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A person’s hand holding a cold pack on an ankle

A person’s hand holding a cold pack on an ankle (AndreyPopov, iStockPhoto)

STEM in Context

The Cold Pack: A Chilly Example of an Endothermic Reaction

Kelly Resmer

Summary

When you hurt your ankle, thermodynamics can help you heal! An endothermic reaction reduces the swelling by cooling your injury.

Has this ever happened to you? You are running in gym class and you twist your ankle. It hurts and starts to swell up. Your teacher grabs the first aid kit and pulls out an instant cold pack. After one good squeeze, the pack becomes really cold, almost instantly. What is happening? How do the chemicals make the pack cold so quickly? The answer can be found in thermodynamics! This is a branch of science that explores the transfer of energy. In thermodynamics, chemical reactions can be classified as either endothermic or exothermic

What are the two main types of thermodynamic reactions?

Exothermic reactions are reactions that release energy in the form of heat. You are probably familiar with many examples of these reactions. For example, burning gasoline in a car’s engine is an exothermic reaction. This particular type of exothermic reaction is known as a combustion reaction. A combustion reaction occurs when a compound, such as the hydrocarbons that make up fuel, react with oxygen to form a new product and produce heat. 

Endothermic reactions are the opposite of exothermic reactions. They absorb heat energy from their surroundings. This means that the surroundings of endothermic reactions are colder as a result of the reaction. Melting ice is an example of this type of reaction.

How do you know what type of thermodynamic reaction is happening?

One way to do this is by looking at the system and surroundings of a reaction. The system is where the reaction takes place, and the surroundings are the area around the system. 

To determine if a reaction is exothermic or endothermic, you could:

  1. measure the temperature change of the system or its surroundings, or
  2. calculate the energy of the system. 

Of these two methods, measuring the temperature change is easier. To do this, you simply measure the temperature of a reaction before and after it is completed. Since it can sometimes be difficult to measure the temperature within the system of a reaction, scientists often measure the temperature of the surroundings instead.

Diagrams showing the systems and surroundings for exothermic and endothermic reactions
Diagrams showing the systems and surroundings for exothermic and endothermic reactions (©2020 Let’s Talk Science).

It is possible to predict whether a reaction will be endothermic or exothermic by doing a little math. For this, it helps to know a bit about chemical reactions and chemical bonds.

There are two sides to any chemical reaction. On one side are the reactants. A reactant is the substance (or substances) that you start with. On the other side are the products. A product is the substance, or substances, that you end up with after the reaction happens. 

In a chemical reaction, the chemical bonds in the reactant molecules are broken. New bonds are formed in the product molecules. An example would be the combustion reaction between methane (CH4) oxygen (O2) (the reactants) that produces carbon dioxide (CO2) and water (H20) molecules (the products). Bonds are broken in the methane and oxygen molecules. Bonds are formed in the carbon dioxide and water molecules.

Combustion of methane showing where chemical bonds are broken and formed in the reactants and products
Combustion of methane showing where chemical bonds are broken and formed in the reactants and products (©2020 Let’s Talk Science).

What is important to know is that energy is needed to both make and to break bonds. To determine if a reaction is exothermic or endothermic, you have to compare the amount of energy needed to break the bonds of the reactants to the amount of energy released when new bonds are made. If the amount of energy released when the new bonds are formed in the products is greater, then it is an exothermic reaction. If the amount of energy needed to break the bonds of the reactants is greater, then it is an endothermic reaction. 

One way to show this is using an energy diagram. Energy diagrams show the energy levels of reactants and products in a reaction.

General energy diagrams for exothermic and endothermic reactions
General energy diagrams for exothermic and endothermic reactions (©2020 Let’s Talk Science).

You can see from the diagram above that the energy level of the products of an exothermic reaction is lower than the energy level of the reactants. The difference between the energy levels of reactants and products is called the enthalpy change (ΔH). In an exothermic reaction, the ΔH is NEGATIVE. In an endothermic reaction, the ΔH is POSITIVE.

Did you know?

Scientists can measure energy in foods by measuring how much heat the food releases when it is burned. They measure this using a tool called a bomb calorimeter.

It is possible to calculate ΔH without even doing an experiment! Scientists have determined experimentally the energies required to make and break specific molecular bonds. These energies are known as average bond energies.

Examples of Average Bond Energies
O=O 119 kcal/mol
C-H 99 kcal/mol
O-H 111 kcal/mol
C=O (in CO2) 192 kcal/mol

 

Using the methane combustion example again, the math works like this:

ΔH = [energy used in reactant bond breaking] - [energy released in product bond making]

= [ 4 C-H bonds + 2 O=O bonds] - [4 O-H bonds + 2 C=O bonds]

= [(4 x 99 kcal/mol) + (2 x 119 kcal/mol)] - [(4 x 111 kcal/mol) + (2 x 192 kcal/mol)]

= [396 + 238] - [444 + 384]

= 634 - 828

= - 194 kcal/mol

Since the enthalpy change is negative, we know that the reaction will be exothermic.

Energy diagram for methane combustion showing the bond energies and enthalpy change
Energy diagram for methane combustion showing the bond energies and enthalpy change (©2020 Let’s Talk Science).

How do thermodynamics work in a cold pack?

Now, let’s go back to our instant cold pack. An instant cold pack is the perfect example of an endothermic reaction. There are many possible ingredients in an instant cold pack, but they often contain solid ammonium nitrate and water. 

Did you know? 

Ammonium nitrate is a nitrate salt. It is heavily used in agriculture as a fertilizer. It is also used as an explosive in the mining industry.

The ammonium nitrate is stored in a sealed plastic bag that is surrounded by water. When you pop the bag, the ammonium nitrate comes into contact with water and dissolves

Chemical dissociation of solid ammonium nitrate in water to form aqueous ammonium and aqueous nitrate
Chemical dissociation of solid ammonium nitrate in water to form aqueous ammonium and aqueous nitrate (©2020 Let’s Talk Science). 

Dissolving an ionic compound, like table salt or ammonium nitrate, involves energy. Like other types of reactions, heat energy may be given off or taken in when the material dissolves. This energy is called the energy of solution and can be written as ΔHsoln

ΔHsoln = ∑ΔH [products] - ∑ΔH [reactants]

Rather than working out the ΔH for the reactants and products using bond energies, scientists often use pre-calculated values on Standard Enthalpy of Formation (ΔH°ftables. From such a table we learn that:

Enthalpy of Formation Table
ΔH°f kJ/mol
NH4+(aq) -132.8
NH4NO3(s) -365.1
NO3-(aq) -206.6

Let’s do the math to calculate the energy of solution

ΔHsoln = ∑ΔH [products] - ∑ΔH [reactants]

= [ mol (NH4+(aq)) + mol (NO3-(aq)) ] - [ mol (NH4NO3(s)) ]

= [ (1 mol)(-132.8 kJ/mol) + (1 mol)(-206.6 kJ/mol) ] - [ (1 mol)(-365.1 kJ/mol) ]

= - 339.4 + 365.1

= 25.7 kJ

Remember at the beginning we said that if ΔH is NEGATIVE the reaction is exothermic and that if ΔH is POSITIVE the reaction is endothermic? Well, that also applies to energy of solution problems. Since we calculated that the ΔHsoln was positive (25.7 kJ), the reaction must be endothermic. We know this to be true because the cold pack made its surroundings very cold!

The chemistry of cold packs (2014) by John Pollard (TED-Ed) (4:31 min).

Summing up...

Exothermic and endothermic reactions are important for our chemical world. These reactions can help keep us warm by giving off energy (exothermic) or help cool us down by taking in energy (endothermic).

Starting Points

Connecting and Relating
  • Have you ever used an instant cold pack? What did you use it for? How long did it take to cool?
  • Have you ever seen or used an item, other than an instant cold pack, that involves an endothermic or exothermic reaction? What was it?
Connecting and Relating
  • Have you ever used an instant cold pack? What did you use it for? How long did it take to cool?
  • Have you ever seen or used an item, other than an instant cold pack, that involves an endothermic or exothermic reaction? What was it?
Relating Science and Technology to Society and the Environment
  • Why were instant cold packs originally developed? What are the advantages and disadvantages of the instant ice pack? 
  • Are instant cold packs environmentally-friendly? What alternatives could be used?
Relating Science and Technology to Society and the Environment
  • Why were instant cold packs originally developed? What are the advantages and disadvantages of the instant ice pack? 
  • Are instant cold packs environmentally-friendly? What alternatives could be used?
Exploring Concepts
  • Name two other endothermic and exothermic reactions not described in this article.
  • Why is the ΔH negative in an exothermic reaction?
  • What chemical elements are found in water? Ammonium nitrate?
  • How does cold help treat injuries such as sprained ankles?
Exploring Concepts
  • Name two other endothermic and exothermic reactions not described in this article.
  • Why is the ΔH negative in an exothermic reaction?
  • What chemical elements are found in water? Ammonium nitrate?
  • How does cold help treat injuries such as sprained ankles?
Media Literacy
  • Commercials for cold packs make it seem like they treat and heal all injuries. Do you find them to be misleading? Explain.
Media Literacy
  • Commercials for cold packs make it seem like they treat and heal all injuries. Do you find them to be misleading? Explain.
Teaching Suggestions
  • This article and embedded videos can be used for supporting teaching and learning in chemistry. The concepts introduced include endothermic and exothermic reactions and enthalpy.
  • After reading the article and viewing the videos, students could complete a Concept Definition Web for the two types of reactions discussed in the resources, endothermic and exothermic. Ready-to-use Concept Definition Web reproducibles are available [Google doc] and [PDF] formats. 
  • Teachers could also have students explore exothermic and endothermic reactions by doing the following hands-on science investigations:
Teaching Suggestions
  • This article and embedded videos can be used for supporting teaching and learning in chemistry. The concepts introduced include endothermic and exothermic reactions and enthalpy.
  • After reading the article and viewing the videos, students could complete a Concept Definition Web for the two types of reactions discussed in the resources, endothermic and exothermic. Ready-to-use Concept Definition Web reproducibles are available [Google doc] and [PDF] formats. 
  • Teachers could also have students explore exothermic and endothermic reactions by doing the following hands-on science investigations:

Learn more

Science: Energy Changes and Reversible Reactions (2014)

Very handy set of pages by the BBC for students at the end of high school including slideshows and a quiz to test your knowledge.

What is Thermodynamics? (2014)

This set of slides from the National Aeronautics and Space Administration (NASA) explains the “zeroth” through second laws of thermodynamics.

What is an Exothermic Reaction?

This Scientific American article includes explanations of the exothermic chemical reactions taking place when a fire burns and when a rocket takes off.

Endothermic vs. exothermic reactions

This page from Khan Academy explains the differences between endothermic and exothermic reactions.

References

American Chemical Society. (2019). Exothermic, endothermic, & chemical change.

Flinn Scientific. (2017). Making an instant cold pack.

Khan Academy. (n.d.). Endothermic vs. exothermic reactions.

Pharma Engineering. (2017). Bond energy calculations.