# Сold and Hot Packs - Formal Essay Introduction

Hot and cold packs are used to treat injuries in the hospital to minor injuries at home. For example, cold packs are used to keep a patient’s body temperature down when they become deathly hot or to decrease inflammation in a sprained ankle. Hot packs can be used to reduce muscle spasms, muscle soreness, inflammation, and relieve pain. Since the demand for hot and cold packs is so great, companies like Dystan Medical Supply produce and sell cold and hot packs in large quantities. These packs are made by dissolving salts in water. When an ionic compound dissociates in water it either absorbs energy from the water or releases energy to the water. When the compound absorbs energy, it does so through heat energy. This is an endothermic process. An Exothermic process would be one in which energy is released to the surroundings. In this case hot packs are exothermic and cold packs are endothermic. In general a pack is created by using a plastic bag which has a compartment of water and a compartment of salt. The bag is broken and the two mix either absorbing or emitting heat. The amount of heat depends on the salt’s concentration in the water.1

In chemistry, calorimeters are constructed to find the enthalpy of reactants and calculate the heat evolved. At constant pressure the enthalpy is the heat gained or lost by a system. A calorimeter is a device that is a closed system. Therefore, no energy can enter the system, so any change in temperature is due to the substances within the calorimeter. For this experiment, water was the substance that is put into the calorimeter and then a salt was added and the initial and final temperatures were recorded. However, a calorimeter is not perfect; therefore it must first be calibrated by having a known amount of substance at a known temperature and adding the same amount of the same substance at a different temperature. In this manner you can find the heat capacity of the calorimeter, which is the amount of heat needed to raise its temperature by 1 degree Kelvin. Once the calibration is done the change in temperature can be recorded and the heat evolved or heat needed for the reaction (heat of reaction) can be determined if the specific heat of, in this case, water is known. Specific heat is the amount of heat required to raise one gram of a substance by one degree Celsius and heat evolved is moles times the molar heat of dissolution. Since the moles can be measured it would be possible to calculate the molar heat of dissolution, which is the change in heat when a solute is dissolved. A change in heat occurs because in dissociation the bonds between the ionic molecules are broken apart. In some cases more energy is needed to break apart these bonds than the amount of energy that is gained from the breaking of the bonds. This would mean the system would have to take energy from the surroundings and would be an endothermic reaction. In an exothermic reaction the energy gained from breaking the bonds is more than the energy needed to break them.

The purpose of this experiment was to determine which salts are most economical for the production of cold and hot packs and how much would each pack cost.1

Experimental section

Equipment used: analytical balance, calorimeter (two styofoam cups, thermometer, cardboard square), second thermometer, wax paper, and roughly 3 grams of ammonium nitrate, lithium chloride, calcium chloride, and potassium chloride.

To begin, a calorimeter was constructed by placing a styrofoam cup inside another one and placing a piece of cardboard with a thermometer tightly stuck through it over the top of the cups. 25 mL of water was placed in the top cup. 25 mL of water heated to 49.0 degrees Celsius measured with a different thermometer was placed in the calorimeter after the temperature of the water in the calorimeter was taken to be 28.0 degrees Celsius. The temperature of the calorimeter system was taken at 5 and 10 seconds and every 15 seconds for three minutes. A second trial was run by drying out the cups and starting over with new water. The temperature of the water in the calorimeter was 28.0 degrees Celsius and the temperature of the added water measured with a different thermometer was 49.0 degrees Celsius.

The cups were again dried and 25 mL of water was added to the top cup. 1.5005 grams of ammonium nitrate was weighed using an analytical balance and transferred, using wax paper, to the calorimeter after recording the temperature of the water to be 27.0 degrees Celsius. The temperature was recorded at the same times as before while swirling the calorimeter between recordings. The cups were dried and a second trial was run with 1.5005 grams of ammonium nitrate and the water was recorded at 16.5 degrees Celsius.

This process was repeated for calcium chlorate where trial one had 1.5030 grams of calcium chlorate and the water temperature was 26.5 degrees Celsius and trial two had 1.5025 grams of calcium chlorate and the water temperature was 27.0 degrees Celsius

Two trials were also run with lithium chloride as the salt. In trial one 1.5025 grams of lithium chloride was used and the water temperature was 16.5 degrees Celsius. In trial two 1.4992 grams of lithium chloride was used and the water temperature was 26.5 degrees Celsius.

A final trial with potassium chloride was run. 1.5005 grams of potassium chloride was used in trial one where the water temperature was 26.5 degrees Celsius. In Trial two 1.5020 grams of potassium chloride was used with water at 27.0 degrees Celsius.

There were no deviations from the procedures in the lab manual.

Results and Discussion
The most economical salt for a cold pack would be the ammonium nitrate. Calcium chloride would be the most economical salt to use for a hot pack. Using these salts hot and cold packs could be manufactured without exceeding the 5 dollar cost limit.

water 1 water 2 Ammon. Nitrate 1 Ammon. Nitrate 2 Calcium Chlor. 1 Calcium Chlor. 2 Lithium chlor. 1 Lithium chlor. 2 Potassium chlor. 1 Potassium chlor. 2
S ⁰C ⁰C ⁰C ⁰C ⁰C ⁰C ⁰C ⁰C ⁰C ⁰C
5 32.0 0.5 24.5 25.0 26.5 28.0 32.0 31.0 25.5 25.5
10 34.0 34.5 23.0 23.5 27.5 29.0 34.5 33.5 24.8 25.0
15 36.0 36.5 22.8 23.0 29.0 30.0 37.0 36.0 24.0 24.0
30 36.0 36.5 22.5 22.8 30.5 31.5 38.0 37.0 23.8 23.8
45 36.0 36.5 22.5 22.5 33.0 32.5 37.5 37.0 23.8 23.8
60 36.0 36.5 22.5 22.5 33.5 33.0 37.0 36.5 23.8 23.8
75 36.0 36.0 22.8 22.8 33.5 33.0 36.8 36.5 23.8 23.8
90 35.8 36.0 22.8 22.8 33.8 33.2 36.5 36.2 23.8 23.8
105 35.8 36.0 22.8 22.8 33.8 33.2 36.5 36.0 23.8 23.8
120 35.8 36.0 22.8 22.8 33.8 33.2 36.2 36.0 23.8 23.8
135 35.8 36.0 22.8 22.8 33.5 33.0 36.0 36.0 23.8 23.8
150 35.8 36.0 22.8 22.8 33.5 33.0 36.0 36.0 23.8 23.8
165 35.8 36.0 22.8 22.8 33.5 33.0 36.0 36.0 23.8 23.8
180 35.8 36.0 22.8 22.8 33.5 33.0 36.0 36.0 23.8 23.8
Overview of data for graphs

From the data in the previous tables and graphs it was determined that ammonium nitrate and potassium chloride absorb heat energy, making the water “colder” and calcium chloride and lithium chloride release heat, making the water “warmer.”

Table 1 – Calibration
Trial 1 Trial 2
Initial temp. Of cal. (⁰C) 28.0 Initial temp. Of cal. (⁰C) 28.0
Initial temp. cold H₂O (⁰C) 28.0 Initial temp. cold H₂O (⁰C) 28.0
Initial mass cold H₂O (g) 25.0 Initial mass cold H₂O (g) 25.0
Initial temp. hot H₂O (⁰C) 49.0 Initial temp. hot H₂O (⁰C) 49.0
Initial mass hot H₂O (g) 25.0 Initial mass hot H₂O (g) 25.0
Temp. H₂O after mixing (⁰C) 35.8 Temp. H₂O after mixing (⁰C) 36.0
∆T(cold H₂O) (⁰C) 7.8 ∆T(cold H₂O) (⁰C) 8.0
∆T(hot H₂O) (⁰C) (-)13.2 ∆T(hot H₂O) (⁰C) (-)13.0
∆T(cal.) (⁰C) 7.8 ∆T(cal.) (⁰C) 8.0
Heat cap. Of cal. (J/K) 72.4 Heat cap. Of cal. (J/K) 65.4

Mean heat cap. Of cal. (J/K) 68.9

Table 2 – Ammonium Nitrate
Trial 1 Trial 2
NH₄NO₃ + H₂O →
Mass of Water (g) 25.0 Mass of Water (g) 25.0
Mass of NH₄NO₃ (g) 1.5005 Mass of NH₄NO₃ (g) 1.5005
Initail temp. Water (⁰C) 27.0 Initail temp. Water (⁰C) 26.5
Initail temp. NH₄NO₃ (⁰C) 27.0 Initail temp. NH₄NO₃ (⁰C) 26.5
average initial temp. (⁰C) 27.0 average initial temp. (⁰C) 26.5
Final Temp. (⁰C) 22.8 Final Temp. (⁰C) 22.8
∆T (⁰C) (-4.2) ∆T (⁰C) (-3.7)
solution mass (g) 26.5005 solution mass (g) 26.5005
heat evolved (⁰C) 4.2 heat evolved (⁰C) 3.7
moles of solute (mol) 0.01874 moles of solute (mol) 0.01874
molar heat of dissolution (kJ/mol) 39 molar heat of dissolution (kJ/mol) 34

Average (kJ/mol) 36.5

Table 3 – Calcium Chloride
Trial 1 Trial 2
CaCl₂ + H₂O → Ca²⁺ + 2Cl⁻ + H₂O CaCl₂ + H₂O → Ca²⁺ + 2Cl⁻ + H₂O
Mass of Water (g) 25.0 Mass of Water (g) 25.0
Mass of CaCl₂ (g) 1.5030 Mass of CaCl₂ (g) 1.5025
Initail temp. Water (⁰C) 26.5 Initail temp. Water (⁰C) 27.0
Initail temp. CaCl₂ (⁰C) 26.5 Initail temp. CaCl₂ (⁰C) 27.0
average initial temp. (⁰C) 26.5 average initial temp. (⁰C) 27.0
Final Temp. (⁰C) 33.5 Final Temp. (⁰C) 33.0
∆T (⁰C) 7.0 ∆T (⁰C) 6.0
solution mass (g) 26.5030 solution mass (g) 26.5025
heat evolved (⁰C) (-7.0) heat evolved (⁰C) (-6.0)
moles of solute (mol) .013543 moles of solute (mol) .013538
molar heat of dissolution (kJ/mol) -89 molar heat of dissolution (kJ/mol) -74

Average (kJ/mol) -81.5

Table 4 – Lithium Chloride
Trial 1 Trial 2
LiCl + H₂O → Li⁺ + Cl⁻ + H₂O⁺ LiCl + H₂O → Li⁺ + Cl⁻ + H₂O⁺
Mass of Water (g) 25.0 Mass of Water (g) 25.0
Mass of LiCl (g) 1.5025 Mass of LiCl (g) 1.4992
Initail temp. Water (⁰C) 26.5 Initail temp. Water (⁰C) 26.5
Initail temp. LiCl (⁰C) 26.5 Initail temp. LiCl (⁰C) 26.5
average initial temp. (⁰C) 26.5 average initial temp. (⁰C) 26.5
Final Temp. (⁰C) 36.0 Final Temp. (⁰C) 36.0
∆T (⁰C) 9.5 ∆T (⁰C) 9.5
solution mass (g) 26.5025 solution mass (g) 26.4992
heat evolved (⁰C) (-9.5) heat evolved (⁰C) (-9.5)
moles of solute (mol) 0.03544 moles of solute (mol) 0.03537
molar heat of dissolution (kJ/mol) -45 molar heat of dissolution (kJ/mol) -45

Average (kJ/mol) -45

Table 5 – Potassium Chloride
Trial 1 Trial 2
KCl + H₂O → K⁺ + Cl⁻ + H₂O KCl + H₂O → K⁺ + Cl⁻ + H₂O
Mass of Water (g) 25.0 Mass of Water (g) 25.0
Mass of KCl (g) 1.5005 Mass of KCl (g) 1.5020
Initail temp. Water (⁰C) 26.5 Initail temp. Water (⁰C) 27.0
Initail temp. KCl (⁰C) 26.5 Initail temp. KCl (⁰C) 27.0
average initial temp. (⁰C) 26.5 average initial temp. (⁰C) 27.0
Final Temp. (⁰C) 23.8 Final Temp. (⁰C) 23.8
∆T (⁰C) (-2.7) ∆T (⁰C) (-3.2)
solution mass (g) 26.5005 solution mass (g) 26.5020
heat evolved (⁰C) 2.7 heat evolved (⁰C) 3.2
moles of solute (mol) 0.02013 moles of solute (mol) 0.02015
molar heat of dissolution (kJ/mol) 23 molar heat of dissolution (kJ/mol) 28

Average (kJ/mol) 25.5

Table 1 – Calibration was used to calculate Tables 2-5. The average heat of dissolution was found using the equation 1.

1. n⋅ΔHdissol.+ mH2O CSH H2O ΔTH2O + Ccal ΔTcal = 0
Where qrxn(heat of reaction) = n (moles of solute) times ΔHdissolution, C is the heat capacity of the calorimeter, and ΔTH2O=ΔTCal because the cold water was the only thing in the calorimeter system and therefore was the initial temperature of the calorimeter

The specific heat of water is 4.184 J/K g and the heat capacity of the calorimeter was calculated in Table 1 using equation 2. The ΔT’s were calculated in Tables 2-5 by subtracting the initial temperature by the final temperature. The number of moles were also recorded in Tables 2-5

2. mhot,H2O C SH,H2O ΔThot + mcold,H2O CSH,H2O ΔTcold + Ccal ΔTcal = 0
Where ΔTH2O= ΔTCal

Now the amount of energy from dissolution per mole was known for each substance.

Dystan Medical Supply Company would want to mass produce these cold and hot packs. Since the more energy you have the colder or hotter you could make a pack, the most important factor is how much energy the company is buying compared to the amount of money they spent on that energy. The given prices were per 500 grams. The 500 grams was converted into moles by multiplying the 500 grams by the compounds molar mass since it is the amount of moles and not the mass in a reaction that determines the energy. This was then substituted to convert to dollars per moles, which was converted to dollars per mole. Now that the price of one mole was known it was compared to the amount of energy (heat of dissolution) per mole. The amount of energy per mole was divided by the cost of one mole to determine the amount of energy per dollar for a specific salt.

3 (energy/mole)/(\$/mole) = energy/\$

Ammonium nitrate, 8.71 kJ/dollar, was compared to potassium chloride, 6.07kJ/dollar, since they were both for cold packs. Calcium chloride, 11.6 kJ/dollar, was compared to lithium chloride, 8.17 kJ/dollar, since they both release heat. Since Ammonium nitrate and calcium chloride give the most energy per amount money, they would be used for cold and hot packs respectively.

Even though when testing 1.5 grams of lithium chloride changed the temperature of the system to a greater degree than calcium chloride (see graph Temp. Cal. vs Time – CaCl2 1&2 and Temp. Cal. Vs Time – LiCl 1&2 or Tables 3&4), calcium chloride was the choice salt because it is not the mass that we want to observe but the moles. Since the molar mass of calcium chloride is more than two and a half times greater than that of lithium chloride, the amount of moles for calcium chloride is less by the same factor. Therefore, the amount of energy per mole would be greater than what would seem logical at first because less moles of calcium chloride were used than that of lithium chloride. Also lithium chloride was more than twice as expensive as calcium chloride.

Now it had to be made sure that using these salts would not cost more than the 5 dollar limit per pack. It was calculated that .288 moles of ammonium nitrate would be needed to cool 100mL of water from 25 degrees Celsius to 0 degrees Celsius, using equation 1 where the heat capacity of the pack = 0 was used in place of the heat capacity of the calorimeter and ∆Hdissol was taken from Tables 2-5 as the average between trial one and two. To determine how much a specific amount of moles of a substance would cost the dollars per mole of a substance was set equal to the dollars (x) per moles needed of that substance.

4 \$/mole = x/moles needed

0.288 moles (23.1 grams) of ammonium nitrate would cost about \$1.21. This plus the cost to make the pack (\$1.28) plus the cost of water (n/a = \$0) plus the cost of research and development that was paid to the person who did this lab divided by the number of packets created (\$0/number of packets created) would be the cost to make one cold pack (\$2.49). It was calculated that .205 moles (22.8 grams) of calcium chloride would be needed to heat 100mL of water from 25 degrees Celsius to 100 degrees Celsius, using equation 1 where the heat capacity of the pack = 0 was used in place of the heat capacity of the calorimeter and ∆Hdissol was taken from Tables 2-5 as the average between the two trials. 0.205 moles of calcium chloride would cost \$1.45. This cost plus the cost to make the pack (\$1.28) would be equal to the cost to make one hot pack (\$2.73). Neither pack would exceed the maximum of five dollars per pack. Therefore, Dystan Medical Supply Company should use ammonium nitrate for their cold packs and calcium chloride for their hot packs. Calcium Chloride, magnesium sulfate, and sodium acetate are commonly used in hot packs and ammonium nitrate is used in cold packs.2 The results of this lab agreed with what actual hot and cold packs are made with.

Significant sources of error in this experiment included not being able to completely seal the calorimeter; this would result in heat transfer between the system and surroundings which would mean the equations used in calculations would not be correct. Also, not all salt being transferred from balance to calorimeter would mean the actual salt put into the calorimeter was less than the amount of salt used in the calculations. This would give a better energy per dollar ratio for any salt in which this error occurred. In addition, using a different thermometer to measure the temperature of the heated water could result in inaccurate measurements since the thermometers could be calibrated differently. If the heated water was measured too high, as compared to the thermometer used to measure the water in the calorimeter and the mixed water, then the heat capacity of the calorimeter would be greater than it was in actuality. This would give higher heat of dissolutions for all salts. And the opposite is true. If the thermometer read the temperature of the heated water lower than then other thermometer would have, the heat capacity of the calorimeter would have been calculated lower than the actual heat capacity which would give lower heat of dissolutions for all salts. Therefore, this experiment would not be a reliable source for Dystan Medical Supply Company. This experiment could be more reliable if a better calorimeter was used, thermometers were calibrated to represent the same temperatures, and salts were immediately dumped into the calorimeter after being weighed instead of being transported to the calorimeter.

A real world application of this experiment would be a company needing to know how much x amount of cold packs would cost using ammonium nitrate if the packs had to drop to 0 degrees Celsius after they were broken. Also, the company could determine if using a different salt could be cheaper.

Conclusion

The purpose of this experiment was to determine which salts are most economical for the production of cold and hot packs and how much each pack would cost. The most economical salt for a cold pack would be the ammonium nitrate. Calcium chloride would be the most economical salt to use for a hot pack. Using these salts, hot and cold packs could be manufactured without exceeding the 5 dollar cost limit. A cold pack using ammonium nitrate would cost \$2.49. \$2.73 would be needed to produce a hot pack using calcium chloride. The significance of the results was that thermochemistry can be applied to real world situations, such as a company needing to know the best way to manufacture hot and cold packs. Also, it shows that the heat of a reaction and heat of dissolution of a certain substance can be estimated without ever actually carrying out the specific reaction being evaluated.

References

1Experiment 8: Dystan Medical Supply Company—Cold Packs and Hot Packs, p 1.

2 Schlaefer, P., Seaburg, S., Spear, M., Seo, J., Simonsen, L. (2007). Cold Packets/ Hot Packets. Retrieved November 11, 2007, from http://dopamine.chem.umn.edu/chempedia/index.php/Cold_Packs/Hot_Packs

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