Overview
This lecture covers enthalpy changes in chemistry, including definitions, types of enthalpy changes (exothermic and endothermic), standard conditions, experimental measurement methods, calculation techniques, mean bond enthalpy, and the application of Hess’s Law to determine enthalpy changes that cannot be measured directly.
Enthalpy Change Basics
- Enthalpy change refers to the energy transferred between the system (the chemicals involved in a reaction) and the surroundings (everything outside the chemicals).
- In exothermic reactions, energy is transferred from the system to the surroundings. The products have less energy than the reactants, and the enthalpy change (ΔH) is negative.
- In endothermic reactions, energy is absorbed from the surroundings into the system. The products have more energy than the reactants, and ΔH is positive.
- Activation energy (Ea) is the minimum energy required for particles to collide and start a reaction.
- Common exothermic processes include combustion of fuels and oxidation of carbohydrates (e.g., glucose in respiration).
Standard Conditions and Enthalpy Types
- Standard conditions for enthalpy changes are: 100 kPa pressure, 298 K (25°C) temperature, solutions at 1 mol dm⁻³, and all substances in their normal state at 298 K.
- Standard enthalpy change of formation (ΔHf): The enthalpy change when 1 mole of a compound is formed from its elements under standard conditions, with all substances in their standard states. The enthalpy of formation for an element in its standard state is zero.
- Standard enthalpy change of combustion (ΔHc): The enthalpy change when 1 mole of a substance is completely combusted in oxygen under standard conditions, with all reactants and products in their standard states. Incomplete combustion produces soot (carbon), carbon monoxide, and water, and is less exothermic than complete combustion.
- Standard enthalpy change of neutralisation: The enthalpy change when solutions of an acid and an alkali react together under standard conditions to produce 1 mole of water.
Measuring Enthalpy Changes Experimentally
- Calorimetry is used to measure enthalpy changes in reactions, typically using the equation:
Q (J) = m (g) × cₚ (J g⁻¹ K⁻¹) × ΔT (K or °C)
- The mass (m) is usually the total mass of the solution(s) involved, assuming a density of 1 g cm⁻³ (so 25 cm³ = 25 g).
- The specific heat capacity (cₚ) is usually taken as 4.18 J g⁻¹ K⁻¹ (the value for water).
- To improve accuracy:
- Take temperature readings at regular intervals before and after mixing, and extrapolate the temperature curve back to the time of mixing.
- Measure the temperature of both reactants before mixing and use the average as the initial temperature.
- Use insulated containers (e.g., polystyrene cups) to minimize heat loss.
- Common sources of error:
- Heat loss to or gain from the surroundings.
- Assuming all solutions have the same specific heat capacity and density as water.
- Neglecting the heat absorbed by the calorimeter itself.
- Incomplete or slow reactions.
- General method for calorimetry:
- Wash and dry equipment with the solutions to be used.
- Place a polystyrene cup in a beaker for insulation.
- Measure and transfer the required volumes of solutions using volumetric pipettes.
- Clamp the thermometer so the bulb is immersed in the solution.
- Record initial temperatures for a few minutes.
- Add the second reagent at a set time, stir, and record temperatures at regular intervals.
- For solids, weigh before and after addition to determine the exact mass used.
Calculations and Examples
- To calculate enthalpy change per mole:
- Calculate the energy change (Q) for the quantities used: Q = m × cₚ × ΔT.
- Determine the number of moles of the limiting reactant.
- Divide Q by the number of moles to get ΔH (in J mol⁻¹), then convert to kJ mol⁻¹ by dividing by 1000.
- Assign the correct sign: negative for exothermic (temperature increase), positive for endothermic (temperature decrease).
- Always include the sign, unit, and use three significant figures.
- Example 1: Reaction of copper sulfate with excess zinc (temperature increase of 7°C, 25.0 cm³ of 0.200 mol dm⁻³ CuSO₄)
- Q = 25 × 4.18 × 7 = 731.5 J
- Moles CuSO₄ = 0.2 × 25/1000 = 0.005 mol
- ΔH = 731.5 / 0.005 = 146,300 J mol⁻¹ = –146 kJ mol⁻¹ (exothermic)
- Example 2: Neutralisation of 25.0 cm³ of 2.00 mol dm⁻³ HCl with 25.0 cm³ of 2.00 mol dm⁻³ NaOH (temperature increase of 13.5°C)
- Q = 50 × 4.18 × 13.5 = 2821.5 J
- Moles HCl = 2 × 25/1000 = 0.05 mol
- ΔH = 2821.5 / 0.05 = 56,430 J mol⁻¹ = –56.4 kJ mol⁻¹ (exothermic)
- Example 3: Combustion of 0.650 g propan-1-ol heating 150 g water from 20.1°C to 45.5°C
- Q = 150 × 4.18 × 25.4 = 15,925.8 J
- Moles propan-1-ol = 0.65 / 60 = 0.01083 mol
- ΔH = 15,925.8 / 0.01083 = 1,470,073 J mol⁻¹ = –1,470 kJ mol⁻¹ (exothermic)
- Notes:
- For solutions, the mass is the total mass of both solutions.
- For combustion, the mass is the mass of water heated, not the fuel.
Mean Bond Enthalpy
- Mean bond enthalpy is the average energy required to break one mole of a specific type of covalent bond in the gaseous state, averaged over different molecules.
- These values are always positive because energy is required to break bonds.
- The definition applies only when all substances are in the gaseous state.
- ΔH = total bond energies broken – total bond energies formed.
- Breaking bonds absorbs energy; making bonds releases energy.
- Calculations using mean bond enthalpies are less accurate than those using formation or combustion data because bond enthalpy values are averages.
- Example: Calculating the enthalpy of combustion of propene using mean bond enthalpies:
- ΔH = [sum of bond energies broken] – [sum of bond energies formed]
- Substitute values as given in the data table for each bond type.
Hess’s Law
- Hess’s Law states that the total enthalpy change for a reaction is independent of the route taken; it depends only on the initial and final states.
- This is a consequence of the first law of thermodynamics (energy conservation).
- Hess’s Law is used to calculate enthalpy changes for reactions that cannot be measured directly by constructing energy cycles or diagrams.
- On an energy level diagram, different routes between reactants and products can be represented by arrows, and the sum of enthalpy changes along each route is equal.
- Hess’s Law can be applied using enthalpy changes of formation or combustion:
- ΔHreaction = ΣΔHf(products) – ΣΔHf(reactants)
- ΔHreaction = ΣΔHc(reactants) – ΣΔHc(products)
- Examples:
- Calculating the enthalpy change for the reaction: Al₂O₃ + 3 Mg → 3 MgO + 2 Al
- ΔH = [3 × ΔHf(MgO)] – [ΔHf(Al₂O₃)]
- Substitute values as given.
- Calculating the enthalpy of combustion of propene using formation data:
- ΔHc = [3 × ΔHf(CO₂) + 3 × ΔHf(H₂O)] – ΔHf(C₃H₆)
- Calculating the enthalpy of reaction using combustion data:
- ΔHreaction = [ΔHc(CO) + 2 × ΔHc(H₂)] – ΔHc(CH₃OH)
- Calculating the enthalpy of formation of propene using combustion data:
- ΔHf = [3 × ΔHc(C) + 3 × ΔHc(H₂)] – ΔHc(C₃H₆)
- Hess’s Law is especially useful for determining enthalpy changes for reactions involving hydrated and anhydrous salts, where direct measurement is not feasible.
Key Terms & Definitions
- System: The chemicals involved in a reaction.
- Surroundings: Everything outside the reacting chemicals.
- Exothermic: A reaction that releases energy to the surroundings; ΔH is negative.
- Endothermic: A reaction that absorbs energy from the surroundings; ΔH is positive.
- Activation Energy (Ea): The minimum energy required for a reaction to occur.
- Standard Enthalpy Change (ΔH°): The enthalpy change under standard conditions (100 kPa, 298 K, 1 mol dm⁻³, substances in standard state).
- ΔHf (Standard Enthalpy of Formation): The enthalpy change when 1 mole of a compound forms from its elements in their standard states.
- ΔHc (Standard Enthalpy of Combustion): The enthalpy change when 1 mole of a substance is completely combusted in oxygen under standard conditions.
- Mean Bond Enthalpy: The average energy required to break one mole of a specific bond in gaseous molecules.
- Hess’s Law: The enthalpy change of a reaction is the same regardless of the pathway taken.
Action Items / Next Steps
- Practice calorimetry calculations and apply the method to different reaction types.
- Work through problems involving mean bond enthalpy calculations.
- Review and construct Hess’s Law cycles for various reactions, including those involving formation and combustion data.
- Ensure clear understanding of all enthalpy definitions and know when to apply each type in calculations.