Enthalpy change, exothermic and endothermic reactions, standard enthalpy changes, calorimetry, Hess's law and enthalpy cycles, and mean bond enthalpy calculations.

What this topic is asking

Edexcel Topic 7 wants you to define enthalpy change and the standard enthalpy terms, measure enthalpy changes by calorimetry using $q = mc\Delta T$, apply Hess's law through enthalpy cycles built from formation or combustion data, and estimate $\Delta H$ from mean bond enthalpies. Almost every question is quantitative, so the marks come from clean working with correct signs and units.

The answer

Enthalpy change and standard conditions

The key standard terms you must define precisely:

• Standard enthalpy of formation $\Delta H_f^{\ominus}$: the enthalpy change when one mole of a compound forms from its elements in their standard states under standard conditions. By definition $\Delta H_f^{\ominus}$ of an element in its standard state is zero.
• Standard enthalpy of combustion $\Delta H_c^{\ominus}$: the enthalpy change when one mole of a substance burns completely in oxygen under standard conditions.
• Standard enthalpy of reaction $\Delta H_r^{\ominus}$: the enthalpy change for the reaction as written in moles.

Reaction profiles

In an exothermic reaction the products sit lower in energy than the reactants, so $\Delta H$ is negative; the activation energy $E_a$ is the hump that must be climbed first. In an endothermic reaction the products sit higher. The difference between reactant and product energy levels is $\Delta H$.

Calorimetry

Measure the temperature rise of a known mass of water (or aqueous solution) and apply the heat equation.

For enthalpy of combustion, the fuel heats the water in a calorimeter. For enthalpy of neutralisation or solution, the temperature change of the reacting solution itself is used, taking the solution density as $1\ \text{g cm}^{-3}$.

Hess's law and enthalpy cycles

From formation data, the arrows in the cycle point up from the elements to both reactants and products, giving

From combustion data, the arrows point down to the common combustion products, giving

Watch the arrow directions: this is the most common place to drop a sign.

Mean bond enthalpies

A mean bond enthalpy is the average energy to break one mole of a particular bond in the gas phase, averaged over many compounds.

Because the values are averages, the result is only an estimate, and it strictly applies only to gaseous species.

Examples in context

Example 1. Self-heating cans and exothermic chemistry. Self-heating coffee cans exploit the strongly exothermic reaction of calcium oxide with water, $\text{CaO} + \text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2$, with $\Delta H \approx -65\ \text{kJ mol}^{-1}$. Engineers use the same $q = mc\Delta T$ relationship to size the reagent quantity so the drink reaches a target temperature, exactly the calorimetry maths Edexcel tests in Topic 7.

Example 2. Fuel comparison by bomb calorimetry. Combustion enthalpies quoted for fuels (petrol, ethanol, hydrogen) are measured in a sealed bomb calorimeter, which minimises the heat loss and incomplete combustion that make a simple school spirit-burner experiment give values far smaller in magnitude than the data book. Edexcel evaluation questions reward naming heat loss, incomplete combustion and evaporation as the reasons the school value is too small.

Try this

Q1. Define the standard enthalpy of formation of a compound. [2 marks]

• Cue. Enthalpy change when one mole of the compound forms from its elements in their standard states under standard conditions ($100\ \text{kPa}$, stated temperature).

Q2. $0.0125\ \text{mol}$ of a fuel raises the temperature of $200\ \text{g}$ of water by $14.0\ \text{K}$. Calculate $\Delta H_c$. [3 marks]

• Cue. $q = 200 \times 4.18 \times 14.0 = 11704\ \text{J}$; $\Delta H_c = -11704 / 0.0125 = -936\ \text{kJ mol}^{-1}$.

Q3. Using $\Delta H_f^{\ominus}$ values, write the Hess expression for $\Delta H_r$ and explain the sign convention. [3 marks]

• Cue. $\Delta H_r = \sum \Delta H_f(\text{products}) - \sum \Delta H_f(\text{reactants})$; elements have $\Delta H_f = 0$.