Enthalpy Calculator

What the enthalpy calculator does

This calculator works out the enthalpy change of a process, the change in a system's total heat content, from the internal energy of the reactants and products, the pressure, and the volumes before and after. It is built for the kind of pressure-volume bookkeeping that comes up in thermodynamics and chemistry.

Below is what enthalpy is, the equation behind it, what the pressure-volume term means, and a worked example.

How to use it

1. Enter the internal energy of the products and of the reactants, in joules.
2. Enter the system pressure and the volumes of the products and reactants.
3. Press Calculate for the enthalpy change, or Reset to clear it.

What enthalpy is

Enthalpy is a measure of the total heat content of a system, combining the energy stored inside it with the energy tied up in the space it occupies against the surrounding pressure. Where internal energy counts only the energy held within, enthalpy also accounts for the work a system does, or has done on it, simply by taking up room in a world that pushes back. It is written H, and for most purposes what matters is how it changes during a process.

That change is what this calculator finds. When a reaction runs or a process unfolds, the system's enthalpy shifts, and the size and direction of that shift tell you whether the process releases heat or soaks it up. Because so much of chemistry and engineering happens out in the open at steady atmospheric pressure, the enthalpy change is one of the most practical quantities in all of thermodynamics.

The equation it uses

The change in enthalpy, ΔH, is the change in internal energy plus the pressure times the change in volume:

ΔH = ΔU + P × ΔV

The calculator finds the internal energy change ΔU as the products' internal energy minus the reactants', and the volume change ΔV as the products' volume minus the reactants', then adds the pressure-volume term. The internal energy change captures what happens to the energy held within the system, while the pressure-volume term captures the energy involved in any change of size against the surrounding pressure. Added together, they give the enthalpy change.

The pressure-volume term

The P times ΔV term is the part that sets enthalpy apart from plain internal energy, and it represents work done on or by the surroundings. When a system expands, it has to push the surrounding atmosphere out of the way, which costs energy; when it contracts, the atmosphere does work on it instead. That exchange of work with the outside world is what this term accounts for.

It matters most when gases are involved, because gases change volume dramatically. A reaction that produces gas swells and pushes back the surroundings, so the pressure-volume term is significant. A reaction among solids and liquids barely changes volume, so the term is tiny and the enthalpy change is almost the same as the internal energy change. By including this term, enthalpy correctly folds in the work of expansion or contraction, which internal energy alone leaves out.

Why enthalpy is so useful

The reason enthalpy earns its central place is a neat coincidence: for a process at constant pressure, the enthalpy change is exactly equal to the heat absorbed or released. Most real chemistry happens at constant pressure, open to the atmosphere, so the enthalpy change directly gives the heat of a reaction without any further calculation. That is why chemists speak of heats of reaction in terms of enthalpy.

The sign tells the story at a glance. A negative enthalpy change means heat is released, an exothermic process, the kind that warms its surroundings, like a fire or a hand warmer. A positive enthalpy change means heat is absorbed, an endothermic process, the kind that cools its surroundings, like an instant cold pack. Knowing the enthalpy change therefore tells you not just how much heat a process involves but which way it flows, which is what this calculator delivers.

Units and precision

The calculator works in SI units, with internal energies in joules, pressure in pascals, and volumes in cubic metres, and it returns the enthalpy change in joules. The pressure times a volume gives an energy in joules, so the two terms add cleanly. The relationship is exact for the constant-pressure case it is built around. Results are shown to two decimal places.

A worked example

Suppose a reaction has products with 5,000 joules of internal energy and reactants with 8,000 joules, runs at a pressure of 100,000 pascals, and expands by 0.01 cubic metres.

The internal energy change is 5,000 − 8,000 = −3,000 joules, and the pressure-volume term is 100,000 × 0.01 = 1,000 joules. The enthalpy change is ΔH = ΔU + PΔV = −3,000 + 1,000 = −2,000 joules. The negative sign means the process is exothermic, releasing 2,000 joules of heat to its surroundings at constant pressure.

Questions people ask

How do you calculate enthalpy change?

Add the internal energy change to the pressure times the volume change, ΔH = ΔU + PΔV. The internal energy change is products minus reactants, and likewise for volume.

What is the difference between enthalpy and internal energy?

Internal energy is the energy held within a system. Enthalpy adds the pressure-volume term, accounting for the work of expanding or contracting against the surrounding pressure.

Why does enthalpy change equal the heat of a reaction?

At constant pressure, the enthalpy change is exactly the heat absorbed or released. Since most chemistry happens at constant atmospheric pressure, the enthalpy change gives the heat of reaction directly.

What does the sign of the enthalpy change mean?

Negative means heat is released, an exothermic process that warms its surroundings. Positive means heat is absorbed, an endothermic process that cools its surroundings.

References

A quick note on where the physics comes from. Enthalpy, its definition through internal energy and pressure-volume work, and its link to the heat of reaction at constant pressure are standard thermodynamics, set out in OpenStax's Chemistry and in Georgia State University's HyperPhysics. The SI units follow the US National Institute of Standards and Technology. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, Chemistry 2e, Section 5.3, Enthalpy. https://openstax.org/books/chemistry-2e/pages/5-3-enthalpy
2. HyperPhysics, Enthalpy. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/enthal.html
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811