Enthalpy change, standard conditions and the definitions

Heat in and heat out

Every chemical change either gives heat to its surroundings or takes heat from them. Sodium hydroxide dissolving in water makes the test tube too warm to hold; ammonium nitrate dissolving makes the outside of the tube mist with condensation as it cools. A sports cold pack is ammonium nitrate and a pouch of water, kept apart until the pack is squeezed.

To keep the sign straight, separate the system, which is the reacting chemicals, from the surroundings, which is everything else: the water they are dissolved in, the beaker, the thermometer and the air. A thermometer in the solution reads the temperature of the surroundings. When it rises, energy has left the chemicals.

The heat content of a substance is its enthalpy, H. Nobody can measure H itself, but the change in it during a reaction can be measured, as heat transferred to or from the surroundings. That change is the enthalpy change, ΔH, and it is defined at constant pressure because a reaction in an open beaker runs at the pressure of the atmosphere. At constant pressure the heat transferred is the whole of the enthalpy change.

In an exothermic reaction the products have less enthalpy than the reactants. The difference is given out as heat, the surroundings warm up, and ΔH is negative. In an endothermic reaction the products have more enthalpy than the reactants, heat is taken in from the surroundings, the surroundings cool, and ΔH is positive. The sign always describes the chemicals, never the beaker. A hot beaker means a negative ΔH.

ΔH is quoted per mole, in kJ mol⁻¹, and its sign is always written. The thermal decomposition of calcium carbonate has ΔH = +178 kJ mol⁻¹, not 178. The plus sign says the reaction takes heat in, and a lime kiln has to be kept hot to supply it. A mark scheme does not credit 178 for an endothermic change, because without its sign the number does not say which way the heat went.

Enthalpy change, ΔH

The heat energy change measured under conditions of constant pressure.

Exothermic

Describes a reaction in which heat energy is transferred to the surroundings, so ΔH is negative.

Endothermic

Describes a reaction in which heat energy is taken in from the surroundings, so ΔH is positive.

Enthalpy profile diagrams

A gas hob does not light itself. Methane and oxygen can sit mixed in the air of a kitchen without reacting, although their combustion is strongly exothermic, because bonds in both molecules must start to break before new ones can form. A spark supplies that energy to a few molecules, and the heat from their reaction then supplies it to the next.

Describe the drawing

Two enthalpy profiles side by side on the same scale. On the left, exothermic, methane and oxygen start high, climb over a hump and fall to carbon dioxide and liquid water far below; an amber arrow up from the reactant level marks the activation energy and a white arrow down to the products marks ΔH = −890 kJ mol⁻¹. On the right, endothermic, calcium carbonate starts low, climbs a hump and settles at calcium oxide and carbon dioxide a little higher; both arrows point up from the reactant level, the ΔH arrow marking +178 kJ mol⁻¹.

An enthalpy profile diagram plots enthalpy against the progress of the reaction. The reactants sit at one level and the products at another, each labelled with its formula. Between them the line rises to a peak, because the partly broken arrangement on the way to products has more enthalpy than either. The height of that peak above the reactants is the activation energy, Ea.

Two arrows are drawn and both are measured from the reactant level. The activation energy arrow points up from the reactants to the peak. The ΔH arrow runs from the reactant level to the product level: down for an exothermic reaction, up for an endothermic one. In an endothermic reaction the activation energy is always at least as large as ΔH, since the peak cannot sit below the products.

Activation energy

The minimum energy that particles must have for a reaction to take place when they collide.

The two arrows answer different questions. ΔH says how much heat the reaction releases or absorbs once it has happened. Ea says how hard it is to start, and so how fast it goes at a given temperature. A mixture can have a large negative ΔH and still be stable for years if its activation energy is high: a sheet of paper in air is the everyday example. Such a mixture is energetically unstable but kinetically stable.

A catalyst provides a different route with a lower peak. It lowers Ea and leaves the reactant and product levels where they were, so ΔH is unchanged. Write that a catalyst provides an alternative route with a lower activation energy; 'gives the particles energy' describes heating, not catalysis.

Kinetically stable

Describes a mixture that does not react at a measurable rate because its activation energy is high, even though ΔH for its reaction is negative.

Standard conditions and standard states

The heat released when a mole of methane burns depends a little on the temperature and pressure, and a lot on whether the water formed ends up as a liquid or as steam. A value in a data book is only useful if everyone knows which conditions it refers to, so tabulated values are standard enthalpy changes, marked with the symbol °: ΔH°.

Standard conditions are a pressure of 100 kPa and a stated temperature, which is almost always 298 K (25 °C). Where solutions take part, their concentration is 1.00 mol dm⁻³. A value measured at another temperature is written with that temperature as a subscript, ΔH°₅₀₀ for 500 K.

Each substance also has a standard state: the physical state it is in at 100 kPa and 298 K. Oxygen and hydrogen are gases, water and bromine are liquids, and sodium chloride and iodine are solids. Carbon is a solid with more than one form, and its standard state is graphite, not diamond. An equation for a standard enthalpy change shows every substance in its standard state, so the water in a standard combustion is H₂O(l), not H₂O(g).

The difference is not small. Condensing a mole of steam to liquid water at 298 K releases 44 kJ, so the formation of H₂O(g) is −242 kJ mol⁻¹ and the formation of H₂O(l) is −286 kJ mol⁻¹. A value quoted without its state symbols cannot be used.

Standard conditions

A pressure of 100 kPa and a stated temperature, usually 298 K, with any solutions at 1.00 mol dm⁻³.

Standard state

The physical state of a substance at 100 kPa and 298 K, such as H₂O(l), O₂(g) and C(graphite).

The four standard enthalpy changes

Four standard enthalpy changes are defined, and each definition names exactly one mole of one substance. That single mole decides how the equation is balanced, and it is why fractions such as ½O₂ appear in them.

The standard enthalpy of formation, ΔfH°, makes one mole of a compound from its elements. The elements must be in their standard states, so carbon appears as C(s), meaning graphite, and oxygen as O₂(g), never as separate O atoms. For ethanol:

2C(s) + 3H₂(g) + ½O₂(g) → C₂H₅OH(l) ΔfH° = −277 kJ mol⁻¹One mole of ethanol, so half a mole of O₂ supplies its one oxygen atom.

Describe the drawing

The equation two C solid plus three H two gas plus half O two gas gives C two H five O H liquid, written large with every state symbol picked out in cyan. Notes under each reactant say carbon is graphite, hydrogen is a diatomic gas and half a mole of oxygen gives one O atom; under the product, one mole of liquid. The enthalpy of formation, minus 277 kilojoules per mole, sits above the arrow, and brackets mark the elements in their standard states and the one mole of compound.

No laboratory makes ethanol by passing hydrogen and oxygen over graphite. The equation defines the quantity; it does not describe a reaction anyone carries out. Most enthalpies of formation are found indirectly, with Hess's law. The enthalpy of formation of an element in its standard state is zero by definition, since making O₂(g) from O₂(g) changes nothing.

The standard enthalpy of combustion, ΔcH°, burns one mole of a substance completely in oxygen. Complete combustion means the carbon ends as CO₂ and the hydrogen as H₂O, and in the standard state that water is liquid:

C₂H₅OH(l) + 3O₂(g) → 2CO₂(g) + 3H₂O(l) ΔcH° = −1367 kJ mol⁻¹

Because the definition fixes one mole of the fuel, the oxygen is balanced last and often comes out as a fraction. Butane has four carbon atoms and ten hydrogen atoms, so one mole of it makes 4CO₂ and 5H₂O. Those hold thirteen oxygen atoms between them, which is six and a half moles of O₂.

C₄H₁₀(g) + 6½O₂(g) → 4CO₂(g) + 5H₂O(l) ΔcH° = −2877 kJ mol⁻¹Doubling to clear the fraction would burn two moles of butane, and the ΔH of that equation would be twice ΔcH°.

Combustion is always exothermic, so every ΔcH° is negative. An enthalpy of formation can have either sign. Most compounds have a negative ΔfH°, but a few, such as ethene at +52 kJ mol⁻¹ and nitrogen monoxide at +90 kJ mol⁻¹, have more enthalpy than the elements they are made from.

The standard enthalpy of neutralisation, ΔneutH°, is defined per mole of water formed, not per mole of acid. Sulfuric acid is diprotic, so one mole of it reacting with sodium hydroxide forms two moles of water and releases about twice the heat that one mole of hydrochloric acid does, but the enthalpy of neutralisation is about −57 kJ mol⁻¹ for both:

H⁺(aq) + OH⁻(aq) → H₂O(l) ΔneutH° = −57 kJ mol⁻¹The ionic equation for any strong acid with any strong alkali.

The enthalpy of neutralisation is therefore a property of the reaction between hydrogen ions and hydroxide ions, not of the particular acid. Hydrochloric acid with sodium hydroxide, and nitric acid with potassium hydroxide, both give −57 kJ mol⁻¹ to two significant figures, because the other ions present take no part. In a definition, write 'one mole of water formed'; 'one mole of acid' gives the wrong value for sulfuric acid and does not describe the quantity at all.

The standard enthalpy of reaction, ΔrH°, belongs to an equation rather than to a substance: it is the enthalpy change when the amounts in the equation, as written, react. Double the equation and ΔrH° doubles. For that reason ΔrH° is always quoted beside its equation.

Standard enthalpy of formation, ΔfH°

The enthalpy change when one mole of a compound is formed from its constituent elements, with all reactants and products in their standard states under standard conditions.

Standard enthalpy of combustion, ΔcH°

The enthalpy change when one mole of a substance is burned completely in oxygen, with all reactants and products in their standard states under standard conditions.

Standard enthalpy of neutralisation, ΔneutH°

The enthalpy change when solutions of an acid and an alkali react together under standard conditions to produce one mole of water.

Standard enthalpy of reaction, ΔrH°

The enthalpy change when the amounts of reactants shown in the equation react under standard conditions, with all substances in their standard states.

Enthalpies of combustion compared

Enthalpies of combustion are among the easiest standard values to measure, and they are how fuels are compared. Down a homologous series each compound has one more CH₂ than the last, and the value grows by a nearly constant step.

Describe the drawing

A graph of standard enthalpy of combustion against number of carbon atoms, with the vertical axis running from zero at the top down to minus 3000. Alkanes from methane to butane are filled cyan circles on a straight line falling to the right; the primary alcohols methanol, ethanol and propan-1-ol are open amber squares on a parallel line a little above it. A bracket between propane and butane marks each CH two adding about minus 650 kilojoules per mole.

Two rows of the table are also enthalpies of formation. Burning a mole of hydrogen makes a mole of liquid water from its elements, so ΔcH°(H₂) and ΔfH°(H₂O, l) are the same equation and the same value, −286 kJ mol⁻¹. Burning graphite makes CO₂ from its elements, so ΔcH°(C) equals ΔfH°(CO₂), −394 kJ mol⁻¹.

The alcohol line sits 160 to 200 kJ mol⁻¹ above the alkane line. Methane and methanol both burn to one CO₂ and two H₂O, but methanol already has an oxygen atom bonded to its carbon. It starts partly oxidised, with less enthalpy than methane relative to the same products, so less heat is released when it burns. The same holds at every chain length.

A molar value converts to the heat from any mass of fuel through the amount in moles. The negative sign stays with ΔH; the heat released is quoted as a positive quantity.

Other boards: diagram names, standard pressure and four definitions

OCR, Edexcel and Cambridge set the definitions of the standard enthalpies of neutralisation and of reaction as questions in their own right, alongside formation and combustion. The wording is the one given here: neutralisation per mole of water formed, reaction for the amounts in the equation as written. On those papers a definition of neutralisation 'per mole of acid' is not credited.

Cambridge calls the profile a reaction pathway diagram, and Edexcel's specification calls it an enthalpy level diagram. The axes, the levels and the arrows are the same. A level diagram may show only the two levels and the ΔH arrow, with no hump between them; the hump and Ea are added when a question asks about the activation energy or a catalyst.

Cambridge states standard pressure as 101 kPa, one atmosphere, rather than 100 kPa. At this level the difference changes no calculated answer, but a Cambridge candidate asked for the standard conditions quotes 101 kPa and 298 K, the values in that syllabus.