# How to Calculate Enthalpies of Reaction ••• BZA/iStock/GettyImages

Enthalpy is related to the heat that is either given off by a reaction or required for a reaction to take place. It is related to the strength of the bonds in a substance because there is potential energy in those bonds.

To understand enthalpy, first energy and thermodynamics need to be understood. What is thermodynamics? It's the quantitative study of energy transfers and transformations.

## Energy Forms

There are many forms of energy: electrical energy, potential versus kinetic energy, chemical (bond) energy or heat. Atoms or molecules can have electrical energy in the sense that the electrons can be gained or donated. Electrical energy is extremely important because the behavior of electrons determines how an atom, molecule or substance reacts.

The electrical energy of molecules relates to the concept of stability: What electrons want to do. Orbitals want to be filled. Positive and negative charges attract each other to obtain the lowest possible energy level. Particles with the same charge will repel each other. This assists with predicting what electrons will do.

In the formation of bonds between atoms, energy is either released or required. The amount of energy that is required to bond elements together is referred to as bond energy.

Energy Transfers and Transformations:

• Collisions transfer kinetic energy from a moving object to another object.
• A hot substance next to a cooler substance will result in a transfer of energy (thermal) from one to the other.
• Potential energy transfers to kinetic energy when a rock falls from a ledge. When the rock hits the ground, its kinetic energy is transformed into thermal energy.
• In a combustion reaction, chemical energy is transformed into thermal energy.
• In reactions that change molecular makeup, energy is either required or released.

The Law of Conservation of Energy states that energy is neither created nor destroyed.

The concept of a system and surroundings in an enclosed system is very important in thermodynamics. When you measure temperature changes, it is the transfer of energy from the system to the surroundings (or vice versa) that you are measuring. The total amount of energy does not change, it is only transferred.

## Definition of Enthalpy

Enthalpy (H) is the thermodynamic function that describes heat flow and is expressed in kJ/mol. It is important to note that enthalpy is not strictly a measure of heat but is related to pressure and volume, as you can see in the formula below.

The enthalpy of formation is the difference in enthalpy between a compound and the elements that it is made of.

## Formula for Enthalpy

H = E + pV

H = enthalpy, E = energy, p = pressure, V = volume

First Law of Thermodynamics states that the energy of a system plus its surroundings remains constant and is a sum of the heat (q) and the work (w) that are taking place in that system.

ΔE = q + w

Work is also a flow of energy between a system and its surroundings. An easy way to visualize work as an energy transfer is to imagine pistons that move when a force is exerted on them.

Hess's Law: When there are two or more balanced chemical equations to show the steps of a reaction, the change in enthalpy for the net equation is the sum of the change in enthalpies for each individual equation.

This supports the fact that enthalpy is a state function, which means that the path taken does not affect the end outcome in terms of measuring enthalpy. This is in line with the law of conservation of energy in which energy is neither created nor destroyed.

When substances transition between phases (solid, liquid, gas) the energy transfer can be described with the following formula:

q = nCmΔT

q = heat, n = moles, C_m = molar heat capacity, _Δ__T = change in temperature

Specific Heat Capacity = the amount of energy required to raise the temperature of 1 kg of material by 1 degree Celsius

Molar Specific Heat Capacity = the amount of energy required to raise the temperature of 1 mole of material by 1 unit

## Calculation of Enthalpy of Reaction

Example 1: Calculate the temperature change that results from adding 250 J of thermal energy to 0.50 moles of mercury.

Visualize the diagram of the Heat System and Surroundings with the arrow direction going into the system.

Use the formula: q = nCmΔT

Since you are asked for the change in temperature, you rearrange the formula:

ΔT = q/nCm

Look up the molar heat capacity of mercury: 28.3 J/mol K

ΔT = 250 J/(p.50 mol)(28.3 J/mol K)
ΔT = 17.7 K

## Enthalpy of Formation

Calculating the enthalpy of formation involves writing balanced chemical equations and combining the change in enthalpy of each step. You must reduce the equations in such a way that you solve for a single atom of the atom that is specified in the question. The process is well defined in the example below.

## Calculation of Enthalpy of Formation

Example 2: Calculate the enthalpy change per mole of carbon monoxide for the reaction of carbon monoxide with oxygen to give carbon dioxide.

Carbon burned with limited oxygen will result in carbon monoxide (CO), however, when there is sufficient oxygen, the product will be carbon dioxide (CO2).

2 C (s) --> + O2 (g) --> 2 CO (g)

ΔH = -221.0 kJ

2 C (s) + O2 (g) --> CO2 (g)

ΔH = -393.5 kJ

Rearrange the first equation and reverse the ΔH, then balance the second equation.

2 CO 9g) --> 2 C (s) + O2 (g)

ΔH = +221.0 kJ

2 C (s) + 2 O2 (g) --> 2 CO2 (g)

ΔH = (2 mol)(-393.5 kJ) = -787.0 kJ

Cancel out the '2 C (s)' and the 'O2' from the right side of the first equation with the equivalents on the left side of the second equation to achieve the following:

2 CO (g) + O2 (g) --> 2 CO2 (g)

ΔH = (221.0 kJ) + (-787.0 kJ) = -566.0 kJ

Since the equation asks for 1 mole of CO2, not 2, divide all parts of the equation by 2 to achieve this.

CO (g) + 1/2 O2 (g) --> CO2 (g)

ΔH = -566.0 kJ/2 = -283.0 kJ

## Methods of Measuring Enthalpy

Calorimetry is the scientific measurement of heat transfer from a system to surroundings or vice versa.There are two types of calorimeters; one in which pressure remains constant and the other where the pressure may change. In a system with constant pressure, if there is a volume change, then expansion work has occurred. One scenario where this may occur is when a chemical process involves gases.

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