Thermochemistry of Hand Warmers in Everyday Life

This Exemplar will teach the following concepts from the ACS Examinations Institute General Chemistry ACCM: 

VI. Energy and Thermodynamics: Energy is the key currency of chemical reactions in molecular-scale systems as well as macroscopic systems. 

A. Most chemical changes are accompanied by a net change of energy of the system. 

2. Energy changes can be considered in terms of heat and work. 

3. There are a wide variety of energy units, so care must be taken to use consistent units when considering energy changes quantitatively. 

 

C. The type of energy associated with chemical change may be heat, light, or electrical energy. 

1. Heat exchange is measured via temperature change.  

a. Heat flow into the system is defined as endothermic; heat flow out of the system is defined as exothermic.  

b. Heat flow is quantitatively obtained from ∆T via molar heat capacity or specific heat and the mass of the substance involved.  

c. By convention, numerical estimates of exothermic processes carry a negative sign, while endothermic processes carry a positive sign.  

d. When observed in the laboratory, exothermic processes will show warming (heat evolved), while endothermic processes will show cooling (heat absorbed).

 

Thermochemistry of Hand Warmers 

Whether you are a winter sports enthusiast, live in a place with freezing temperatures, or are simply afraid of the cold, hand warmers have probably helped you stay warm at some point in your life. But have you ever wondered how these little pouches are able to emit heat? Well, the chemistry behind hand warmers is actually just a straightforward exothermic reaction^[1], demonstrating how even the most basic chemistry concepts can be applied to make important impacts on our everyday lives.  

 

[2]

 

A typical disposable hand warmer found in stores contains a mixture of iron powder, activated carbon, salt, and an absorbent material, such as a silicon-based mineral called vermiculite.^[1] The salt and the absorbent material help the reaction occur, with the salt acting as a catalyst and the absorbent material retaining moisture to help the reaction continue to progress. Meanwhile, the activated carbon serves to disperse the heat evenly within the hand warmer.^[3] The main component of the hand warmer that we will be focusing on is the iron, since it is the primary contributor to the reaction that produces the heat.  

 [4]

When the packaging of a disposable hand warmer is opened, the iron powder in the hand warmer comes into contact with the air, which contains oxygen. Iron and oxygen react to form iron(III) oxide in the following reaction^[1]: \[2Fe(s) + \frac{3}{2}O_{2}(g) \to Fe_{2}O_{3}(s)\]

When this reaction occurs, energy is released into the surroundings in the form of heat, known as the heat of formation. The heat of formation describes the energy that is released when a compound (iron oxide in this example) is made from its constituent elements (solid iron and oxygen gas) in a chemical reaction.^[5]

Note

Iron(III) oxide is colloquially known as “rust”. A hand warmer is essentially forming rust inside the pouch.^[1]

 

The heat of formation of a compound can be determined experimentally; it can also be calculated with sufficient information about the heats of formation of other substances in the reaction. The example below shows a typical problem on calculating the heat of formation of a compound.  

Example \(\PageIndex{1}\)

Fe₂O_3(s) can be formed from FeO_(s) and O_2(g) with ΔH˚ = -280 kJ/mol. Calculate the heat of formation of FeO_(s) given that ΔH˚_f = -824.2 kJ/mol for Fe₂O_3(s). 

Solution

Using correct molar ratios, we obtain the following equation for the reaction: \[2FeO(s) + \frac{1}{2}O_{2}(g) \to Fe_{2}O_{3}(s)\]

The standard enthalpy of a reaction is given by the following equation: \[\Delta H_{reaction}^{o} = \sum \Delta H_{f}^{o}(products) - \sum \Delta H_{f}^{o}(reactants)\]

Since we are given the heat of formation of Fe₂O₃(s) and the ΔH˚ of the reaction, we only need the heat of formation of O₂(g) to obtain heat of formation of FeO(s). Conveniently, the heat of formation of O₂(g) is 0 as oxygen is naturally diatomic and gaseous. Therefore, we can easily calculate the heat of formation of FeO(s) with the correct molar ratios.

\[-280\; kJ/mol = -824\; kJ/mol - \left ( 2\Delta H_{f}^{o}\;FeO(s) + \frac{1}{2}(0) \right )\]

\[\Delta H_{f}^{o}\;FeO(s) = -272 kJ/mol\]

The heat of formation of FeO(s) is therefore -272 kJ/mol. 

 

Previously, we mentioned that the heat of formation of a compound can also be determined experimentally. In fact, for most chemical reactions, not just this particular one, the amount of energy released to or absorbed from its surroundings, known as change in enthalpy, can be measured through a process called calorimetry.

Using a calorimeter, a device with a closed system that can measure energy change, usually through temperature, we can determine how much energy is released or absorbed when a reaction occurs. For example, we can place iron in an oxygen tank and measure the increase in temperature at the end of the reaction. Using the measured change in temperature, we can then solve for the change in energy, or heat, with the following equation: \[q=mc\Delta T\]

where q = heat, c = specific heat, m = mass, and ΔT = change in temperature.

 

Through experiments similar to the one described above, the heat of formation of iron oxide has been determined to be –824 kJ/mol, with the negative sign denoting that 824 kJ of energy is released (as opposed to absorbed, denoted by a positive sign) to the surroundings for every mole of iron oxide that is formed. Since the change in enthalpy is negative, indicating that energy is released, the reaction is described as exothermic. If the reaction instead absorbed energy from its surroundings, resulting in a positive change in enthalpy, the reaction would be considered endothermic.  

Note

In the equation, we see “specific heat” represented by the letter ‘c’. This is a value that changes depending on the quantity of heat required raise the temperature of one gram of the surrounding substance by one degree Celsius (Unit: J*g^-1*°C^-1).^[6]

 

Using the handy equation above, we can also calculate the amount of substance reacted, the change in temperature, the initial/final temperature, or the specific heat capacity, depending on the information that is available. In the example below, we will calculate the final temperature after the occurrence of a reaction equivalent to the one that occurs in hand warmers.

Example \(\PageIndex{1}\)

A 75.0 g hand warmer filled 25% by mass with iron powder is placed in a 10.00 liter oxygen tank under 136.0 atm and at 298 K. Given that the heat of formation of iron (III) oxide is -824 kJ/mol, calculate the resulting temperature of the oxygen after all the iron powder has been oxidized. Specific heat of oxygen is 0.92 J/(g*K). 

Solution

The reaction between iron powder in the hand warmer with oxygen from the air can be described with this equation: \[2Fe(s) + \frac{3}{2}O_{2}(g) \to Fe_{2}O_{3}(s)\;\;\;\Delta H_{f}^{o}\;=\;-824\;kJ/mol\]

Using stoichiometric calculations, we can determine the number moles of Fe(s) present: \[\left ( 75.0g \right )\left ( \frac{0.25g\;Fe(s)}{1g} \right )\left ( \frac{1\;mol\;Fe(s)}{55.845g} \right )=0.336\;mol\;Fe(s)\]

Then using the ideal gas law, PV = nRT, with R = 0.0821, we can find number of moles n of O₂(g) present in the tank: \[\left ( 136.0\;atm \right )\left ( 10.0\;L \right )=n\left ( 0.0821\frac{atm*L}{mol*K} \right )\left ( 298K \right )\]

\[n=55.59\;moles\;of\;O_{2}(g)\;in\;tank\]

The limiting and excess reactant is determined to be Fe(s) with the following calculation with their molar ratios in the reaction: \[0.336\;mol\;Fe(s)\;\left ( \frac{1\;mol\;rxn}{2\;mol\;Fe(s)\ } \right )=0.168\;mol\;rxn\]

\[55.59\;mol\;O_{2}(g)\left ( \frac{1\;mol\;rxn}{3/2\;mol\;O_{2}(g)} \right )=37.06\;mol\;rxn\;(excess)\]

With Fe(s) being the limiting reactant, we can thus calculate the moles of Fe₂O₃(s) produced. Multiplying this amount by the negative of the heat of formation results in the amount of heat released.   

\[0.168\;moles\;Fe(s)\left ( \frac{1\;Fe_{2}O_{3}(s)}{1\;mol\;Fe(s)} \right )=0.168\;mol\;Fe_{2}O_{3}(s)\]

\[0.168\;Fe_{2}O_{3}(s) \left ( \frac{824\;kJ\;released}{1\;Fe_{2}O_{3}(s) } \right )=138\;kJ\;released\]

After we obtain the total heat released by the hand warmer, we can use the calorimetry equation q = mCΔT to determine the temperature change. q in this case would be the 138kJ that was released into the surroundings. The mass of oxygen gas can be obtained with the number of moles of oxygen. Both specific heat and initial temperature are given. And thus, we get:  

\[q=mC\left ( T_{f}-T_{i} \right )\]

\[55.59\;mol\;O_{2}\left ( \frac{31.999g}{1\;mol\;O_{2}} \right )=1778.8g\;of\;O_{2}(g)\]

\[138\;kJ\left ( \frac{1000J}{1\;kJ} \right )=\left ( 1778.8g \right )\left ( 0.92\frac{J}{g*K} \right )\left ( T_{f}-298K \right )\]

\[T_{f}=382\;K\]

The final temperature inside the gas tank is 382 K. 

Notice that 382 K is a very high temperature; we certainly don’t want to be touching a hand warmer this hot! (Companies also don’t want to make hand warmers that end up creating more lawsuits than profits). Therefore, typical hand warmers contain much less iron inside the pouch, and the material of the pouch itself also limits the amount of oxygen that the iron can come in contact with, thereby producing a temperature that is just comfortably warm for a wintry day. 

 

References

(1) Wang, L. hand warmers. Chemical & Engineering News 2010, 88 (4), 36. DOI: http://doi.org/10.1021/cen-v088n004.p036. 

(2) Almaty, V. Person Wearing Blue Winter Jacket Carrying Snowboard Under Sunny Sky. 2016. https://www.pexels.com/photo/person-wearing-blue-winter-jacket-carrying-snowboard-under-sunny-sky-848612/ 

(3) Sands, W.; Kimmel, W.; Wurtz, B.; Stone, M.; McNeal, J. Comparison of Commercially Available Disposable Chemical Hand and Foot Warmers. Wilderness & Environmental Medicine Wilderness & Environmental Medicine 2009, 20 (1), 33-38. DOI: https://doi.org/10.1580/08-WEME-OR-243.1. 

(4) Mann, P.B. A pair of air-activated disposable hand warmers, US quarter for scale. 2006. https://en.wikipedia.org/wiki/Hand_warmer#/media/File:Handwarmers.JPG 

(5) Britannica, T. E. o. E. heat of formation. In Encyclopedia Britannica, 2020. 

(6) Britannica, T. E. o. E. specific heat. In Encyclopedia Britannica, 2021.