Energetics I

Full Notes

Enthalpy Change (ΔH)

Enthalpy is a measure of the heat content of a substance.

ΔH (Enthalpy change) is the overall heat energy transferred to or from a system (at constant pressure). For chemistry, it is enthalpy change of reactions that we are interested in.

If a reaction has a negative enthalpy change (-ΔH), the reaction is described as exothermic. Heat energy is released to the surroundings.

• Products have less energy than reactants.
• Examples:
  • Combustion (e.g., CH₄ + O₂ → CO₂ + H₂O)
  • Neutralisation (acid + base → salt + water)

If a reaction has a positive enthalpy change (+ΔH), the reaction is described as endothermic. Heat energy is absorbed from the surroundings.

• Products have more energy than reactants.
• Examples:
  • Thermal decomposition of calcium carbonate

Enthalpy Level Diagrams

Enthalpy level diagrams are used to show relative energy levels of reactants and products:

For exothermic reactions: products are lower than reactants.

For endothermic reactions: products are higher than reactants.

These diagrams do not show activation energy, only the net enthalpy change. Reaction profile diagrams (used in kinetics, see here) show activation energy as they show how energy changes during a reaction. Energy and enthalpy level diagrams just show the overall difference in energy between reactants and products.

Standard Conditions

Standard conditions are used so that experimental enthalpy values can be compared. These are usually:

• Pressure: 100 kPa
• Temperature: 298 K (25 °C)
• All reactants and products are in their standard physical states

Standard Enthalpy Changes – Definitions

Standard enthalpy changes are always measured under standard conditions and for substances in their standard states.

You need to know the following definitions.

• Standard Enthalpy of Reaction (ΔH_r°):
  The enthalpy change when a reaction occurs in the molar quantities shown in the balanced equation, under standard conditions.
• Standard Enthalpy of Formation (ΔH_f°):
  The enthalpy change when 1 mole of a compound is formed from its elements in their standard states.
• Standard Enthalpy of Combustion (ΔH_c°):
  The enthalpy change when 1 mole of a substance is completely burned in oxygen.
• Standard Enthalpy of Neutralisation (ΔH_n°):
  The enthalpy change when an acid and alkali react to form 1 mole of water.

Measuring Enthalpy Changes – Calorimetry

Calorimetry is an experimental technique used to measure enthalpy changes.

The key equation used is:

q = mcΔT

where:

• q = heat energy change (J)
• m = mass of substance heated (g)
• c = specific heat capacity (J g⁻¹ K⁻¹) (for water, c = 4.18 J g⁻¹ K⁻¹)
• ΔT = temperature change (K)

The enthalpy change per mole of reactant is found using:
ΔH = -q / n
where n = moles of the limiting reactant.

Assumptions made:

• All energy goes into heating the solution
• Specific heat capacity of solution = water
• No heat lost to surroundings

Measuring Enthalpy Change of Combustion (ΔH_c)

Method:

1. Measure a known volume of water in a calorimeter (beaker or copper can).
2. Record the starting temperature of the water.
3. Weigh the spirit burner containing the fuel.
4. Light the burner and allow it to heat the water.
5. Stir and measure the final temperature of the water.
6. Reweigh the burner to determine mass of fuel burned.
7. Calculate q using q = mcΔT, then use ΔH = q / n.

Sources of Error:

• Heat loss to surroundings (e.g., air, beaker).
• Incomplete combustion (producing CO instead of CO₂).
• Evaporation of fuel from the wick.

Measuring Enthalpy Change of Neutralisation (ΔH_neut)

The enthalpy of neutralisation is the energy change when one mole of water is formed from an acid-alkali reaction.

Method:

1. Use a polystyrene cup (to reduce heat loss).
2. Add a known volume of acid and record the starting temperature.
3. Add a known volume of alkali, stir, and record the maximum temperature.
4. Use q = mcΔT to calculate heat energy change, then use ΔH = q / n.

Sources of Error:

• Heat loss to surroundings.
• Assumption that the solution has the same specific heat capacity as water.

Measuring Enthalpy Change of Solution (ΔH_sol)

Method:

1. Add a known mass of solute to a known volume of water in a polystyrene cup.
2. Stir and record the temperature change.
3. Use q = mcΔT to calculate the heat energy change, then use ΔH = q / n.

Sources of Error:

• Heat loss to surroundings.
• Incomplete dissolution of solute.

Hess’s Law

Hess’s Law is based on the Law of Conservation of Energy, which states that energy cannot be created or destroyed, only transferred.

Definition of Hess’s Law:
The total enthalpy change for a reaction is the same, regardless of the route taken, provided the initial and final conditions are the same.

Hess’s Law and Enthalpy Cycles

Hess’s Law is useful when it is difficult to directly measure an enthalpy change. Instead, we use enthalpy cycles to calculate it indirectly.

You need to know how we can use Hess cycles for:

• Enthalpy of formation (ΔH_f) calculations
• Enthalpy of combustion (ΔH_c) calculations

Hess’s Law for Enthalpy of Formation

The enthalpy of formation (ΔH_f) is the enthalpy change when one mole of a compound is formed from its elements in their standard states.

Elements in their standard states (for example, O₂(g)) have an enthalpy of formation, ΔH_f, of zero — this is really important for calculations involving standard enthalpies of formation.

Formula for Hess’s Cycle using enthalpy of formation:
ΔH_r = ΣΔH_f (products) − ΣΔH_f (reactants)

Hess’s Law for Enthalpy of Combustion

The enthalpy of combustion (ΔH_c) is the enthalpy change when one mole of a substance is completely burned in oxygen.

Constructing and Using Hess’s Cycles

1. Identify known enthalpy values (formation or combustion).
2. Draw an enthalpy cycle showing the different reaction pathways.
3. Apply Hess’s Law equation to calculate the unknown enthalpy change.

Bond Enthalpies

Bond enthalpy (sometimes also called bond dissociation energy) is "the energy required to break one mole of a particular bond in the gaseous state."

• Breaking bonds requires energy = Endothermic process (ΔH is positive).
• Making bonds releases energy = Exothermic process (ΔH is negative).

For example:

• Breaking H–H bond: H₂ (g) → 2H (g), ΔH = +436 kJ mol⁻¹
• Forming H–H bond: 2H (g) → H₂ (g), ΔH = −436 kJ mol⁻¹

Mean Bond Enthalpy

Mean bond enthalpy is the average energy required to break a bond. It is calculated using different molecules that have that bond type in.

This means calculations using mean bond enthalpies to find enthalpy changes in reactions won’t be as accurate as those calculated using experimental data (such as from calorimetry). See below.

Example The C–H bond has a mean bond enthalpy of +412 kJ mol⁻¹

However, the exact bond enthalpy of a C–H bond will be slightly different depending on the exact environment (molecule) it’s in.

Calculating Enthalpy Change Using Bond Enthalpies

The enthalpy change of a reaction can be estimated using:

Where:

• Bonds broken (reactants) = Energy absorbed (endothermic, positive ΔH).
• Bonds formed (products) = Energy released (exothermic, negative ΔH).

Matt’s exam tip

Remember bond enthalpies are for substances in gaseous states. It is really important to make sure the states of all substances are in gaseous phase when dealing with bond enthalpy calculations — sometimes you need to use enthalpy of vaporisation first in calculations.

Ex

Worked Example

Calculate the enthalpy of Combustion of Methane (CH₄) using the following data.

Reaction:

Bond enthalpies:
C–H = +412 kJ mol⁻¹
O=O = +498 kJ mol⁻¹
C=O = +805 kJ mol⁻¹
O–H = +463 kJ mol⁻¹

1. Step 1: Bonds Broken (Reactants – Energy Absorbed)
   Bonds in CH₄: 4 × C–H = 4 × 412 = 1648 kJ
   Bonds in O₂: 2 × O=O = 2 × 498 = 996 kJ
   Total energy to break bonds = 1648 + 996 = 2644 kJ
2. Step 2: Bonds Formed (Products – Energy Released)
   Bonds in CO₂: 2 × C=O = 2 × 805 = 1610 kJ
   Bonds in H₂O: 4 × O–H = 4 × 463 = 1852 kJ
   Total energy released = 1610 + 1852 = 3462 kJ
3. Step 3: Calculate Enthalpy Change
   ΔH = Bonds broken – Bonds formed
   ΔH = 2644 – 3462
   ΔH = –818 kJ mol⁻¹ (exothermic reaction)

Accuracy of Bond Enthalpy Calculations

Bond enthalpy calculations are estimates:

• They use mean bond enthalpies instead of exact bond enthalpies in a specific molecule.
• They assume all substances are in the gaseous state, which may not be true in real reactions.

For more accurate enthalpy changes, use Hess’s Law cycles instead of bond enthalpy calculations.

Summary

• Enthalpy change describes heat transfer at constant pressure and can be exothermic or endothermic.
• Calorimetry uses q = mcΔT then ΔH = −q ÷ n to find molar enthalpy change.
• Hess’s Law allows enthalpy changes to be found using indirect routes and cycles.
• Mean bond enthalpies estimate ΔH using bonds broken minus bonds formed.
• Standard conditions are 100 kPa and 298 K and substances are in standard states.