How to Read and Interpret Thermodynamic Data Tables

A thermodynamic data table gives properties such as enthalpy, entropy, and Gibbs free energy for a substance under specified conditions. Before using an entry in a calculation, check its temperature, phase, units, and reference state.

For example, the standard enthalpy of formation of liquid water at 298.15 K is about −285.8 kJ/mol. This value applies to liquid water under the stated standard conditions. It does not apply to water vapor, and it is not the enthalpy change for every reaction that produces water.

Read the headings first

Common table headings include:

• T (K): temperature in kelvin. A common reference temperature is 298.15 K, equivalent to 25 °C.
• ΔfH°: standard enthalpy of formation, usually in kJ/mol. It is the enthalpy change for the formation reaction, as written, that produces one mole of a compound from its elements in their specified reference forms and standard states. For special entries, follow the table’s conventions.
• S°: standard molar entropy, usually in J/(mol·K).
• ΔfG°: standard Gibbs free energy of formation, usually in kJ/mol.
• Cp°: standard heat capacity at constant pressure. It can help account for temperature changes.

The degree symbol marks a standard-state quantity. “Standard” refers to specified reference conditions, and does not guarantee that the substance is at 1 atm. Current conventions use a standard pressure of 1 bar (100 kPa); check the source’s definitions when precision matters. The IUPAC Gold Book defines standard pressure.

By definition, elements in their reference forms have ΔfH° = 0 and ΔfG° = 0. These values set the baseline for formation quantities. The reference form varies by element: graphite is the reference form for carbon, so diamond does not have a zero formation enthalpy.

Match the phase and reference state

A table may list a substance as a solid, liquid, or gas. Choose the row that matches the reaction or process you are studying. The standard enthalpies of formation for H₂O(l) and H₂O(g) differ because forming liquid water releases heat as vapor condenses. Using the wrong phase changes the result.

The same care applies to allotropes and other reference forms. If a reaction contains an element in a form other than its reference form, use the appropriate table entry instead of assigning it a zero formation value.

Check the temperature as well. A value at 298.15 K cannot automatically be used in a calculation at another temperature. Some tables give values at several temperatures; others provide a reference-temperature value and heat-capacity data for adjustments.

Formation values and reaction values

Formation quantities describe one mole of a compound formed from its elements. Reaction quantities describe the balanced reaction as written. To calculate a reaction quantity from formation data, multiply each entry by its stoichiometric coefficient, add the products, then subtract the reactants:

ΔrH° = ΣνΔfH°(products) − ΣνΔfH°(reactants)

The same product-minus-reactant method applies to ΔrG° and ΔrS°, using the corresponding formation or molar values. Here, ν represents each substance’s coefficient in the balanced equation.

Example: choosing the water entry

Suppose a reaction produces liquid water at 298.15 K. The table entry for H₂O(l) is approximately −285.8 kJ/mol; the entry for H₂O(g) is approximately −241.8 kJ/mol. Use the liquid value for liquid product and the gas value for water vapor. The difference is about 44 kJ/mol per mole of water, so choosing the wrong phase can materially change a reaction enthalpy.

These values alone do not give the reaction enthalpy. You also need the formation enthalpies for every reactant and product, and you must apply the coefficients in the balanced equation.

Keep units and signs consistent

Enthalpy and Gibbs free energy are commonly listed in kJ/mol, while entropy is commonly listed in J/(mol·K). Before using the relation

ΔrG° = ΔrH° − TΔrS°

make sure ΔrH° and TΔrS° use the same energy units. If entropy is in J/(mol·K), convert it to kJ/(mol·K) before combining it with enthalpy in kJ/mol.

Signs also need context. A negative ΔfH° means formation from the reference-form elements has a negative enthalpy change. A negative ΔrG° means the forward reaction is favorable in the standard-state comparison. It does not, by itself, tell you how quickly the reaction occurs.

Use the right conditions to assess spontaneity

For a reaction compared in the standard states, a negative ΔrG° indicates that the forward direction is thermodynamically favorable. At other temperatures, or when reactant and product amounts differ from their standard states, the result may change. A standard-state value alone does not determine spontaneity for every real mixture.

Temperature matters because Gibbs energy includes the term TΔS. When reliable reaction enthalpy and entropy values are available, this relation can show how the standard reaction Gibbs energy changes with temperature, if the values are suitable for that temperature. For substantial temperature changes, use temperature-dependent data or account for heat capacities.

Pressure and solution composition can also matter. For gases or solutions far from standard-state conditions, activities or other corrections may be needed. Use tabulated standard values as inputs to a calculation, not as a direct prediction for every operating condition.

Check the source and the uncertainty

The NIST Chemistry WebBook provides thermochemical information for individual substances. The NIST-JANAF Thermochemical Tables provide tabulated data across temperatures. Read each source’s notes on units, phases, temperature, and reference states. When values differ, compare those conditions before deciding whether the entries conflict.

Some tables report uncertainties or label values as estimated or calculated. These notes affect the confidence you can place in a result. If uncertainty is reported, consider how it carries through the reaction sum. A result calculated from several entries can have greater uncertainty than any one input.

For a calculation that needs to be checked or repeated, record the source, the specific entry, its phase and temperature, and any unit conversion. This helps prevent errors from mixing entries that use different conditions or conventions.

Key Takeaways

• Check the temperature, phase, units, and reference-state notes before using a table value.
• Use the phase that matches the reaction. Liquid water and water vapor have different formation enthalpies.
• Calculate reaction quantities by summing the stoichiometrically weighted products and subtracting the reactants.
• Convert entropy units before using ΔrG° = ΔrH° − TΔrS°.
• A negative standard reaction Gibbs energy indicates a favorable forward direction in the standard-state comparison; actual conditions may change the result.