 # Energy Unit Conversions Chemistry Tutorial

## Key Concepts

• The SI unit for energy is the joule(1).
• The joule has been given the symbol J(2)
• Most common energy unit conversion is between joules (J) and kilojoules (kJ):
There are 1000 J in 1 kJ

so 1000 J = 1 kJ

How to convert initial unit to final unit
initial unit conversion final unit
joules (J) ÷ 1000 = kilojoules (kJ)
kilojoules (kJ) × 1000 = joules (J)

• The calorie(3) is a non SI unit of measurement for energy(4).
• 1 calorie ≈ 4.18 joules(5)

1 cal ≈ 4.18 J

How to convert initial unit to final unit
initial unit conversion final unit
calories (cal) × 4.18 = joules (J)
joules (J) ÷ 4.18 = calories (cal)

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## SI and Metric Units of Energy

The SI unit of energy is the joule (J).
1 J is actually quite a small amount of energy.
We need only 4.18 J of energy to increase the temperature of 1 gram of liquid water by 1°C(6)
If you want to boil 500 g of water to make a cup of tea, you will need 500 × 4.18 = 2090 J of energy just to increase its tempertaure by 1°C.
If the temperature of the water you put in the kettle is 25°C you need to raise the temperature by 75°C to get it to the boiling point of water at 100°C.(7)
The amount of energy to do this will by 75 × 2090 J = 156,750 J

The energy involved in most of the chemical reactions you will meet in your chemistry course is of the order of thousands of joules of energy per gram of reactant.
The prefix "kilo" is used to refer to a multiplication by 1000
This means that 1 kilojoule = 1000 × 1 joules = 1000 joules
The prefix "kilo" is given the symbol k, so 1 kilojoule = 1 kJ
1000 J = 1 kJ

If divide both sides of this equation by 1000 we can find out how many kilojoules are in 1 J:
1000 J ÷ 1000 = 1 kJ ÷ 1000
1 J = 0.001 kJ = 1 × 10-3 kJ

So, if it takes 156,750 J of energy to raise the temperature of water in my kettle to its boiling point, this is equivalent to:
156,750 × 1 J = 156,750 × 10-3 kJ = 156.75 kJ

Chemists commonly use kilojoules (kJ) as the unit of measurement when talking about the energy involved in chemical reactions in the laboratory.
But, if you are using chemical reactions like the burning of coal, or nuclear fission reactions, to generate electricity in a power station, you need to use a much, much, bigger unit of energy like megajoules (MJ) or gigajoules (GJ) to express the total amount of energy being produced.
1 megajoule is 1 million joules: 1 MJ = 1,000,000 J = 106 J
1 gigajoule is 1 billion joules: 1 GJ = 1,000,000,000 J = 109 J

The table below lists the common metric prefixes, symbols, and their multiplication factor given in scientific notation:

 factors prefix symbol larger → → → → → → → → → → smaller 1012 109 106 103 102 101 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18 tera giga mega kilo hecto deca deci centi milli micro nano pico femto atto T G M k h da d c m µ n p f a

Using this table we find that:

 1 kilojoule (1 kJ) = 103 joules (1000 J) 1 joule (1 J) = 1 ÷ 103 kilojoules = 0.001 kJ 1 millijoule (1 mJ) = 10-3 joules (0.001 J) 1 joule (1 J) = 1 ÷ 10-3 millijoules = 1,000 mJ 1 microjoule (1 µJ) = 10-6 joules (0.000001 J) 1 joule (1 J) = 1 ÷ 10-6 microjoules = 106 µJ

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## Converting One Metric Unit of Energy into A Different Metric Unit of Energy

The most likely conversions you will have to make during your chemistry course will be between joules (J) and kilojoules (kJ)

1. To convert kilojoules (kJ) to joules (J):

multiply the number of kilojoules (kJ) by 1000 to give an energy value in units of joules (J)

energy (J) = energy (kJ) × 1000

2. To convert joules (J) to kilojoules (kJ):

divide the number of joules (J) by 1000 to give an energy value in kilojoules (kJ)

energy (kJ) = energy (J) ÷ 1000

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## Worked Examples of Converting Joules to Kilojoules, and, Kilojoules to Joules

Question 1: Convert 1 kilojoule to joules

Solution:

From the table above we see that kilo = 103 = 1,000

1 kJ = 103 J = 1,000 J

1 kilojoule = 1,000 joules

Question 2: Convert 2.5 kJ to joules

Solution:

From the table above we see that kilo = 103 = 1,000

1 kJ = 1,000 J

Multiply both sides of equation by 2.5:

2.5 × 1 kJ = 2.5 × 1,000 J

2.5 kJ = 2,500 J

Which we can express in scientific notation as:

2,500 J = 2.5 × 103 J

Question 3: Convert 5 millijoules to joules

Solution:

From the table above we see that milli = 10-3

1 mJ = 10-3 J

Multiply both sides of the equation by 5:

5 × 1 mJ = 5 × 10-3 J = 0.005 J

5 mJ = 0.005 J

Question 4: Convert 250 J to kilojoules

Solution:

From the table above we see that:

103 J = 1 kJ

Divide both sides of the equation by 1000 to find the number of kilojoules in 1 joule:

103 J ÷ 103 = 1 kJ ÷ 103

1 J = 10-3 kJ = 0.001 kJ

Multiply both sides of the equation by 250:

250 × 1 J = 250 × 0.001 kJ

250 J = 0.250 kJ

Question 5: Convert 25 µJ to kilojoules

Solution:

From the table above we see tha µ = 10-6

1 µJ = 10-6 J

Multiply both sides of this equation by 25 to determine the number of joules in 25 µJ :

25 × 1 µJ = 25 × 10-6 J

25 µJ = 2.5 × 10-5 J

Convert 2.5 × 10-5 J to kilojoules:

From the table above we see that:

1 kJ = 103 J

Divide both sides of this equation by 103:

1 kJ ÷ 103 = 1 J ÷ 103

10-3 kJ = 1 J

Multiply both sides of the equation by 2.5 × 10-5 to find the number of kJ in 2.5 × 10-5 J

(2.5 × 10-5) × 10-3 kJ = (2.5 × 10-5) × 1 J

2.5 × 10-8 kJ = 2.5 × 10-5 J

State the answer to the question:

25 µJ = 2.5 × 10-8 kJ

Quick Question

Question 1.

Convert 0.343 kJ to J

0.343 kJ = J     Check

## Converting Between Non-metric Units of Energy and Metric Units of Energy

A calorie is non-metric unit of energy. It is a larger measure of energy than the SI unit of energy, joule.

• 1 calorie ≈ 4.18 joules

1 kilocalorie ≈ 4.18 kilojoules

1 kilocalorie ≈ 1000 × 4.18 joules = 4180 joules

• 1 joule ≈ 1 calorie ÷ 4.18 = 0.239 calories

1 kilojoule ≈ 1 kilocalorie ÷ 4.18 = 0.239 kilocalories

1 kilojoule ≈ 1000 × 0.239 calories = 239 calories

The most likley conversions you will need to make are between joules (J) and calories (cal)

1. To convert energy in calories (cal) to energy in joules (J):

multiply the energy in calories (cal) by 4.18 to give an energy value in joules (J)

energy (J) = 4.18 × energy (cal)

2. To convert energy in joules (J) to energy in calories (cal):

divide the energy in joules (J) by 4.18 to give an energy value in calories (cal)

energy (cal) = energy (J) ÷ 4.18

Alternative method to convert energy in joules (J) to energy in calories (cal)

multiply the energy in joules (J) by 0.239 ( since 1 ÷ 4.18 = 0.239) to give energy in calories (cal)

energy (cal) = energy (J) × 0.239

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## Worked Examples of Converting Calories to Joules, and, Joules to Calories

Question 1: Convert 100 calories to joules

Solution:

1 calorie = 4.18 joules

multiply both sides of the equation by 100:

100 × 1 calorie = 100 × 4.18 J

100 cal = 418 J

Question 2: Convert 12.0 kilocalories to kilojoules

Solution:

1 kilocalorie = 4.18 kilojoules

multiply both sides of the equation by 12.0

12.0 × 1 kilocalorie = 12.0 × 4.18 kJ

12.0 kcal = 50.2 kJ

Question 3: Convert 150 kilocalories to joules

Solution:

Calculate the number of kilojoules in 150 kilocalories:

1 kilocalorie = 4.18 kilojoules

multiply both sides of the equation by 150

150 × 1 kilocalorie = 150 × 4.18 kJ

150 kcal = 627 kJ

Calculate the number of joules in 622 kJ

1 kilojoule = 1000 joules

multiply both sides of the equation by 622

627 × 1 kJ = 627 × 1000 J

627 kJ = 627 000 J

Write the answer to the question:

150 kcal = 627,000 J

Question 4: Convert 10 joules to calories

Solution:

1 joule = 0.239 calories

multiply both sides of the equation by 10

10 × 1 J = 10 × 0.239 cal

10 J = 2.39 cal

Question 5: Convert 1.2 kilojoules to kilocalories

Solution:

1 kilojoule = 0.239 kilocalories

multiply both sides of the equation by 1.2

1.2 × 1 kJ = 1.2 × 0.239 kcal

1.2 kJ = 0.287 kcal

Question 6: Convert 1500 joules to kilocalories

Solution:

Calculate the number of calories in 1500 joules

1 joule = 0.239 calories

multiply both sides of the equation by 1500

1500 × 1 J = 1500 × 0.239 cal

1500 J = 359 calories

Calculate the number of kilocalories in 539 calories

1000 calories = 1 kilocalorie

Divide both sides of the equation by 1000

1000 calories ÷ 1000 = 1 kilocalorie ÷ 1000

1 calorie = 0.001 kilocalories

multiply both sides of the equation by 539

359 × 1 calorie = 359 × 0.001 kilocalories

359 calories = 0.359 kilocalories

1500 J = 0.359 kcal

Quick Question

Question 1.

Convert 12.5 J to cal

12.5 J = cal     Check

(1) The Ninth International Conference on Weights and Measures (1948) recommended the use of the joule (volt coulomb) as the unit of heat.
The joule is a derived SI unit for the measurement of energy.
The SI base unit for the measurement of energy is kg.m2 s-2

1 J = 1 kg.m2 s-2

(2) The joule is named after the English physicist James Prescott Joule.

(3) The calorie, from the Latin calor meaning heat, was first defined by Nicolas Clément in 1824 as a unit of heat.

(4) Other units for measuring energy are:

• erg (1 J = 107 ergs)

• British Thermal Units, BTU (1 J = 9.48 × 10-4 BTU)

• electronvolts, eV (1 J = 6.24 × 1018 eV)

• kilowatt hours, kWh (1 J = 2.78 × 10-7 kWh)

(5) National Bureau of Standards defined a calorie as equal to exactly 4.1840 J
You will find this approximated to 1 cal = 4.18 J, even 1 cal = 4.2 J, when used in schools.
Note that this will effect the number of significant figures that you will be able to use in your calculations.

(6) The calorie, another unit of energy was defined as the amount of energy required to raise the temperature of 1 gram of liquid water at 1 atmosphere pressure by 1 °C.
1 calorie = 4.18 joules
So it requires 4.18 joules of energy to raise the temperature of 1 gram of liquid water at 1 atmosphere pressure by 1 °C.