Enthalpy Calculator

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.

Enthalpy measures the total energy of a thermodynamic system — either in the form of internal energy 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).

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, by definition, is the sum of the internal energy of the system and the product of the system's volume and pressure:

where $U$ stands for internal energy, $p$ for pressure and $V$ for volume. Notice that the second part closely remembers the equations we met at the combined gas law calculator: the relationship between pressure and volume allows us to find a similar connection between quantity of matter and temperature.

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:

or, simplified:

where:

• $U_2$ and $V_2$ — Internal energy and volume of the products of the reaction, respectively;
• $U_1$ and $V_1$ — Internal energy and volume of the reactants, respectively;
• $p$ — Constant pressure;
• $ΔU$ — Change in internal energy;
• $ΔV$ — Change in volume; and
• $ΔH$ — Change in enthalpy.

For more specific problems, we can define the standard enthalpy of formation of a compound, denoted as $ΔH_\mathrm{f}\degree$. It represents the change in enthalpy during the formation of one mole of a substance under standard conditions of temperature and pressure ($p = 10^5\ \mathrm{Pa} = 1\ \mathrm{bar}$ and $T = 25 \degree \mathrm{C} = 298.15\ \mathrm{K}$), from its pure elements in their respective reference states.

The reference state of an element is its most stable configuration under the above-mentioned conditions. Some examples of reference states are nitrogen in the form of gas molecules $\mathrm N_{2}$ and carbon in the form of graphite.

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

where:

• $ΔH\degree_\mathrm{reaction}$ — Standard enthalpy change of formation expressed in kJ;
• $ΔH_\mathrm{f}\degree(\mathrm{products})$ — Sum of the standard enthalpies of formation of the products expressed in kJ/mol; and
• $ΔH_\mathrm{f}\degree(\mathrm{reactants})$ — Sum of the standard enthalpies of formation of the reactants, expressed in kJ/mol.

If you're paying attention, you might have observed that $ΔH_\mathrm{f}\degree(\mathrm{products})$ and $ΔH_\mathrm{f}\degree(\mathrm{reactants})$ have different units than $ΔH\degree_\mathrm{reaction}$. 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:

The symbols in the brackets indicate the state: $\mathrm{s}$ — solid, $\mathrm{l}$ — liquid, $\mathrm{g}$ — gas, and $\mathrm{aq}$ — 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:

What is the enthalpy change in this case? We sum $ΔH_\mathrm{f}\degree$ for $\mathrm{SO}_{2\mathrm{(g)}}$ and $O_{2\mathrm{(g)}}$ and subtract the $ΔH_\mathrm{f}\degree$ for $\mathrm{SO}_{3\mathrm{(g)}}$. Remember to multiply the values by corresponding coefficients!

Notice that the coefficient units $\mathrm{mol}$ eliminates the $\mathrm{mol}$ in the denominator, so the final answer is in $\mathrm{kJ}$:

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

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, enter the values of the coefficients and select the additional substances from the list (or select Custom option).

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 the 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 Chemistry LibreTexts).

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 $2000\ \mathrm{J}$.

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

4. Input all of these values to the equation $ΔH = ΔU + p\cdot ΔV$ to obtain the change in enthalpy:

5. Our enthalpy calculator can also find the enthalpy based on the initial and final internal energy and volume.