An Experimental Demonstration of Hess's Law

Prologue: The application of Hess's Law frequently presents students with conceptual problems, and I believe that performing a series of experiments that confirms Hess's Law, is probably the best way to impart a robust understanding of this principle. A plaque on the wall of the Oxford University Biochemistry Department reads:

I hear and I forget.

I see and I remember.

I do and I understand.

The experiments described here are designed to perform this function. A search of the internet for easy to perform experiments, using cheap, easily improvised equipment, readily available, cheap, and non-toxic chemicals, revealed few documented options. The only experiment I encountered involved measuring the enthalpy (∆H) of a solution of sodium hydroxide (NaOH) and the ∆H of neutralization of 1M hydrochloric acid (HCl) with 1M sodium hydroxide (NaOH) solution, and showing that the sum of these two enthalpy values equaled the (∆H)  for the reaction of solid sodium hydroxide (NaOH) with a stoichiometric quantity of hydrochloric acid. What I didn't like about this demonstration is that it only involved one exothermic chemical reaction process, with the second exothermic process being a physical rather than a chemical change. Thus I designed a series of experiments that involved only chemical processes with three different chemical pathways that could be used to progress from the initial to the final state, all of which should have the same net enthalpy value.

A theoretical class could be given as an introduction to the topic of thermochemistry, prior to performing the series of described experiments. Then these experiments which involve a total of five reactions could be performed over five classes by the teacher as a demonstration; or alternatively, the students could be divided up into five groups who would each perform one of the five reactions in a single class. The data could then be shared and the experiment written up in a subsequent class, or as a homework assignment. This series of reactions would also be useful for demonstrating the metal reactivity series, and so these classes could perform a dual function. I would also recommend the students perform the experiments as it has been my experience that many students seem to need practice at performing simple tasks, such as competence in the use of measuring cylinders, gravimetric balances, and generating reagent solutions of known concentration. The students should work through the mathematics with the teacher's guidance, presumably all the students would have already covered mathematical operations involving experimental data and would already be aware of calculations involving significant figures and standard deviations. If not, the students must be informed that the answer has to be reported in such a way that it reflects the reliability of the least precise measurement, and an answer can be no more precise that the least precise number used to get that answer. If due to time constraints there is insufficient lesson time remaining in the curriculum for the class to perform all the necessary reactions, the class could merely study and process the data presented in this manuscript for themselves, and then perform one of the described reactions and compare their data to the manuscript's data. I would recommend the zinc dust, and 1M copper(II) sulfate reaction for this single experiment, because it involves a relatively large extrapolated temperature change (∆T ~ 41°C), occurs rapidly with the peak temperature being achieved in around 15 minutes, no side reactions are present, and the reaction temperature only needs to be followed for a total of about 30 minutes. Furthermore, this reaction involves a pronounced color change: the loss of the blue color of the 1M copper(II) sulfate solution, and the appearance of the red/orange copper metal precipitate. If the class is a more advanced one, involving AP chemistry students, the teacher could point out that in the zinc dust/1M copper(II) sulfate reaction is the same net reaction as occurs in the electrochemical Daniel cell,

Zn_(s) + Cu(H₂O)₆²⁺ → Cu_(s) + Zn(H₂O)₆²⁺

and that the ∆S° for this process should be very small as there is essentially no net change in disorder in the above reaction, especially when considering the equivalently hydrated Cu²⁺ and Zn²⁺ ions are essentially identical in size (1).  Since ∆G° = ∆H° -T∆S°, and in this particular reaction ∆S° is very small ∆G° ≈ ∆H°. The ∆G° for the Daniel cell electrochemical reaction can be calculated using the following equation:

ΔG° = -nFE°

where E° is the potential of the Daniel cell (1.10 volts) and F is Faraday’s constant 96.5 kJV^-1mol^-1.

A Faraday is 1 mole of electrons (6.022 x 10²³) or 96,500 coulombs. 1 coulomb of charge equals 6.25 ⨯ 10¹⁸ electrons or 1 amp.second. Thus, the calculated ΔG° for the Daniel cell electrochemical reaction equals -212 KJ/mol. Since in this particular case ∆G° ≈ ∆H° it therefore follows that ∆H° ≈ -212 KJ/mol. This is in good agreement with our experimental value for ∆H of  -200 KJ/mol ± -20 KJ/mol.

Introduction: Hess's Law states that regardless of the number of reaction steps, the total enthalpy (heat energy) change (∆H) for the overall reaction being considered, is always the same and equal to the sum of all the ∆H values for the all the individual steps. This law is a manifestation of enthalpy being a state function (like Gibbs free energy and entropy). In chemistry, a state function is a property of a system that depends only upon its current conditions, and is independent of the route by which it was created. Thus if A is converted to B the heat released (enthalpy or ∆H) would be identical if this reaction proceeded directly or via compounds C or D (see figure 1). Hess's law is essentially the chemistry equivalent of the law of the conservation of energy in physics, which states that the total energy of an isolated system remains constant.

 

Figure 1: If A is converted to B the heat released (enthalpy or ∆H) would be identical if this reaction proceeded directly or via compounds C or D.

 

Materials and Methods

In this demonstration of Hess's law the following five reactions are used.

Zn + CuSO₄ → ZnSO₄ + Cu                  Fe + CuSO₄ → FeSO₄ + Cu                  Mg + CuSO₄ → MgSO₄ + Cu

Mg + FeSO₄ → MgSO₄ + Fe                 Mg + ZnSO₄ → MgSO₄ + Zn

You will need the following materials: finely divided metals and salts - magnesium, zinc, iron, zinc sulfate, iron sulfate, copper sulfate, and distilled water (figure 2); an insulated housing constructed from thick expanded polystyrene foam board (figure 4), a weighing scale, and an accurate thermometer.

The following information will be required: the mass of the 50 mL polypropylene test tubes (this was ~15 grams for the tubes I utilized), specific heat polypropylene (1.9 J/g/°C) (1), mass of water (50 grams), specific heat of water (4.2 J/g/°C) (2). The net specific heat of experimental system using (water + 50 mL polypropylene tube) = 239 J/ °C.

The specific heats and masses of the metals and the salts are much smaller than that of the water, and the polypropylene tube, and do not make a significant contribution to the overall heat capacity, and can therefore be ignored.

Fine iron or steel wool is the preferred source of iron, zinc dust is the preferred source of zinc, and magnesium turnings (used for camp fire starting, and sold at camping stores etc.) are the preferred source of magnesium (figure 2).

Figure 2: Required solutions and metals 

 

Readily available divalent metals (and divalent metal salts) have been used exclusively in the described experiments, (many other metal/metal salt combination could of course be utilized). Using divalent metals and divalent metal salts results in a very simple 1:1 molar reaction ratio. However, other metals could be also be used. A 10% molar excess of the metals was used to ensure complete reaction of the salt.

The reactions involving Mg metal were the most exothermic, particularly the Mg/copper(II) sulfate reaction, because of this 0.5 M solutions of the various salts were utilized to eliminate the risk of boil over when using Mg. It is best to seal the magnesium turnings in a small homemade paper 'teabag' to cause a short delay in the start of the reaction. This gives sufficient time to seal the tube and mix the reagents. To demonstrate Hess's law only two routes from the initial to the final state are required, however in the demonstration described 3 routes (A+B, C, and D+E) are used (see figure 3).

Figure 3: Three optional reaction routes

 

The experimental equipment required is as follows: Insulated reaction container, screw cap 50 mL polypropylene reaction tubes, and thermometer (kitchen digital thermometers, are inexpensive and generally work quite well).              

Figure 4: Required experimental equipment                   

 

Figure 4 shows the apparatus I used: left assembled polystyrene insulated container composed of a total of 9 layer of ~2.8 cm thick 15 x15 cm polystyrene, 6 layers glued together forming the base, and 3 layers glued together to form the lid (total height ~25 cm); image second from left, polystyrene insulated container opened showing enclosed 50 mL reaction tube, and the lid with a cutout to fit the reaction tube cap, and hole for a suitable temperature sensor; image third from the left, lid housing the temperature probe; far right image, electronic temperature probe.

If the temperature is plotted versus time (see figure 5) a correction can be easily made for the heat lost during the reaction, and an extrapolated ∆T can be determined. This extrapolated ∆T value should be used to calculate the molar enthalpies (∆H values) of the reactions. The use of a vacuum flask, as a reaction vessel, would probably negate the requirement for any heat loss correction. During the rising temperature phase, (before the end of the reaction) the whole apparatus should be vigorously shaken every few minutes to ensure complete reaction of the metal with the salt.

Figure 5: Temperature vs time showing heat lost during reaction

 

When the experiment is complete and the apparatus is being disassembled, it should be observed that the reactions that involved copper(II) sulfate should have had the blue color completely discharged and replaced with the orange color of copper powder; similarly reactions involving iron(II) sulfate should have lost their light green color, and the dark grey/black color of powdered iron should now be present. Zinc sulfate is colorless so there is no profound color change in this case.

 

Results

Typical data is given below (3 repeats for each reaction). The thermometer/temperature probe used only allowed the data to be given to two significant figures.

 

• Mg (0.028 mol, 0.7g ~10% molar excess) reacting with 0.05 L of 0.5 M CuSO₄ (extrapolated ∆T ~ 44°C) calculated ∆H/mole = - 420 ±-30 KJ/mol  (route #2 reaction 'C')
• Mg (0.028 mol, 0.7g ~10% molar excess) reacting with 0.05 L of 0.5 M ZnSO₄ (extrapolated ∆T ~ 25 °C) calculated ∆H/mole =  -240 ±-20  KJ/mol (first half route #1 reaction 'A')
• Mg (0.028 mol, 0. 7g ~10% molar excess) reacting with 0.05 L of 0.5 M FeSO₄ (extrapolated ∆T ~ 16 °C) calculated ∆H/mole = -250 ±-20  KJ/mol (first half route #3 reaction 'D')
• Zn (0.055 mol, 3.6g ~10% molar excess) reacting with 0.05 L of 1.0 M CuSO₄ (extrapolated ∆T ~ 41 °C) calculated ∆H/mole =  -200 ±-20 KJ/mol (second half route #1 reaction 'B')
• Fe (0.055 mol, 3.1g, ~10% molar excess) reacting with 0.05 L of 1.0 M CuSO4 (extrapolated ∆T ~ 31 °C) calculated ∆H/mole = -150 ±-10 KJ/mol (second half route #3 reaction 'E')

 

A small proportion of the magnesium will react with hydrogen ions present in the solutions producing hydrogen gas as a minor side reaction. This is because ZnSO₄, CuSO₄ and FeSO₄ all form somewhat acidic solutions. This side reaction will contribute towards the observed errors.

 

Conclusion

We should find that the sum of the ∆H values for reactions A and B, equals the ∆H for reaction C, and sum of the ∆H values for reactions D and E. Thus the ∆H for reaction A (-240 ±-20  kJ/mol) + the ∆H for reaction B (-200 ±-20  KJ/mol) equals the ∆H for reaction C (-420 ±-30  KJ/mol), and also equals the ∆H for reaction D (-250 ±-20  KJ/mol) + the ∆H for reaction E (-150 ±-20  KJ/mol); that is

-440 KJ/mol ±-40  KJ/mol = -420 KJ/mol ±-30  KJ/mol = -400 KJ/mol ±-40  KJ/mol

which is true within the limits of the experimental error. If these experiments had been modified to decrease any side reactions, had involved more repeats, and more precise instrumentation had been used (to determine the temperature increases, masses of reactants, and volumes of the solutions etc.) a much closer agreement would have been expected.  

 

References

(1) Kielland, J. Individual activity coefficients of ions in aqueous solutions, J. Am. Chem. Soc. 59:1675-1678, 1937.

(2) Specific Heat of some common Substances  www.engineeringtoolbox.com