An enthalpy change 焓变, $\Delta H$, is the heat energy change at constant pressure. Standard conditions mean a pressure of 100 kPa and a stated temperature, usually 298 K. State symbols matter: making liquid water releases a different amount of energy from making water vapour. An exothermic 放热的 reaction has $\Delta H<0$; an endothermic 吸热的 reaction has $\Delta H>0$. In an enthalpy-level diagram, put reactants and products on horizontal levels. The arrow runs from reactants to products; its vertical change gives $\Delta H$.
These definitions specify different reactions, each under standard conditions with substances in their standard states:
| Change |
What the equation must represent |
| Standard enthalpy of reaction |
The reaction exactly as written, including its coefficients |
| Standard enthalpy of formation |
Formation of one mole of compound from its elements |
| Standard enthalpy of combustion |
Complete burning of one mole of substance in oxygen |
| Standard enthalpy of neutralisation 中和 |
Formation of one mole of water by reaction of an acid and an alkali |
| Standard enthalpy of atomisation 原子化 |
Formation of one mole of gaseous atoms from the element |
For example, $\frac12\mathrm{Cl_2(g)\rightarrow Cl(g)}$ is an atomisation equation, whereas $\mathrm{Cl_2(g)\rightarrow2Cl(g)}$ describes twice that amount. The standard formation enthalpy of an element in its standard state is zero by convention, not because the element has no energy.
A complete calorimetry calculation
Mix 50.0 cm³ of 1.00 mol dm⁻³ HCl with 50.0 cm³ of 1.00 mol dm⁻³ NaOH. Both start at the same temperature; the corrected rise is 6.8 °C. Assume density 1.00 g cm⁻³, specific heat capacity 4.18 J g⁻¹ °C⁻¹ and negligible cup heat capacity.
$$m=\rho V=1.00\ \mathrm{g\,cm^{-3}}\times100.0\ \mathrm{cm^3}=100.0\ \mathrm g$$
$$q_{\mathrm{solution}}=mc\Delta T=100.0\ \mathrm g\times4.18\ \mathrm{J\,g^{-1}\,{}^{\circ}C^{-1}}\times6.8\ {}^\circ\mathrm C=2842\ \mathrm J$$
$$n(\mathrm{H_2O})=cV=1.00\ \mathrm{mol\,dm^{-3}}\times0.0500\ \mathrm{dm^3}=0.0500\ \mathrm{mol}$$
$$\Delta H_{\mathrm{neut}}=-\frac{q_{\mathrm{solution}}}{n(\mathrm{H_2O})}=-\frac{2.842\ \mathrm{kJ}}{0.0500\ \mathrm{mol}}=-56.8\ \mathrm{kJ\,mol^{-1}}$$
The solution gains energy, so the reaction loses it. Use the total heated mass, but the limiting reacting amount. For unequal acid and alkali amounts, calculate both before finding the water amount. In a combustion experiment, water heated is not the fuel amount: obtain the latter from the burner's mass loss and the fuel molar mass.
Use a lid, insulation and stirring, and measure temperatures before and after mixing at regular times. Extrapolate the post-reaction cooling line to the mixing time when the method requires a cooling correction. Heat lost to the surroundings or absorbed by the cup makes an uncorrected exothermic result less negative. Incomplete combustion and fuel evaporation also make a combustion result less negative. Repeats help random variation; they do not remove these systematic effects. A large temperature rise reduces percentage thermometer uncertainty but must remain safe.
Hess cycles and bond enthalpies
Hess's law 赫斯定律 says that the enthalpy change depends on the initial and final states, not the route. Reverse an equation: reverse the sign. Multiply its coefficients: multiply its enthalpy. Add equations and cancel species, including their states, before adding the enthalpies.
For $\mathrm{C(s)+\frac12O_2(g)\rightarrow CO(g)}$, use $\mathrm{C+O_2\rightarrow CO_2}$, $\Delta H=-394$ kJ mol⁻¹, and the reverse of $\mathrm{CO+\frac12O_2\rightarrow CO_2}$, whose forward $\Delta H=-283$ kJ mol⁻¹. The target is the sum, so $\Delta H=-394-(-283)=-111$ kJ mol⁻¹. A cycle using formation data gives $\sum\Delta H_f(\text{products})-\sum\Delta H_f(\text{reactants})$, with coefficients included. A combustion cycle gives the reactant combustion sum minus the product combustion sum.
Core practical 2 compares dissolution/reaction routes to the same final solution. Match amounts and final states, account for each measured temperature change, and test whether experimental error explains disagreement. A cycle with unmatched final concentrations is not exactly the same thermodynamic route.
A mean bond enthalpy 平均键焓 is the average energy needed to break one mole of a specified covalent bond in gaseous molecules. Bond breaking takes energy; bond formation releases it.
$$\Delta H\approx\sum E(\text{bonds broken})-\sum E(\text{bonds formed})$$
For $\mathrm{H_2(g)+Cl_2(g)\rightarrow2HCl(g)}$, let H–H = 436, Cl–Cl = 243 and H–Cl = 431 kJ mol⁻¹. Then $\Delta H\approx436+243-2(431)=-183$ kJ mol⁻¹. Conversely, if $\Delta H=-184$ kJ mol⁻¹, $E(\mathrm{H-Cl})=[436+243-(-184)]/2=431.5$ kJ mol⁻¹. Mean values average different molecular environments and assume gas-phase bonds, so the estimate may differ from measured reaction enthalpy. A weak bond may break more readily, but reaction speed also depends on the whole activation pathway; $\Delta H$ alone does not predict rate.