# Enthalpy Calculator

Created by Bogna Szyk and Dominik Czernia, PhD candidate
Reviewed by Steven Wooding
Last updated: Feb 15, 2022

This enthalpy calculator will help you calculate the change in enthalpy of a reaction. Read on to learn how to calculate enthalpy and its definition. We will also explain the difference between endothermic and exothermic reactions, as well as provide you with an example of calculations.

Check out our ideal gas law calculator, too!

## What is enthalpy?

Enthalpy measures the total energy of a thermodynamic system — either in the form of heat or volume multiplied by pressure. It is a state function, depending only on the equilibrium state of a system.

The more interesting quantity is the change of enthalpy — the total energy that was exchanged within a system. It is a simplified description of the energy transfer (energy is in the form of heat or work done during expansion).

## Endothermic or exothermic reaction?

There are two main types of thermodynamic reactions: endothermic and exothermic. An endothermic reaction causes absorption of heat from the surroundings. An exothermic one releases heat to the surroundings.

Both these reaction types cause energy level differences and therefore differences in enthalpy. All you need to remember for the purpose of this calculator is:

• If the reaction is endothermic, the change in enthalpy is positive, as heat is gained (absorbed from the surroundings).
• If the reaction is exothermic, the change in enthalpy is negative, as heat is lost (released to the surroundings).

## Enthalpy formula

Enthalpy, by definition, is the sum of heat absorbed by the system and the work done when expanding:

H = Q + pV

where Q stands for internal energy, p for pressure and V for volume.

If you want to calculate the change in enthalpy, though, you need to consider two states — initial and final. We will assume that the pressure is constant while the reaction takes place. Then, the change in enthalpy is actually:

ΔH = (Q₂ - Q₁) + p * (V₂ - V₁)

or, simplified:

ΔH = ΔQ + p * ΔV

where:

• Q₂ and V₂ — Internal energy and volume of the products of the reaction, respectively;
• Q₁ and V₁ — Internal energy and volume of the reactants, respectively;
• p — Constant pressure;
• ΔQ — Change in internal energy;
• ΔV — Change in volume; and
• ΔH — Change in enthalpy.

## Standard enthalpy of formation table and definition

For more particular problems, we can define the standard enthalpy of formation of a compound, denoted as ΔH°f. It's the change in enthalpy, ΔH, during the formation of one mole of the substance in its standard state, ° (pressure 10⁵ Pa = 1 bar and temperature 25 °C = 298.15 K), from its pure elements, f.

The standard enthalpy of formation formula for a reaction is as follows:

ΔH°reaction = ∑ΔH°f(products) - ∑ΔH°f(reactants)

where:

• ΔH°reaction — Standard enthalpy change of formation expressed in kJ;

• ∑ΔH°f(products) — Sum of the standard enthalpies of formation of the products expressed in kJ/mol; and

• ∑ΔH°f(reactants) — Sum of the standard enthalpies of formation of the reactants, expressed in kJ/mol.

If you're paying attention, you might have observed that ΔH°f(products) and ∑ΔH°f(reactants) have different units than ΔH°reaction. This is because you need to multiply them by the number of moles, i.e., the coefficient before the compound in the reaction. We'll show you later an example that should explain it all.

But before that, you may ask, "How to calculate standard enthalpy of formation for each compound?" The most straightforward answer is to use the standard enthalpy of formation table! Here's an example one:

Substance
ΔH°f (kJ/mol)
O₂(g)
0
SO₂(g)
−296.83
SO₃(g)
−395.72
H₂O(l)
−285.8
Cu₂O(s)
−168.6
Mg²⁺(aq)
-466.85

The symbols in the brackets indicate the state: s - solid, l - liquid, g - gas, and aq - dissolved in water. If you need the standard enthalpy of formation for other substances, select the corresponding compound in the enthalpy calculator's drop-down list. We included all the most common compounds!

Let's practice our newly obtained knowledge using the above standard enthalpy of formation table. For example, we have the following reaction:

2 SO₃(g) → 2 SO₂(g) + O₂(g)

What is the enthalpy change in this case? We sum ΔH°f for SO₂(g) and O₂(g) and subtract the ΔH°f for SO₃(g). Remember to multiply the values by corresponding coefficients!

ΔH°reaction = 2 mol * (−296.83 kJ/mol) + 1 mol * 0 kJ/mol - 2 mol * (−395.72 kJ/mol)

Notice that the coefficient units mol eliminates the mol in the denominator, so the final answer is in kJ:

ΔH°reaction = 197.78 kJ

That's it! Still, isn't our enthalpy calculator a quicker way than all of this tedious computation?

## How to calculate the enthalpy of a reaction?

The enthalpy calculator has two modes. You can calculate the enthalpy change from the reaction scheme or by using the enthalpy formula. If you select the former:

1. Look at the reaction scheme that appeared at the top of the calculator. Do you need an additional reactant/product (C or F)? If so, click the advanced mode button.
2. Fill in the fields in the Reactants section. You need to provide the coefficient before the compound and select your substance from the drop-down list (they're ordered alphabetically). If you can't find a right one, select the Custom option and enter the standard enthalpy of formation in kJ/mol (if you don't have this on hand, check some online reference tables, like this one at ).
3. Do the same thing for the Products.
4. Verify the reaction scheme below and read the result. That's the standard enthalpy change of formation for your reaction!
5. Optionally, check the standard enthalpy of formation table (for your chosen compounds) we listed at the very bottom.

If you want to calculate the enthalpy change from the enthalpy formula:

1. Begin with determining your substance's change in volume. Let's assume your liquid expanded by 5 liters.

2. Find the change in the internal energy of the substance. Let's say your substance's energy increased by 2000 J.

3. Measure the pressure of the surroundings. We will assume 1 atmosphere.

4. Input all of these values to the equation ΔH = ΔQ + p * ΔV to obtain the change in enthalpy:

ΔH = 2000 J + 1 atm * 5 l = 2000 J + 101,325 Pa * 0.005 m³ = 2506.63 J

5. You can also open the advanced mode of our enthalpy calculator to find the enthalpy based on the initial and final internal energy and volume.

Bogna Szyk and Dominik Czernia, PhD candidate
Calculate enthalpy change from
reaction scheme
anA + bnB + cnC → dnD + enE + fnF

By default, you can only calculate for two reactants/products. Click the advanced mode button to include more compounds in the reaction.
Reactants
aₙ coefficient
Reactant A
SO₃(g)
bₙ coefficient
Reactant B
None
Products
dₙ coefficient
Product D
SO₂(g)
eₙ coefficient
Product E
O₂(g)
Results
Change in enthalpy
kJ
2 SO₃(g) → 2 SO₂(g) + O₂(g)
Standard enthalpies of formation:
SO₃(g): Hf = -395.72 kJ
SO₂(g): Hf = -296.83 kJ
O₂(g): Hf = 0 kJ
Please note that we don't check if your reaction scheme makes chemical sense.
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