In this explainer, we will learn how to express energy in different units and convert between them.

Energy is the capacity for doing work. There are different categories of energy; some of them include electric potential energy, chemical potential energy, kinetic energy, and gravitational potential energy.

### Definition: Energy

Energy is the capacity for doing work.

Energy cannot be created or destroyed. The total energy of a self-contained system remains constant. However, energy can be transferred. When using a Bunsen burner, chemical potential energy becomes heat energy. The Bunsen burners combust propane () fuels, and during this reaction, the chemical potential energy of the bonds becomes heat and sound energy. The chemical potential energy is released as the chemical bonds in the propane and oxygen molecules are broken.

Energy is required to break a chemical bond, and energy is released when a new bond is created. This energy is called the bond energy, or bond enthalpy, and it is a measure of the bond strength. Bond energy is sometimes referred to as the bond dissociation energy. The bond energy can be determined as the amount of energy (enthalpy) that is needed to break one mole of molecules into its component atoms.

### Definition: Bond Energy (BE)

Bond energy is the average amount of energy required to break a particular bond in one mole of gaseous particles. This is also referred to as bond enthalpy.

There are many different categories of energy and all can be measured with different units. The SI unit for energy is the joule. SI units are a set of seven standardized units that are the same across the whole world. Fundamental constants, such as the speed of light in a vacuum, are used to calculate these units.

### Definition: International System of Units (SI)

It is a set of seven standardized base units derived from the seven fundamental constants. The SI units are the metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).

The joule is represented with a single uppercase J letter. A joule is defined as the amount of thermal energy required to raise the temperature of 1 g of water by .

### Definition: Joule

A joule is the quantity of energy needed to raise the temperature of one gram of water by .

A joule is an extremely small amount of energy, and we regularly expend and consume much larger quantities of energy when we eat and move. It is usually more appropriate to describe energy with the kilojoule (kJ) unit. The energy contained in a single slice of bread is approximately 250 000 J of energy! This is a very large number, and most nutritionists would choose to express this value as 250 kJ.

We can use the following relationship to convert between joule (J) and kilojoule (kJ) units.

The relationship shows that joules can be divided by 1 000 to determine the same value in kilojoules . The relationship also shows that kilojoules can be multiplied by 1 000 to determine the same value in joules. 250 000 J can be divided by 1 000 to express it as a value of 250 kJ.

The following conversion factors can also be used to convert between the joule (J) and kilojoule (kJ) units:

The following calculation shows how the conversion factor on the right-hand side can be used to transform a value of 250 000 J into a value of 250 kJ:

The unit conversion factor is appropriate here as the units of J will cancel out, leaving only units of kJ.

Enthalpy is the energy content of a chemical system. It is difficult to measure enthalpy directly, and chemists usually measure the change in enthalpy instead. The change in enthalpy is the amount of heat energy that is lost or gained by atoms during a chemical reaction.

### Definition: Enthalpy

Enthalpy describes the energy of a system.

The change in enthalpy can be determined for a single molecule or it can be determined for one mole of molecules. There are particles in one mole of a chemical substance, so the enthalpy change for one mole is the enthalpy change for particles. The enthalpy change for one mole is expressed with the kilojoules per mole (kJ/mol) unit.

### Definition: Molar Enthalpy

Molar enthalpy describes the energy of a system of one mole of a substance.

A particular type of bond, such as a bond, will have a slightly different bond energy depending on the molecule that the bond is found in. For this reason, bond energies are given as average values. The table below shows the average bond energy of some single bonds.

Type of Single Bond | Average Bond Energy (kJ/mol) |
---|---|

436 | |

427 | |

363 | |

413 | |

347 | |

305 | |

358 | |

154 | |

146 | |

239 |

The bond energy of double bonds is higher than that of similar single bonds but not necessarily twice as much. The following table compares the bond energies of a single carbon–carbon bond (), a double carbon–carbon bond (), and a triple carbon–carbon bond ().

The bond energy of 1 molecule can be used to determine the bond energy for one mole of molecules. The process for determining the bond energy of one mole of hydrogen bromide molecules is shown below.

The first step is to state that a single hydrogen bromide molecule has a bond energy value of J. The next step is to write the following equation:

This equation can then be used to produce the following conversion factors:

The first conversion factor can be used to determine the bond energy of one mole of molecules and the second conversion factor can be used to determine the bond energy of a single molecule.

The first conversion factor can then be used to determine the bond energy of one mole of hydrogen bromide molecules:

Rounding this value to two decimal places gives

Molar bond energies are usually expressed with kilojoule per mole units. We therefore need to convert from joule per mole to kilojoule per mole using the following conversion:

Therefore, the bond energy for hydrogen bromide is 370 kJ/mol.

From knowing the energy required to break the bond in a single molecule of hydrogen bromide, we have determined the bond energy required to break the hydrogen–bromine bond in a mole of hydrogen bromide molecules.

### Example 1: Converting between Energy per Molecule and Energy per Mole Units

Every molecule of iodine () has an iodine–iodine bond, . The energy required to break one of these bonds is J. How much energy is required to break 1.00 mole of these bonds?

- J
- J
- J
- J
- J

### Answer

The energy required to break the bond in one molecule is J. We need to calculate the energy required to break 1.00 mole of molecules. This is equivalent to molecules of iodine ().

The solution can be set out in different ways. We can say and

Then, we can solve for :

The “molecule(s)” can be canceled out to leave us with the following answer:

This is the energy that is needed to break 1.00 mole of iodine molecules.

Another way to set out the problem is to multiply the value given to us by the unit conversion factor for the number of molecules in 1 mole:

We can then cancel out the “molecule(s)” to leave us with the following answer:

Again, this shows that J of energy is required to break 1.00 mole of iodine molecules.

Both approaches suggest that option C is the correct answer for this question.

A molar bond energy value can similarly be multiplied by a conversion factor to determine the energy of a single chemical bond. The following set of calculations shows how a conversion factor can be used to determine how much energy is required to break the hydrogen–hydrogen bond in a single molecule of hydrogen gas ().

The molar bond energy of hydrogen gas molecules is known to be 436 kilojoules per mole. This means that molecules of hydrogen () have a net energy value of 436 kJ. We can use this information to construct the following mathematical equation:

The right-hand side of the mathematical equation would give us the energy per molecule, but the energy would be shown with kilojoule per molecule units. We need to multiply the right-hand side term by another conversion factor if we want the energy term to have the joule per molecule unit:

The action of canceling the kilojoule terms and multiplying all the numbers together gives us a value of . Each chemical bond in hydrogen molecules has an energy of J.

### Example 2: Converting between Energy per Mole and Energy per Molecule

The molar bond energy of is 159 kJ/mol. Calculate the energy of one bond.

- J
- J
- J
- J
- J

### Answer

We are given the molar bond energy of . This is the bond energy for one mole of fluorine () molecules or molecules of . We can use a conversion factor to determine the bond energy of one fluorine molecule:

The right-hand side of this equation would give us the bond energy of one fluorine molecule, but the energy would be in kilojoules rather than in joules. The right-hand side expression can be multiplied by another conversion factor to determine the associated joule energy value:

From this calculation, we can conclude that the energy for a single bond is J, and so option A is the correct answer.

### Example 3: Converting between Energy per Molecule and Energy per Mole Units

Which of the following quantities of bonds requires the most energy to break?

### Answer

The question asks us to determine which option requires the most energy to break the given quantity of bonds. The bond energy of each substance is given in parentheses after each answer. These values are the energies required to break the bonds in one mole of each substance. The answer options, however, give a specified number of moles of each substance. We need to calculate the total bond energy for the given number of moles of each substance as follows:

Then, we need to compare the values for A, B, C, D, and E to determine which one is biggest.

For answer option A, the total bond energy is calculated as follows:

This is the total energy required to break all the bonds in 1.7 mol of .

The same calculation can be done for the other answer options:

For answer option B,

For answer option C,

For answer option D,

For answer option E,

The largest value is 872 kJ, which means the most energy is required to break 2.0 mol of ; thus, the correct answer is D.

Another unit that can be used for energy is the calorie. Historically, one calorie is defined as the amount of energy that is needed to raise one gram of water by one degree of temperature. However, the calorie is now defined as being precisely 4.184 joules.

### Definition: Calorie

A calorie is the quantity of energy needed to raise the temperature of one gram of water by one degree Celsius. It is equivalent to 4.184 J exactly.

Joules can be converted into calories if they are divided by a value of 4.184, and calories can be converted into joules if they are multiplied by a value of 4.184.

The following conversion factors can also be used to convert between joules (J) and calories (cal):

One thousand calories can be defined as a kilocalorie (kcal). The calorie and kilocalorie unit relationship is expressed on the next line:

Note that in some textbooks and Internet sources and on some food packagings, the unit Cal is used, with an uppercase C. A Cal is equivalent to a kilocalorie, or 1 000 calories.

The following image shows the nutritional information label from a cereal box. The energy in each 30 g serving is expressed in two units, kilojoules and kilocalories.

The following calculation shows how the value in kilojoules is converted to the equivalent value in kilocalories in one step:

The unit conversion factors are chosen for the following reasons:

- The first unit conversion factor is used to introduce cal into the expression.
- The second conversion factor has a kJ in the denominator, and thus, kJ is eliminated from the expression. It also has J in the numerator, and this eliminates the J in the first conversion factor.
- The third conversion factor introduces kcal and eliminates cal.

### Example 4: Converting between Kilocalorie and Kilojoule Units

It is estimated that the average adult should consume around 2 000 kcal per day to maintain a healthy lifestyle. What is this value in units of kilojoules?

- 8.368 kJ
- 8 368 000 kJ
- 8 368 kJ
- 83.68 kJ
- 836.8 kJ

### Answer

To answer this question, we need to be able to convert from the unit kcal to the unit kJ. To do this conversion, several unit conversion factors, or relationships, are needed: and

First, kilocalories can be converted to a value in calories (cal) with the first unit conversion factor as follows:

The kcal unit terms cancel out to give the 2 000 000 cal answer. This value can then be converted to a value in joules if it is multiplied by a second conversion factor as follows:

This value in joules (J) can be converted to kilojoules (kJ) using another conversion factor:

These calculations suggest that option C is the correct answer for this question.

### Key Points

- Bond energy is the energy required to break a bond.
- Bond energies are often given in units of kilojoules per mole (kJ/mol) but can be converted to give the bond energy per molecule.
- Energy is usually expressed with either joule (J), kilojoule (kJ), calorie (cal), or kilocalorie (kcal) units.
- Joules and calories are related to each other according to the 4.184 J = 1 cal equation.
- Kilojoules and joules are related to each other according to the 1 kJ = 1 000 J equation.
- Kilocalories and calories are related to each other according to the 1 kcal = 1 000 cal equation.