Systems, surroundings and conservation of energy

A system is the part of the universe chosen for study, such as the chemicals reacting in a beaker. The surroundings are everything outside the system that can exchange energy, and sometimes matter, with it. For the thermochemical model, the system and surroundings together are treated as the universe.

Energy is conserved overall. It is not created or destroyed during a chemical or physical change; instead, energy changes where it is stored and how it moves from one place to another. 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; 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, so a higher temperature means a greater average kinetic energy of particles. Link this back to the particulate model: 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. The temperature change is calculated using

A temperature change of 1 °C has the same size as a temperature change of 1 K, which is why either scale may appear in practical data for $\Delta T$.

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 moves 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 crossing 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 get warmer, so a thermometer or temperature probe in the solution usually shows a temperature increase. For an exothermic reaction, $\Delta H$ is negative, where $\Delta H$ is the enthalpy change of reaction ($\mathrm{kJ\ mol^{-1}}$).

An endothermic reaction is a chemical reaction that transfers energy from the surroundings to the system as heat. The surroundings get cooler, so the measured temperature usually drops. For an endothermic reaction, $\Delta H$ is positive.

In class, I often put it like this: “Follow the energy, then decide the sign.” If the system loses energy, $\Delta H$ is negative. If the system gains energy, $\Delta H$ 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 may 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 reduces heat exchange with the room while still letting us stir and monitor the temperature.

Bond breaking and bond forming

During a reaction, bonds in the reactants break and new bonds in the products form. 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 comparison: most combustion reactions are exothermic, but forming nitrogen monoxide from nitrogen and oxygen is endothermic. The $N\equiv N$ bond in $N_2$ 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 substance is more stable when it sits at a lower potential energy level. There’s no judgement being made about the molecule; less energy is stored in that arrangement of particles and bonds.

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 form 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 the products and the reactants is $\Delta H$. In an exothermic reaction, the products line is lower than the reactants line, so $\Delta H$ is negative. In an endothermic reaction, the products line is higher, so $\Delta H$ is positive.

Most energy profiles include a hump. Its top represents the highest-energy arrangement reached during the reaction pathway. $E_a$ is the activation energy ($\text{kJ mol}^{-1}$), the minimum energy required for particles to react successfully. You’ll use activation energy more in rate chemistry, but here you need to be able to locate it on the profile.

When sketching, include labelled axes, reactants and products, a single curve with a peak, $\Delta H$, and $E_a$. If those labels are missing, the chemistry may be right in your head, but it has not yet been communicated on the page.

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 as

The standard symbol refers to standard conditions and standard states, not to “room conditions chosen casually”.

A standard state is the physical state of a substance in its most stable form under the stated standard conditions. So, at 298 K and 100 kPa, water’s standard state is liquid water, not steam. Standard thermochemical data are usually quoted at 100 kPa and 298 K unless a different temperature is stated.

Specific heat capacity and $Q = mc\Delta T$

Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 K. In calorimetry, the relationship is

For water, $c$ is given in the data booklet, commonly $4.18\ \mathrm{kJ\ kg^{-1}\ K^{-1}}$.

Check the units before substituting. If mass is in grams and $c$ is in $\mathrm{kJ\ kg^{-1}\ K^{-1}}$, convert grams to kilograms. If $c$ is given in $\mathrm{J\ g^{-1}\ K^{-1}}$, you can keep mass in grams and get $Q$ in joules. The arithmetic is usually simple; mismatched units are where marks disappear.

From heat transfer to enthalpy change

For a reaction measured by calorimetry,

A limiting reactant is the reactant present in the smallest stoichiometric amount, so it sets 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 $\Delta H$ 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 $\Delta H$ 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. This gives a more reliable $\Delta T$ than just using the highest raw temperature reading.

Calorimetry experiments often give a smaller temperature change than theoretical values predict. The main cause is heat transfer between the apparatus and the surroundings: hot solutions cool while they are being measured, and combustion flames transfer energy to the air and apparatus rather than only to the water. These are systematic errors because they tend to shift the result in the same direction each time, usually making the magnitude of $\Delta H$ too small.

Random errors still count. Thermometer readings, slight changes in stirring, balance uncertainty, or a fluctuating flame can spread out repeated results. Digital temperature probes and data logging help because they collect 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 placed 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 $\Delta T$, and calculate the 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 the temperature is measured. The maximum temperature occurs when the acid and base have reacted in stoichiometric amounts, so a temperature–volume graph can identify the equivalence volume and allow concentration and enthalpy change to be calculated.

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 takes place in a controlled oxygen atmosphere, heat loss is reduced, stirring evens out the water temperature, and a temperature probe records small temperature changes. The principle is the same: a measured temperature change in a known heat-absorbing system is converted into an energy change.