ΔH° < 0), the equilibrium constant (K) decreases with increasing temperature, as the reaction shifts towards the reactants to release the added heat
- The magnitude of the temperature dependence of the equilibrium constant is proportional to the magnitude of the enthalpy change of the reaction
- The van 't Hoff equation assumes that the enthalpy change of the reaction is constant over the temperature range considered, which is a reasonable approximation for small temperature changes
Examples of Enthalpy Change and Equilibrium Constant Relationship
- For the endothermic reaction N₂(g) + O₂(g) ⇌ 2NO(g), ΔH° = +180.7 kJ/mol, so the equilibrium constant increases with increasing temperature
- In the exothermic synthesis of ammonia, N₂(g) + 3H₂(g) ⇌ 2NH₃(g), ΔH° = -92.2 kJ/mol, so the equilibrium constant decreases with increasing temperature
- The endothermic decomposition of calcium carbonate, CaCO₃(s) ⇌ CaO(s) + CO₂(g), has ΔH° = +178 kJ/mol, so the equilibrium constant increases with increasing temperature
- For the exothermic formation of sulfur trioxide, 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), ΔH° = -198 kJ/mol, so the equilibrium constant decreases with increasing temperature
Equilibrium Constant vs Temperature
Using the van 't Hoff Equation to Calculate Changes in Equilibrium Constant
- The integrated form of the van 't Hoff equation is: $ln(K₂/K₁) = -ΔH°/R * (1/T₂ - 1/T₁)$, where K₁ and K₂ are the equilibrium constants at temperatures T₁ and T₂, respectively
- To calculate the change in equilibrium constant with temperature, one needs to know the initial equilibrium constant (K₁), the initial temperature (T₁), the final temperature (T₂), and the standard enthalpy change of the reaction (ΔH°)
- The gas constant (R) should be used in the appropriate units, consistent with the units of ΔH° and temperature
- For endothermic reactions (ΔH° > 0), K₂ will be greater than K₁ when T₂ > T₁, while for exothermic reactions (ΔH° < 0), K₂ will be less than K₁ when T₂ > T₁
- The van 't Hoff equation can be used to predict the equilibrium constant at a given temperature, provided that the equilibrium constant is known at another temperature and the enthalpy change of the reaction is known
Examples of Calculating Equilibrium Constant Changes with Temperature
- For the endothermic reaction N₂(g) + O₂(g) ⇌ 2NO(g) with ΔH° = +180.7 kJ/mol, if K₁ = 1.2 × 10⁻¹⁵ at T₁ = 298 K and T₂ = 500 K, then K₂ = 1.7 × 10⁻⁸, showing an increase in equilibrium constant with temperature
- In the exothermic synthesis of ammonia, N₂(g) + 3H₂(g) ⇌ 2NH₃(g) with ΔH° = -92.2 kJ/mol, if K₁ = 1.2 × 10³ at T₁ = 500 K and T₂ = 400 K, then K₂ = 3.7 × 10⁵, showing a decrease in equilibrium constant with temperature
- For the endothermic decomposition of calcium carbonate, CaCO₃(s) ⇌ CaO(s) + CO₂(g) with ΔH° = +178 kJ/mol, if K₁ = 2.5 × 10⁻³ at T₁ = 800 K and T₂ = 1000 K, then K₂ = 0.18, showing an increase in equilibrium constant with temperature
- In the exothermic formation of sulfur trioxide, 2SO₂(g) + O₂(g) ⇌ 2SO₃(g) with ΔH° = -198 kJ/mol, if K₁ = 4.5 × 10⁴ at T₁ = 600 K and T₂ = 500 K, then K₂ = 1.8 × 10⁶, showing a decrease in equilibrium constant with temperature