Measuring enthalpy changes — IB Chemistry SL Revision Notes & Topical Questions

Section 1 of 24Heat and temperature

Temperature

• Temperature a measure of the average kinetic energy of the particles, in K or °C.

Heat

• Heat energy transferred from a hotter to a colder body, and a measure of energy content that depends on the amount.

Comparison

• Comparison a beaker and a pipette drop of boiling water have the same temperature, but the beaker has far more heat content.

Intensive and extensive

• Intensive and extensive temperature is independent of the amount, whereas heat depends on it.

Interval

• Interval a change of 1 K equals a change of 1 °C.

Section 2 of 24Systems and conservation of energy

Systems and conservation of energy

System and surroundings

• System and surroundings the system is the reacting substances and the surroundings are everything else, such as the flask and air.

Open system

• Open system exchanges matter and energy with the surroundings, e.g. an uncovered beaker, and is the most common.

Closed system

• Closed system exchanges energy but not matter, e.g. a sealed flask.

Isolated system

• Isolated system exchanges neither, which a calorimeter tries to approach.

Law of conservation of energy

• Law of conservation of energy energy cannot be created or destroyed, only transferred.

Section 3 of 24Exothermic and endothermic reactions

• Enthalpy change ΔH H(products) − H(reactants) at constant pressure, in kJ mol⁻¹.

Feature	Exothermic	Endothermic
Energy flow	Out of the system	Into the system
Surroundings	Temperature rises	Temperature falls
Sign of ΔH	Negative	Positive
Products	Lower in enthalpy, more stable	Higher in enthalpy, less stable
Origin	Bonds formed release more energy than bonds broken	Bonds broken need more energy than bonds formed
Examples	Combustion, neutralisation, respiration	Thermal decomposition of CaCO3, photosynthesis, dissolving NH4NO3

Section 4 of 24Energy profiles

1Diagram

• Diagram plots enthalpy against reaction progress for reactants, transition state and products.

2Transition state

• Transition state the highest-energy point, with bonds partly broken and partly formed;
  • it is unstable, exists fleetingly and cannot be isolated.

3Activation energy Ea

Activation energy Ea the minimum energy colliding particles need for a successful collision, measured from the reactants to the transition state.

4Enthalpy change

• Enthalpy change measured between the reactant and product levels.

5Exothermic profile

• Exothermic profile products lie below the reactants, and E_a is generally lower.

6Endothermic profile

• Endothermic profile products lie above the reactants.

7Catalyst

• Catalyst lowers the hump but does not change ΔH.

8Kinetic stability

• Kinetic stability an exothermic reaction with high E_a may be too slow to observe, e.g. petrol and air need a spark.

Section 5 of 24Standard enthalpy changes

Standard conditions

• 100 kPa, solutions at 1 mol dm⁻³, substances in their standard states, usually quoted at 298 K.

Symbol

• ΔH^⦵ shows standard conditions.

Enthalpy change	Definition	Sign
Reaction, ΔHr	Reactants in the stoichiometric equation form products	Either
Formation, ΔHf	One mole of a compound formed from its elements	Either
Combustion, ΔHc	One mole of a substance burned completely in excess oxygen	Always negative
Neutralisation, ΔHneut	One mole of water formed from an acid and an alkali, about −57 kJ mol−1 for strong acid and base	Always negative

• Scaling
  • ΔH refers to the amounts in the equation as written, so doubling the equation doubles ΔH and reversing it changes the sign.

Section 6 of 24Calorimetry calculation

Heat transferred

Heat transferred q = mcΔT, with q in J, m in g, c in J g⁻¹ K⁻¹ and ΔT in K.

What the symbols mean: E, Q or q = energy transferred (J) · m = mass (kg; g in chemistry calorimetry) · c = specific heat capacity (J kg⁻¹ °C⁻¹; water 4.18 J g⁻¹ °C⁻¹) · ΔT or Δθ = temperature change (°C or K)

Water

• Water c = 4.18 J g⁻¹ K⁻¹ .
  • (IB data booklet)

Enthalpy change per mole

ΔH = −q/n, with q converted from J to kJ by dividing by 1000.

What the symbols mean: ΔH = enthalpy change (kJ mol⁻¹) · q = heat energy measured (J, divide by 1000 for kJ) · n = amount of the limiting reactant (mol); negative sign = exothermic

Sign

• ΔH is negative if the temperature rose.

Temperature units

• Temperature units no conversion is needed because ΔT in °C equals ΔT in K.

1

Measure the mass of water or solution.

2

Record the corrected temperature change.

3

Calculate q = mcΔT in joules.

4

Find the moles of the limiting reactant or fuel burned.

5

Calculate ΔH = −q/n in kJ mol⁻¹.

6

Compare with the literature value and evaluate errors.

Section 7 of 24Calorimetry of reactions in solution

Calorimetry of reactions in solution

Design

• Design one reagent is in excess and the temperature change is measured over a few minutes in an insulated cup.

Assumptions

• Assumptions the solution has the specific heat capacity (4.18 J g⁻¹ K⁻¹) and density (1.00 g cm⁻³) of water, the cup absorbs negligible heat, the reaction is complete and heat losses are negligible.

Mass

• Mass m is the total solution mass.

Temperature correction graph

• Temperature correction graph take readings before mixing, add the second reactant,
  • then extrapolate the cooling line back to the time of mixing to find the true ΔT.

Endothermic reactions

• Endothermic reactions the extrapolated line is the warming section.
• Assumption — the rate of cooling is constant.

Section 8 of 24Calorimetry of combustion

Method

• Method a spirit burner heats water in a copper can, and the mass of fuel burned is found from the mass loss.

Energy transfer

• Energy transfer not all heat reaches the water, as some is lost to the surroundings and some is absorbed by the calorimeter.

Errors

• Errors heat loss and incomplete combustion make the measured |ΔH| smaller than the literature value.

Error	Effect on |ΔH|	Improvement
Heat loss to surroundings	Too small	Insulate, add a lid, shield from draughts, extrapolate
Incomplete combustion	Too small	Supply more oxygen
Heat absorbed by the calorimeter	Too small	Include its heat capacity
Evaporation of fuel or water	Uncertain mass	Cap the burner and weigh promptly

• Random error
  • arises from thermometer readings.

Section 9 of 24More from the specification

1Calorimetry heat equation (q

Calorimetry heat equation (q mc Delta T)

• Calculates thermal energy transferred in calorimetry experiments using mass (m), specific heat capacity (c), and maximum temperature change (Delta T).

2Enthalpy change definition (Delta H)

• The energy difference between the enthalpy of products and reactants under constant pressure conditions (Delta H = H_products - H_reactants).

3Sources of calorimetry experimental error

• Heat losses to the surrounding atmosphere and thermal absorption by the calorimeter container underestimate true enthalpy changes.

4Temperature extrapolation graphs

• Cooling curves plotted against time allow correction for thermal loss by extrapolating back to the theoretical maximum temperature.

Section 10 of 24Heat and temperature

Heat

• Heat energy transferred from a hotter object to a colder one.

Temperature

• Temperature a measure of the average kinetic energy of the particles.

In reactions

• In reactions energy flows into or out of the vessel, and the effect on the surroundings appears as a rise or fall in temperature.

Energy transferred

• Energy transferred q = mcΔT depends on mass, specific heat capacity and temperature change.

Section 11 of 24Exothermic and endothermic reactions

• Enthalpy change ΔH the energy of the products minus the energy of the reactants at constant pressure.

Feature	Exothermic	Endothermic
Surroundings	Temperature rises	Temperature falls
Energy of products	Less than the reactants	More than the reactants
ΔH	Negative	Positive
Examples	Combustion, neutralisation, rusting	Thermal decomposition, photosynthesis

• Temperature clue
  • a thermal decomposition needs continued heating,
  • but a combustion continues once started because the energy released supplies the activation energy for the next particles.

Section 12 of 24Energy profile diagrams

Content

• Content an energy profile shows the energy of the reactants, transition state and products.

Activation energy

• Activation energy the difference between the reactants and the transition state.

Enthalpy change

• Enthalpy change the difference between the reactants and the products.

1

Label the vertical axis as enthalpy (or potential energy) and the horizontal axis as progress of reaction.

2

Put the reactants on the left and the products on the right at the correct relative levels.

3

Draw a smooth curve with a peak for the transition state.

4

Draw arrows for E_a (from reactants to the peak) and for ΔH (between the levels).

5

Label the species.

• Exothermic reactions still need a spark
  • the activation energy must be supplied before the reaction begins.

Section 13 of 24Checking an energy diagram

Axes

• Axes both are labelled.

Species

• Species reactants and products are named.

Activation energy arrow

• Activation energy arrow starts at the reactants and ends at the peak.

ΔH arrow

• ΔH arrow drawn between the two levels, with its direction showing the sign.

Consistency

• Consistency the diagram must agree with the sign given to ΔH.

Section 14 of 24Combustion as an energy source

Combustion as an energy source

Type

• Type combustion is an oxidation reaction.

Non-metals

• Non-metals burn to give non-metal oxides, e.g. sulfur + oxygen → sulfur dioxide.

Fuels

• Fuels hydrocarbons and alcohols burn exothermically in excess oxygen to give CO₂ and H₂O.

Energy released

• Energy released measured as the enthalpy of combustion.

Balancing method

• Balancing method count the oxygen atoms on the product side and halve for O₂, so C₄H₁₀ needs 6.5 O₂ to give 4CO₂ + 5H₂O.
  • (13 oxygen atoms)

Section 15 of 24Measuring an enthalpy change

1

Calculate q = mcΔT from the temperature change of a known mass of water.

2

Convert q to kilojoules.

3

Divide by the moles of the substance reacting.

4

Give the result a negative sign if the temperature rose.

Solution reactions

• Solution reactions the mass of solution is taken as the mass of water because the solute adds little.

Heat loss

• Heat loss some energy escapes, so the experimental value is smaller in magnitude than the data-book value.

Section 16 of 24More from the specification

More from the specification

Principle of Calorimetry and Heat Exchange

• In calorimetry experiments, the enthalpy change of a reaction system is determined by measuring temperature changes in a known mass of water: q = m c ΔT,
• where c is the specific heat capacity.
  • (4.18 J g^-1 K^-1

Standard Enthalpy Changes and Conditions

• Standard enthalpy changes, represented by the symbol ΔH°, are measured under standard thermodynamic conditions: a pressure of 100 kPa, temperature of 298 K,
• and solute concentrations of 1.0 mol dm^-3 with substances in their standard states.

Experimental Errors in Simple Beaker Calorimetry

• Performing reactions in an open glass beaker or uninsulated calorimeter introduces systematic errors due to heat loss to surroundings, incomplete combustion of boiling fuels,
• and heat capacity absorption by glassware.

Graphical Extrapolation for Accurate Temperature Rise

• In reaction calorimetry, temperature is plotted on a graph against time before and after mixing reactants,
• allowing cooling curve extrapolation back to the time of mixing to correct for conductive heat loss.

Calorimeter

• An insulated container used to measure temperature changes in reactions.

Calorimetry

• Measuring heat energy changes

Symbol

• Shorthand for an element, e.g. Na.

Boiling

• Liquid to gas throughout the liquid at the boiling point.

Standard conditions

• 298 K and 101 kPa.

Section 17 of 24Combustion calorimeter set-up

Principle

• Principle the heat released by burning a fuel raises the temperature of water.

Apparatus

• Apparatus a spirit burner heats a known mass of water in a copper calorimeter.

Measurements

• Measurements the initial and final water temperature, and the mass of the burner before and after heating.

Aim

• Aim the enthalpy change of combustion per mole of fuel.

Section 18 of 24Heat gained by the water

Formula

Formula q = mcΔT, where m is the mass of water in g, c is 4.18 J g⁻¹ K⁻¹ and ΔT is the rise in °C or K.

Sign of q

• Sign of q positive for the water because it is heated.

Sign of ΔH

• Sign of ΔH negative for the fuel because combustion releases energy.

Section 19 of 24Moles of fuel burned

Mass burned

• Mass burned the difference in burner mass before and after heating.

Amount

• Amount n = mass ÷ molar mass.

Section 20 of 24Enthalpy of combustion

Assumption

• Assumption the heat released by the fuel equals the heat gained by the water.

Formula

ΔH = −q ÷ n.

What the symbols mean: ΔH = enthalpy change (kJ mol⁻¹) · q = heat energy measured (J, divide by 1000 for kJ) · n = amount of the limiting reactant (mol); negative sign = exothermic

1

Calculate q in joules.

2

Convert q to kilojoules by dividing by 1000.

3

Divide by the moles of fuel burned.

4

Give a negative sign because combustion is exothermic.

5

Quote the answer in kJ mol⁻¹ to the number of significant figures of the data.

Section 21 of 24Evaluating the experiment

1Heat losses

• Heat losses not all heat from the flame reaches the water, because some escapes into the surroundings and some warms the apparatus.

2Incomplete combustion

• Incomplete combustion reduces the heat measured.

3Consequence

• Consequence the calculated magnitude is smaller than the accepted combustion enthalpy.

4Improvements

• Improvements place the calorimeter close to the flame without blocking the air supply, use a lid and shield the set-up from draughts.

5Exam link

• Exam link tie each improvement to the particular heat-loss route that it reduces.

Section 22 of 24More from the specification

1

Calorimetric heat exchange in aqueous solution

• Calorimetric heat exchange in aqueous solution measuring temperature changes in an insulated solution calorimeter determines enthalpy changes within the reaction system.

2

Standard enthalpy change of reaction

• Standard enthalpy of reaction (delta H°_r) is the heat energy change accompanying a reaction under standard conditions (100 kPa, 298 K) with reactants and products in standard states.

3

Calorimetric measurement of enthalpy

• Calorimetry determines reaction enthalpy using q = m * c * delta T, correcting for heat loss to surroundings through cooling curve extrapolation.

4

Hess's law and thermochemical cycles

• Hess's law states that total enthalpy change for a chemical reaction is independent of the pathway taken between initial reactants and final products.

5

Enthalpy profile diagrams

• Enthalpy profile diagrams illustrate activation energy barriers and energy differences between initial reactants and final formed products.

6

Exothermic versus endothermic enthalpy

• Exothermic versus endothermic enthalpy exothermic reactions release heat to surroundings with negative ΔH,
  • while endothermic reactions absorb heat with positive ΔH.

7

Transition state complex

• Transition state complex transient high-energy molecular arrangement formed at the summit of the reaction activation energy pathway.

8

Boiling

• Liquid to gas throughout the liquid at the boiling point.

9

Activation energy

• The minimum energy colliding particles need to react.

10

Standard conditions

• 298 K and 101 kPa.

11

Energy profile

• Diagram showing energy during a reaction

12

Temperature correction

• Extrapolating a temperature-time graph back to the mixing time to estimate the true temperature change.

13

Endothermic

• A reaction that takes in thermal energy from the surroundings.

14

Product

• A substance formed in a reaction.

15

Substance

• A material with only one type of particle.

Section 23 of 24Key terms

Term	Meaning
Heat	Energy transferred between a system and surroundings because of a temperature difference.
Enthalpy change (ΔH)	The heat energy transferred at constant pressure during a reaction.
Exothermic	A reaction that releases heat; ΔH is negative.
Endothermic	A reaction that absorbs heat; ΔH is positive.
Activation energy	The minimum energy colliding particles need to react.
Specific heat capacity	The energy needed to raise the temperature of 1 g of a substance by 1 K.
Calorimetry	The measurement of heat changes from the temperature change of a known mass of water or solution.

Term	Meaning
Heat	Energy transferred due to a temperature difference.
Temperature	A measure of the average kinetic energy of particles.
Enthalpy change	The energy change at constant pressure, products minus reactants.
Activation energy	The energy barrier between the reactants and the transition state.
Transition state	The peak of the energy profile where bonds are partly broken and partly formed.

Term	Meaning
Specific heat capacity	The energy needed to raise the temperature of 1 g of a substance by 1 K.
Enthalpy of combustion	The enthalpy change when one mole of a substance burns completely in excess oxygen.
Calorimeter	A vessel used to measure heat transferred to water.
Incomplete combustion	Burning in limited oxygen that releases less energy.
Heat loss	Energy that escapes to the surroundings instead of heating the water.

Section 24 of 24Exam technique

1

Using temperature as a measure of heat — temperature measures average kinetic energy, not energy content.

2

Showing E_a from reactants to products — it is from reactants to the transition state.

3

Writing a positive ΔH for an exothermic reaction — it is negative.

4

Forgetting to convert J to kJ — ΔH is quoted in kJ mol⁻¹.

1

Using temperature as a measure of heat — temperature measures average kinetic energy.

2

Showing E_a from reactants to products — it runs from reactants to the transition state.

3

Writing a positive ΔH for an exothermic reaction — the sign is negative.

4

Forgetting to label the axes of a profile diagram — enthalpy and progress of reaction must be labelled.

1

Using the mass of fuel instead of moles — divide by molar mass before calculating ΔH.

2

Giving a positive ΔH for combustion — it is negative.

3

Leaving q in joules while quoting kJ mol⁻¹ — convert to kJ.

4

Blaming only thermometer error for a low result — heat loss and incomplete combustion are the main causes.