R1.1: Measuring enthalpy changes
Master IB Chemistry R1.1: Measuring enthalpy changes with notes created by examiners and strictly aligned with the syllabus.
IB Syllabus Requirements for Measuring enthalpy changes
R1.1.1 Energy transfer between system and surroundings
R1.1.2 Endothermic and exothermic reactions
R1.1.3 Relative stability and energy profiles
R1.1.4 Standard enthalpy change and calorimetry
Systems, surroundings and conservation of energy
A system is the part of the universe chosen for study, for example the chemicals reacting in a beaker. The surroundings are everything outside that system that can exchange energy, and sometimes matter, with it. For the thermochemical model, system plus surroundings make up the universe.
Energy is conserved overall. It is not created or destroyed during a chemical or physical change; it is stored in different places and transferred in different ways. In chemistry, it helps to picture energy stored as chemical potential energy in bonds and as kinetic energy in moving particles.
An open system can exchange both matter and energy with its surroundings. A closed system can exchange energy but not matter with its surroundings. An isolated system is an ideal system that exchanges neither matter nor energy with its surroundings. Most classroom calorimetry is not truly isolated, so we just try to reduce energy transfer to the room.
Heat is not temperature
Temperature is a physical property that measures the average kinetic energy of the particles in a sample. The absolute temperature scale is the kelvin scale; a higher temperature means the particles have greater average kinetic energy. Back in the particulate model, that means hotter particles are, on average, moving faster.
A state function is a property whose change depends only on the initial and final states, not on the route taken between them. Temperature is a state function. Calculate temperature change using ΔT = Tᶠ − Tᵢ, where ΔT is the temperature change (K), Tᶠ is the final temperature (K) and Tᵢ is the initial temperature (K). A temperature change of 1 °C has the same size as a temperature change of 1 K, so either scale may appear in practical data for ΔT.
Heat is energy transferred from a hotter object or region to a colder object or region because of a temperature difference. Be fussy with the wording here: a reaction does not “contain heat”; energy is transferred as heat. Heat can be transferred by conduction, convection and radiation.
For example, when magnesium reacts with hydrochloric acid, the reacting chemicals are the system. Energy is transferred from that system to the aqueous solution and then to the surroundings, so the measured temperature rises. The temperature reading tells us about particle kinetic energy; the heat transfer tells us about energy moving across the system boundary.
Direction of energy transfer
An exothermic reaction is a chemical reaction that transfers energy from the system to the surroundings as heat. The surroundings warm up, so a thermometer or temperature probe in the solution usually shows a temperature increase. For an exothermic reaction, ΔH is negative, where ΔH is the enthalpy change of reaction (kJ mol⁻¹).
An endothermic reaction is a chemical reaction that transfers energy from the surroundings to the system as heat. The surroundings cool down, so the measured temperature usually drops. For an endothermic reaction, ΔH is positive.
In class, I often say: “Follow the energy, then decide the sign.” If the system loses energy, ΔH is negative. If the system gains energy, ΔH is positive. The thermometer sits in the surroundings, or in the reaction mixture that receives or loses heat, so its reading gives us the practical clue.
What you would observe
For an exothermic reaction, the container may feel warmer, a probe may show a temperature rise, or, if the reaction is vigorous, energy may be transferred as light and sound. For an endothermic change, the container may become cold, condensation or frost can appear on the outside in extreme cases, or the temperature may fall during dissolving.
A calorimeter is an apparatus that measures heat transfer by recording a temperature change in a known mass of substance, usually water or an aqueous solution in school practicals. A polystyrene cup calorimeter is simple but useful: it cuts down heat exchange with the room while still letting us stir and monitor temperature.
Bond breaking and bond forming
During a reaction, bonds in the reactants break and new bonds form in the products. Breaking bonds requires energy to be absorbed; forming bonds releases energy. A reaction is exothermic overall when bond formation releases more energy than bond breaking absorbs. A reaction is endothermic overall when bond breaking absorbs more energy than bond formation releases.
This links to a useful example: most combustion reactions are exothermic, but forming nitrogen monoxide from nitrogen and oxygen is endothermic. The N≡N bond in N₂ is exceptionally strong, so breaking it requires a very large input of energy. The energy released when N–O bonds form is not enough to compensate.
Stability means lower potential energy
In thermochemistry, a more stable substance sits at a lower potential energy level. That isn’t a moral judgement on the molecule; it just means that arrangement of particles and bonds stores less energy.
In an exothermic reaction, the reactants have higher potential energy than the products. So the products are relatively more stable, and the energy difference is released to the surroundings. In an endothermic reaction, the products have higher potential energy than the reactants. They are relatively less stable, because energy has been absorbed from the surroundings.
Energy profiles
An energy profile is a graph showing how the potential energy of the reacting system changes as reactants become products. Label the x-axis reaction coordinate and the y-axis potential energy. The reaction coordinate is not time; it’s a progress line from reactants, through the reaction pathway, to products.
The vertical difference between products and reactants is ΔH. For an exothermic reaction, the products line is lower than the reactants line, so ΔH is negative. For an endothermic reaction, the products line is higher, so ΔH is positive.
Most energy profiles include a hump. The top of the hump shows the highest-energy arrangement reached during the reaction pathway. Eₐ is the activation energy (kJ mol⁻¹), the minimum energy particles need to react successfully. You’ll use activation energy more in rate chemistry, but here you need to be able to find it on the profile.
When sketching, include labelled axes, reactants and products, a single curve with a peak, ΔH, and Eₐ. Without those labels, the chemistry may be right in your head, but it hasn’t been communicated on the page yet.
Standard enthalpy change
The standard enthalpy change of reaction is the heat transferred at constant pressure when the molar quantities in the chemical equation react under standard conditions, with every substance in its standard state. It is written ΔH⦵, where ΔH⦵ is the standard enthalpy change (kJ mol⁻¹). The standard symbol refers to standard conditions and standard states, not “room conditions chosen casually”.
A standard state is the physical state of a substance in its most stable form under the stated standard conditions. At 298 K and 100 kPa, for instance, water’s standard state is liquid water, not steam. Standard thermochemical data are usually quoted at 100 kPa and 298 K unless another temperature is stated.
Specific heat capacity and Q = mcΔT
Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 K. In calorimetry, the relationship used is Q = m**cΔT, where Q is the heat energy transferred to the substance being heated (kJ), m is the mass of that substance (kg), c is its specific heat capacity (kJ kg⁻¹ K⁻¹) and ΔT is its temperature change (K). For water, the data booklet gives c, commonly 4.18 kJ kg⁻¹ K⁻¹.
Check the units before substituting. If mass is in grams and c is in kJ kg⁻¹ K⁻¹, convert grams to kilograms. If c is given in J g⁻¹ K⁻¹, you can keep mass in grams and obtain Q in joules. The calculation itself is straightforward; inconsistent units are where students lose marks.
From heat transfer to enthalpy change
For a reaction measured by calorimetry, ΔH = −Q ÷ n, where n is the amount of limiting reactant (mol). A limiting reactant is the reactant present in the smallest stoichiometric amount, so it fixes the maximum amount of product that can form.
The negative sign matters. In an exothermic reaction, the water or solution gains heat, so Q for the surroundings is positive; the reacting system has lost that energy, so ΔH is negative. In an endothermic reaction, the water or solution loses heat, so Q is negative for the surroundings; the system has gained energy, so ΔH is positive.
Coffee-cup calorimetry
In a typical school experiment, reactants are mixed in a polystyrene cup, stirred, and the temperature is recorded before and after mixing. For aqueous reactions, we usually assume the solution has the same specific heat capacity as water and that the heat capacity of the cup and thermometer is negligible.
A better method records temperature at regular intervals. After the reaction, the cooling curve is extrapolated back to the mixing time to estimate the maximum temperature that would have been reached without heat loss. That gives a more reliable ΔT than just taking the highest raw temperature reading.
Calorimetry experiments often give a smaller temperature change than theoretical values predict. The main reason is heat transfer between the apparatus and the surroundings: hot solutions cool while they are being measured, and combustion flames lose energy to the air and the apparatus rather than only to the water. These are systematic errors because they tend to push the result in the same direction each time, usually making the magnitude of ΔH too small.
Random errors still count. Thermometer readings, slight differences in stirring, balance uncertainty, or a fluctuating flame can scatter repeated results. Digital temperature probes and data logging help by collecting frequent readings, but they don’t magically remove heat loss.
Combustion experiments
The enthalpy change of combustion of a fuel, such as an alcohol or a food sample, can be investigated by burning a measured mass of fuel and using the flame to heat a known mass of water. The water temperature change gives Q, and the mass loss of fuel gives the amount burned. Oxygen is normally in excess, so the fuel is the limiting reactant.
For alcohols, the usual school apparatus is a spirit burner below a beaker or metal calorimeter of water. You measure the initial and final mass of the burner, the mass of water, and the temperature rise of the water. Alcohols are flammable and volatile, so the practical needs eye protection, small quantities, good ventilation, no open bottles near flames, and disposal following local safety rules.
Food calorimetry uses the same idea: burn the sample, heat water, measure ΔT, and calculate energy transferred. In both cases, the experimental value is usually less exothermic than data-book values because some combustion may be incomplete and much of the energy heats the air, clamp, can, or room.
Neutralization as another calorimetry example
Neutralization reactions between acids and bases are exothermic. In a thermometric titration, one solution is added gradually to another while temperature is measured. The maximum temperature occurs when the acid and base have reacted in stoichiometric amounts, so a temperature–volume graph can be used to identify the equivalence volume and calculate concentration as well as enthalpy change.
Research calorimetry
A bomb calorimeter is a sealed calorimeter in which a sample is burned in oxygen inside a strong chamber surrounded by water. It improves accuracy and precision because combustion happens in a controlled oxygen atmosphere, heat loss is reduced, stirring evens out the water temperature, and a temperature probe records small temperature changes. The same principle is still being used: a measured temperature change in a known heat-absorbing system is converted into an energy change.
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