DP Chemistry HL R1.1 Measuring Enthalpy Changes

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DP Chemistry HL | R1.1 Measuring Enthalpy Changes

DP CHEMISTRY · REACTIVITY

R1.1

Measuring Enthalpy Changes

Full notes for HL · IB-style

Contents

1	Energy, heat and the system
2	Exothermic and endothermic reactions
3	Enthalpy change and energy profiles
4	Calorimetry: measuring heat energy
5	Enthalpy of combustion and neutralization
6	Errors and improving calorimetry
7	System and surroundings
8	Energy profiles
9	Standard conditions and units
10	Specific heat capacity
11	Enthalpy of combustion by calorimetry
12	Enthalpy of reaction in solution
13	Extrapolating temperature-time graphs
14	Errors and uncertainties in calorimetry
15	Bond enthalpy and energy changes (preview)
16	Exothermic and endothermic processes in daily life
17	Temperature and heat
18	Mixed review: worked problems
19	Additional exam-style practice
20	Energy density and specific energy
21	Thermochemical equations
22	Common misconceptions and links
23	Exam-style question with markscheme
24	Check your understanding
25	Summary and topic map

These are full teaching notes. Read each section in order, try the Think about it question before you read on, and do every Quick check before moving to the next section.

Before you start

Rate yourself on each statement now, and again after you've worked through the notes. Shade R (not yet), A (getting there) or G (confident).

I can…	R	A	G
distinguish the system and surroundings, and heat and temperature
distinguish exothermic and endothermic reactions with examples
define standard enthalpy change and draw energy profiles
calculate heat energy using Q = mcΔT
calculate enthalpy changes of combustion and neutralization from experimental data
evaluate sources of error in calorimetry experiments

There is no additional HL content in this subtopic. SL and HL students study the same material.

Guiding questions

How can we measure the energy transferred in a chemical reaction? Why do some reactions release energy and others absorb it?

How this topic is examined

R1.1 is examined through calorimetry calculations (often the main calculation in a Paper 2 question), energy profile diagrams and evaluation of experimental errors.

Remember the sign convention: ΔH is negative for exothermic reactions. Use the mass of the solution or water heated, not the mass of reactant.

Command term	What the examiner wants
State / Identify	a brief answer, no explanation
Outline / Describe	a brief or detailed account, without reasons
Explain	a detailed account with causes, reasons or mechanisms
Calculate / Determine	a numerical answer with working, correct significant figures and units
Deduce / Predict	reach a conclusion from given information
Draw / Sketch	a clear labelled diagram, structure or graph
Evaluate / Discuss	weigh strengths and limitations; reach a judgement

How to use these notes

Each section teaches one part of the syllabus in full. You'll see these boxes throughout; each has one job:

Box	What it's for
Think about it	a question to get you thinking before a section; the answer comes in the section
Key point	the one idea you must not forget
Common mistake	an error examiners see every year, and how to avoid it
In the real world	where the chemistry shows up outside the classroom
Try this	something quick you can do yourself to test the idea
Worked example	full solutions with IB-style marks (M1 method, A1 answer, R1 reasoning)
Quick check	short questions to test yourself at the end of each section

1 Energy, heat and the system

Energy is conserved; it moves between system and surroundings.

Think about it

When you dissolve ammonium nitrate in water in a cold pack, the pack gets cold. Where has the energy gone?

Chemical reactions involve energy changes. The system is the reacting chemicals; the surroundings are everything else, including the solvent, the container and the air. Energy is conserved: it is transferred between the system and surroundings, but not created or destroyed.

Heat is a form of energy transferred because of a temperature difference. Temperature is a measure of the average kinetic energy of particles (S1.1). Adding the same amount of heat to a large and a small mass of water gives a smaller temperature rise in the larger mass.

2 Exothermic and endothermic reactions

Releasing or absorbing heat.

In an exothermic reaction, heat is released from the system to the surroundings: the surroundings get hotter. The products have less stored chemical energy (enthalpy) than the reactants, so ΔH is negative. Examples: combustion, respiration, neutralization, reactions of metals with acids.

In an endothermic reaction, heat is absorbed from the surroundings into the system: the surroundings get colder. The products have more enthalpy than the reactants, so ΔH is positive. Examples: photosynthesis, thermal decomposition of calcium carbonate, dissolving ammonium nitrate, melting and boiling.

	Exothermic	Endothermic
Heat flow	system to surroundings	surroundings to system
Temperature of surroundings	rises	falls
Sign of ΔH	negative	positive
Stability of products	more stable (lower enthalpy)	less stable (higher enthalpy)
Examples	combustion, neutralization	photosynthesis, decomposition of CaCO3

Quick check

1. What is the sign of ΔH for an exothermic reaction?

2. Give an example of an endothermic reaction.

Answers: 1. negative 2. photosynthesis / thermal decomposition

3 Enthalpy change and energy profiles

Comparing the energy of reactants and products.

Enthalpy (H) is the total heat content of a system; it cannot be measured directly, but the enthalpy change (ΔH) can: ΔH = H(products) − H(reactants), measured at constant pressure. Standard enthalpy changes (ΔH⊖) are measured under standard conditions: 100 kPa, a stated temperature (usually 298 K), and solutions at 1 mol dm−3, with all substances in their standard states.

An energy profile (enthalpy level diagram) shows the enthalpy of reactants and products and the energy path of the reaction. The activation energy (Ea) is the minimum energy needed for the reaction to occur; it appears as a hump between reactants and products. For an exothermic reaction, the products are lower than the reactants; for an endothermic reaction, higher.

A thermochemical equation includes state symbols and ΔH: CH4(g) + 2O2(g) → CO2(g) + 2H2O(l) ΔH = −890 kJ mol−1.

Figure 1. Energy profile of an exothermic reaction: products lower than reactants.

Figure 2. Energy profile of an endothermic reaction: products higher than reactants.

Quick check

1. State the standard conditions for ΔH⊖.

2. What does the hump on an energy profile represent?

Answers: 1. 100 kPa, 298 K, 1 mol dm−3 2. activation energy

4 Calorimetry: measuring heat energy

Q = mcΔT.

Calorimetry measures the heat released or absorbed by a reaction by measuring the temperature change of a known mass of water or solution. The heat energy transferred is:

Q = mcΔT

where Q is the heat energy (J), m is the mass of the water or solution heated (g), c is the specific heat capacity (water: 4.18 J g−1 K−1), and ΔT is the temperature change (K or °C; a change of 1 K = a change of 1 °C).

To find the enthalpy change per mole: ΔH = −Q ÷ n, where n is the amount (moles) of the limiting reactant. The negative sign is added because if the temperature rises (exothermic), ΔH is negative.

Figure 3. A simple polystyrene cup calorimeter.

Common mistake

Using the mass of the solid reactant in Q = mcΔT. Use the mass of the water or solution whose temperature changes (1 cm3 of dilute solution ≈ 1 g).

Quick check

1. What does c represent?

2. Why is a minus sign used in ΔH = −Q/n?

Answers: 1. specific heat capacity 2. temperature rise means heat released: ΔH negative

5 Enthalpy of combustion and neutralization

Two standard experiments.

The standard enthalpy of combustion (ΔHc⊖) is the enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions. It can be measured by burning a fuel in a spirit burner under a metal can (calorimeter) containing water, and measuring the mass of fuel burned and the temperature rise of the water.

The enthalpy of neutralization is the enthalpy change when an acid and a base react to form one mole of water. It can be measured by mixing known volumes and concentrations of acid and alkali in a polystyrene cup and recording the temperature change. For strong acids and bases, it is about −57 kJ mol−1, because the reaction is always H+(aq) + OH−(aq) → H2O(l).

Figure 4. Measuring the enthalpy of combustion of a fuel with a spirit burner.

WORKED EXAMPLE 1 Enthalpy of combustion

Burning 0.460 g of ethanol (M = 46.08 g mol−1) heated 200.0 g of water from 20.0 °C to 34.5 °C. Calculate the enthalpy of combustion of ethanol.

Solution

Q = mcΔT = 200.0 × 4.18 × 14.5 = 12 122 J = 12.1 kJM1

n(ethanol) = 0.460 ÷ 46.08 = 0.00998 molM1

ΔHc = −12.1 ÷ 0.00998 = −1.21 × 103 kJ mol−1A1

The literature value is −1367 kJ mol−1; heat losses make the experimental value less negativeR1

WORKED EXAMPLE 2 Enthalpy of neutralization

50.0 cm3 of 1.00 mol dm−3 HCl is mixed with 50.0 cm3 of 1.00 mol dm−3 NaOH. The temperature rises by 6.8 °C. Calculate the enthalpy of neutralization.

Solution

m = 100.0 g (total solution); Q = 100.0 × 4.18 × 6.8 = 2842 JM1

n(H2O) = 0.0500 molM1

ΔH = −2.842 ÷ 0.0500 = −56.8 kJ mol−1A1

Quick check

1. Define standard enthalpy of combustion.

2. Why is the total volume of solution used for m in neutralization experiments?

Answers: 1. enthalpy change when one mole burns completely in oxygen under standard conditions 2. the whole solution is heated

6 Errors and improving calorimetry

Most experimental values are less negative than literature values.

Heat loss to the surroundings is the largest source of error: heat escapes from the calorimeter, the beaker and the flame, so the measured temperature rise is too small, and the calculated ΔH is less exothermic than the true value. Other errors: incomplete combustion (soot forms; less energy released); evaporation of fuel from the wick; heat absorbed by the calorimeter itself; assumptions that the solution has the density and specific heat capacity of water.

Improvements: insulate the calorimeter (lid, polystyrene cup, draught shield); reduce the distance between flame and can; stir the solution; use a more accurate thermometer or data logger.

For reactions that are slow or where heat is lost during measurement, a cooling curve correction can be used: record temperatures before and after mixing, plot temperature against time, and extrapolate the cooling line back to the time of mixing to estimate the maximum temperature that would have been reached with no heat loss.

Figure 5. Extrapolation corrects for heat loss: the maximum temperature at mixing is about 27.9 °C.

Quick check

1. Why are experimental ΔHc values less exothermic than literature values?

2. How does extrapolation improve accuracy?

Answers: 1. heat loss, incomplete combustion 2. estimates maximum temperature without heat loss

7 System and surroundings

Where does the energy go?

The system is the reacting chemicals; the surroundings are everything else (solvent, container, air). In an exothermic reaction, energy is transferred from the system to the surroundings, so the surroundings get warmer and ΔH is negative. In an endothermic reaction, energy is absorbed from the surroundings, which cool, and ΔH is positive.

WORKED EXAMPLE 3 Classifying (basic)

When ammonium nitrate dissolves in water, the temperature falls. Is the process exothermic or endothermic? State the sign of ΔH.

Solution

EndothermicA1

ΔH positiveA1

Common mistake

Saying that in an exothermic reaction 'the reaction gets hotter'. The surroundings (including the solution) get hotter because energy is released by the system.

Quick check

1. Classify combustion, photosynthesis and neutralization.

2. Why does a cold pack feel cold?

Answers: 1. exothermic, endothermic, exothermic 2. it absorbs heat from your skin (endothermic process)

8 Energy profiles

Reactants, products and activation energy.

An energy profile plots enthalpy against reaction progress. For an exothermic reaction, products are lower than reactants; for an endothermic reaction, higher. The activation energy Ea is the energy difference between the reactants and the transition state.

Figure 6. Energy profiles of an exothermic and an endothermic reaction.

WORKED EXAMPLE 4 Reading a profile (standard)

From a profile, the reactants are at 100 kJ, the peak at 180 kJ and the products at 40 kJ. Find Ea and ΔH.

Solution

Ea = 180 − 100 = 80 kJA1

ΔH = 40 − 100 = −60 kJA1

Quick check

1. For the reverse reaction, find Ea and ΔH.

Answers: 1. 140 kJ; +60 kJ

9 Standard conditions and units

Comparing like with like.

Standard enthalpy changes (ΔH⦵) refer to 100 kPa, a specified temperature (usually 298 K), solutions of 1 mol dm−3, and substances in their standard states. ΔH is usually given in kJ mol−1, per mole of the reaction as written.

WORKED EXAMPLE 5 Scaling (standard)

N2(g) + 3H2(g) → 2NH3(g), ΔH = −92 kJ mol−1. Find ΔH for forming 1 mol NH3 and for the reverse reaction.

Solution

−46 kJ per mol NH3A1

Reverse: +92 kJ mol−1A1

Quick check

1. Write a thermochemical equation for 2 mol of H2 burning if ΔHc(H2) = −286 kJ mol−1.

Answers: 1. 2H2(g) + O2(g) → 2H2O(l), ΔH = −572 kJ

10 Specific heat capacity

q = mcΔT.

The heat energy q transferred to a substance is q = mcΔT, where m is mass (g), c the specific heat capacity (water: 4.18 J g−1 K−1) and ΔT the temperature change (K or °C).

WORKED EXAMPLE 6 Heating water (basic)

How much energy is needed to heat 250 g of water from 20 °C to 100 °C?

Solution

q = 250 × 4.18 × 80M1

= 83 600 J = 83.6 kJA1

Quick check

1. Find the temperature rise when 5.00 kJ is added to 100 g of water.

2. Find c for a metal if 900 J raises 50 g by 20 K.

Answers: 1. 12.0 K 2. 0.90 J g−1 K−1

11 Enthalpy of combustion by calorimetry

Spirit burner experiments.

A fuel heats a known mass of water in a calorimeter. q = mcΔT for the water; n(fuel) from the mass burned; ΔHc = −q/n.

WORKED EXAMPLE 7 Ethanol (exam level)

Burning 0.92 g of ethanol raises the temperature of 200 g water by 21.5 K. Find ΔHc.

Solution

q = 200 × 4.18 × 21.5 = 17 974 JM1 A1

n = 0.92/46.08 = 0.0200 molA1

ΔHc = −17.97/0.01997 = −900 kJ mol−1A1

Quick check

1. The data-book value is −1367 kJ mol−1. Calculate the percentage error.

2. Give two reasons for the difference.

Answers: 1. 34.2% 2. heat loss to surroundings; incomplete combustion; heating the calorimeter

12 Enthalpy of reaction in solution

Coffee-cup calorimetry.

For reactions in solution, assume the solution has the density and specific heat capacity of water. Use the total volume for m. Calculate n of the limiting reactant, then ΔH = −q/n.

WORKED EXAMPLE 8 Neutralization (exam level)

50.0 cm3 of 1.00 mol dm−3 HCl and 50.0 cm3 of 1.00 mol dm−3 NaOH, both at 21.0 °C, give a maximum of 27.7 °C. Find ΔH.

Solution

q = 100 × 4.18 × 6.7 = 2800.6 JM1 A1

n(H2O) = 0.0500 molA1

ΔH = −2.80/0.0500 = −56.0 kJ mol−1A1

Quick check

1. 2.0 g of Zn (excess) reacts with 50.0 cm3 of 0.500 mol dm−3 CuSO4, raising the temperature by 25.0 K. Find ΔH.

Answers: 1. q = 50 × 4.18 × 25 = 5225 J; n(Cu2+) = 0.025: −209 kJ mol−1

13 Extrapolating temperature-time graphs

Correcting for heat loss.

Heat is lost while the reaction proceeds, so the maximum recorded temperature underestimates ΔT. Plot temperature against time, extrapolate the cooling line back to the time of mixing, and read the theoretical maximum.

Figure 7. Temperature–time graph: extrapolate the cooling line back to mixing time (3 min).

WORKED EXAMPLE 9 Extrapolation (standard)

From the graph, estimate the corrected ΔT if mixing occurred at 3 minutes.

Solution

Cooling line extrapolated to 3 min gives about 33.6 °CM1

ΔT ≈ 13.6 KA1

14 Errors and uncertainties in calorimetry

Evaluating results.

Systematic errors in calorimetry: heat loss to surroundings (largest), heat absorbed by the calorimeter, incomplete combustion (soot), evaporation of fuel. Random errors: thermometer readings, mass measurements. Improvements: insulation, a lid, a draught shield, extrapolation, using a bomb calorimeter.

WORKED EXAMPLE 10 Percentage uncertainty (standard)

A thermometer reads ±0.1 °C; ΔT = 6.7 °C. Find the percentage uncertainty in ΔT.

Solution

Two readings: ±0.2 °CM1

0.2/6.7 × 100 = 3.0%A1

Quick check

1. Suggest one improvement to a spirit burner experiment.

Answers: 1. use a draught shield and lid; reduce the distance between flame and calorimeter

15 Bond enthalpy and energy changes (preview)

Bonds breaking and forming.

Breaking bonds is endothermic; forming bonds is exothermic. If more energy is released forming bonds in the products than is absorbed breaking bonds in the reactants, the reaction is exothermic. (Calculations are covered in R1.2.)

WORKED EXAMPLE 11 Qualitative (standard)

Explain why the combustion of methane is exothermic in terms of bonds.

Solution

Energy released forming C=O and O–H bondsR1

is greater than energy absorbed breaking C–H and O=O bondsR1

16 Exothermic and endothermic processes in daily life

Applications.

Exothermic: hand warmers (iron oxidation), self-heating cans (CaO + H2O), combustion of fuels. Endothermic: instant cold packs (NH4NO3 dissolving), photosynthesis, thermal decomposition of CaCO3.

In the real world

Self-heating coffee cans use the exothermic reaction of calcium oxide with water: CaO(s) + H2O(l) → Ca(OH)2(s), ΔH = −65 kJ mol−1.

Quick check

1. Calculate the energy released when 28 g of CaO reacts with water.

Answers: 1. 0.50 mol × 65 = 32.5 kJ

17 Temperature and heat

Distinguishing the two.

Temperature measures the average kinetic energy of particles; heat is energy transferred because of a temperature difference. A large mass of water at 40 °C contains more thermal energy than a small mass at 90 °C.

WORKED EXAMPLE 12 Distinguishing (standard)

A bath (100 kg) at 40 °C and a cup (0.25 kg) of tea at 90 °C: which contains more thermal energy above 20 °C?

Solution

Bath: 100 000 × 4.18 × 20 = 8.36 MJ; cup: 250 × 4.18 × 70 = 73 kJM1

The bathA1

18 Mixed review: worked problems

Bringing the ideas together.

WORKED EXAMPLE 13 Mixed problem (exam level)

When 1.60 g of NH4NO3 dissolves in 50.0 g water, the temperature falls from 22.0 °C to 19.6 °C. Calculate ΔHsol.

Solution

q = 50.0 × 4.18 × 2.4 = 501.6 J (absorbed)M1 A1

n = 1.60/80.06 = 0.0200 molA1

ΔH = +25.1 kJ mol−1A1

Quick check

1. Find the final temperature when 10.0 g of KOH (ΔHsol = −57.6 kJ mol−1) dissolves in 100 g water at 20.0 °C.

Answers: 1. n = 0.178 mol; q = 10 270 J; ΔT = 24.6 K: 44.6 °C

19 Additional exam-style practice

Paper 1 and Paper 2.

WORKED EXAMPLE 14 Paper 1 question (standard)

Which is endothermic? A. H2O(g) → H2O(l) B. Na(g) → Na+(g) + e− C. CH4 + 2O2 → CO2 + 2H2O D. HCl + NaOH → NaCl + H2O

Solution

B (ionization absorbs energy)A1

WORKED EXAMPLE 15 Paper 2 question (exam level)

A student finds ΔHc of propan-1-ol: 0.60 g burned heats 150 g water by 25.0 K. (a) Calculate ΔHc. (b) Suggest why the value is less exothermic than the literature value (−2021 kJ mol−1).

Solution

(a) q = 15 675 J; n = 0.00998 mol: −1570 kJ mol−1M1 A1 A1

(b) heat loss; incomplete combustionR1

20 Energy density and specific energy

Comparing fuels.

Specific energy (kJ g−1) = |ΔHc|/M; energy density (kJ dm−3) relates energy to volume. Hydrogen has a very high specific energy but low energy density as a gas. (Developed in R1.3.)

WORKED EXAMPLE 16 Specific energy (standard)

Calculate the specific energy of methane (ΔHc = −891 kJ mol−1).

Solution

891/16.05M1

= 55.5 kJ g−1A1

21 Thermochemical equations

ΔH belongs to the equation as written.

A thermochemical equation includes state symbols and ΔH. Doubling the equation doubles ΔH; reversing it changes the sign. State symbols matter: forming H2O(l) releases more energy than H2O(g), because condensation is exothermic.

WORKED EXAMPLE 17 States matter (standard)

Explain why ΔHc of hydrogen to H2O(l) (−286 kJ) is more negative than to H2O(g) (−242 kJ).

Solution

Condensing water releases energy (44 kJ mol−1)R1

22 Common misconceptions and links

Students often think…	Actually…
ΔH is positive when temperature rises	temperature rise means exothermic, ΔH negative
use the mass of reactant in Q = mcΔT	use mass of water / solution
heat and temperature are the same	heat is energy transferred; temperature is average kinetic energy

How R1.1 connects to the rest of the course

Topic	Connection
R1.2 Energy cycles	Hess's law and bond enthalpies
R1.3 Energy from fuels	combustion
R2.2 How fast?	activation energy
S1.4 The mole	moles from mass and concentration

23 Exam-style question with markscheme

Try this under exam conditions (about 15 minutes) before reading the markscheme.

Figure 8. Temperature during a neutralization experiment.

Text A. 25.0 cm3 of 2.00 mol dm−3 HCl was added to 25.0 cm3 of 2.00 mol dm−3 NaOH at 3 minutes.

(a) Estimate the maximum temperature change using extrapolation. [1]

(b) Calculate the heat released. [2]

(d) Suggest why the value is less exothermic than −57 kJ mol−1. [1]

(e) Sketch and label the energy profile for this reaction. [2]

Markscheme

Part	Answer	Marks
(a)	about 7.9 °C (27.9 − 20.0)	A1
(b)	Q = 50.0 × 4.18 × 7.9	M1
	= 1651 J	A1
(c)	n = 0.0500 mol	M1
	ΔH = −33.0 kJ mol−1	A1
(d)	heat loss to surroundings	A1
(e)	products below reactants; ΔH labelled	A1
	activation energy hump labelled	A1

Examiner's comments. In (c), forgetting the negative sign or using moles of acid incorrectly were the most common errors.

24 Check your understanding

Section A: multiple choice

1. In an exothermic reaction

A. the surroundings get hotter B. ΔH is positive C. products have more enthalpy D. heat is absorbed

2. The specific heat capacity of water is

A. 1.00 J g−1 K−1 B. 8.31 J K−1 mol−1 C. 4.18 J g−1 K−1 D. 4180 kJ g−1

3. Standard pressure is

A. 1 kPa B. 100 kPa C. 101 Pa D. 1000 kPa

4. Q = 50 g × 4.18 × 10 K equals

A. 209 J B. 20.9 kJ C. 500 J D. 2090 J

5. The main error in calorimetry is

A. using too much water B. heat loss C. using a thermometer D. stirring

6. Dissolving NH4NO3 in water is

A. endothermic B. exothermic C. neither D. combustion

Section B: structured

7. Distinguish exothermic and endothermic reactions. [3]

8. Describe an experiment to measure the enthalpy of combustion of propanol. [4]

9. Calculate ΔH if 0.0250 mol of a solid dissolves in 50.0 g water and the temperature falls by 4.0 °C. [2]

Answers

1. A 2. C 3. B 4. D 5. B 6. A

7. Exothermic: releases heat, surroundings warm, ΔH negative; endothermic: absorbs heat, cools, ΔH positive.

8. Weigh burner; known mass of water in can; record initial T; burn; record max T; reweigh burner; Q = mcΔT; ΔH = −Q/n.

9. Q = 836 J; ΔH = +33.4 kJ mol−1.

25 Summary and topic map

Idea	Remember
System and surroundings	energy conserved
Exothermic	ΔH negative; surroundings warm
Endothermic	ΔH positive; surroundings cool
Standard conditions	100 kPa, 298 K, 1 mol dm−3
Calorimetry	Q = mcΔT; ΔH = −Q/n
Errors	heat loss, incomplete combustion; extrapolation

Before the exam, make sure you…

•use the mass of water or solution
•include the sign of ΔH
•convert J to kJ
•evaluate errors and improvements

Measuring Enthalpy Changes on one page

Cover this page with a sheet of paper and try to rebuild it from memory. Whatever you can't recall is what to revise next.

Figure 9. Topic map for Measuring Enthalpy Changes.

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