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JChemEd.chem.wisc.edu • Vol. 75 No. 1 January 1998 • Journal of Chemical Education 61

Demonstrations on Paramagnetismwith an Electronic Balance

Adolf CortelInstitut de Batxillerat El Cairat,Gorgonçana 1, 08292Esparreguera, Barcelona, Spain

A paramagnetic substance is attracted by a magneticfield with a force proportional to its magnetic susceptibility,which is related to the number of unpaired electrons of theatoms (1). Thus, magnetic data, together with spectroscopicmeasurements, are used to establish oxidation states andbonding properties (2). This important feature is a motive fordesigning experiments to observe and measure this phenom-enon. The simple setup described below allows demonstratingthe paramagnetism of common inorganic compounds, mea-suring the force with which they are attracted by a magnetover the plate of an electronic balance. The balance musthave a sensitivity of 0.01 g or better. A powerful magnet1 isneeded with its magnetic field directed vertically. Themagnet must be placed on a wooden block, which rests on theplate of the balance.2

A test tube containing the substance or its concen-trated aqueous solution is held by a clamp, so that thebottom of the tube is just over the magnet. A small piece ofpaper is wrapped around the test tube and the clamp is ad-justed so that the tube can be moved easily up or down (Fig.1). The variation of weight is easily measured if the balanceis tared before lowering the test tube over the magnet.

Paramagnetic substances (e.g., CoCl2�6H2O, FeCl3�6H2O,FeSO4�7H2O, and especially MnSO4�H2O) attract the mag-net with a force—perfectly measurable with the balance(Tables 1, 2)—equal and opposite to that which the magnetexerts on the substances.

If magnets as powerful as neodymium magnets are notavailable,3 a “force multiplier” can be built. This multiplieris simply a lever made with a rigid aluminium strip, a coun-terweight, and the magnet, whose pivot is a spatula heldby a support and a nut, as shown in Figure 2. The shortarm of the lever, with the counterweight, rests over theplate of the balance. Its pressure increases when the mag-net, in the long arm, is attracted by the paramagnetic sub-stance in the test tube. The multiplication factor of the forcewill be approximately the ratio of the lengths of the twoarms of the lever. The use of this setup allows observingparamagnetism with Alnico magnets, but this assembly is

Figure 1. Three neodymium magnets provide a powerful magneticfield, suitable for measuring the attraction over paramagnetic sub-stances with an electronic balance.

Filtrates & Residuesedited by

James O. SchreckUniversity of Northern Colorado

Greeley, CO 80639

Continued on page 62

In the Classroom

62 Journal of Chemical Education • Vol. 75 No. 1 January 1998 • JChemEd.chem.wisc.edu

sensitive to vibrations and it is difficult to repro-duce results.

The magnetic field of a magnet decreaseswith distance. Therefore the value of the force isvery sensitive to the distance between the mag-net and the bottom of the tube. To compare theparamagnetism of different substances it is con-venient to measure the highest force of attraction,gradually lowering the tube (making it rotate in-side the clamp) and taking readings of the bal-ance. Just before contact with the magnet, themeasured weight will be minimum and from thispoint on the weight will increase. The force of at-traction also depends on the quantity of sub-stance in the tube, so all the measures in Table 1were done with the same amount of sample (3 g)in the tube.4 The results with test tubes contain-ing 3 g of aluminium, potassium, calcium, andzinc sulfate and silver nitrate (none of them is at-tracted) are not included. Because of the atomicnature of the force, the paramagnetism of the dif-ferent samples must be compared on the basis of ∆m/n, thedecrease of weight per mole of the substance.

From the data it can be deduced that:

1. Paramagnetism is associated with the unpairedelectrons. The salts whose ions have complete elec-tronic subshells (Al3+, Zn2+, Ca2+, Cu+, Ag+) are notparamagnetic. The comparison between Cu2+ (d9)with one unpaired electron and Cu+, with completesubshell d10, confirms this fact.

2. The different paramagnetism of the compounds ofthe same metal can be associated with a differentnumber of unpaired electrons. Thus, the compari-son of the attraction over the ammonium dichro-mate and chromium(III) sulfate samples or be-tween potassium ferrocyanide and ferricyanideshows the relationship between the magnetic prop-erties and the oxidation state of the metallic ion.

3. In a free atom the five d orbitals are equivalent, butin a coordination compound there is a splitting ofthose orbitals according to the crystal field theory(2). The different behavior of the listed iron com-pounds (as in ferrocyanide and iron(II) sulfate orin ferricyanide and iron(III) chloride) arises fromthe different energy gap between the two groups ofd orbitals in both compounds: the cyanide ligand hasa strong field, whereas chloro, aqua, or oxo ligandsdo not have such a strong field. As a result, the 6 delectrons in ferrocyanide are paired in the lower 3orbitals, whereas in the ferrous sulfate there are 4electrons in the 3 lower orbitals and 2 electrons inthe higher ones, with 4 unpaired electrons. The dif-ferent attraction of potassium ferricyanide andiron(III) chloride can be understood in a similarway (Fig. 3). The similar attraction over potassiumferricyanide (d5) and copper(II) compounds (d9) sug-gests the presence of one unpaired electron in thisiron compound.

4. There is a correlation between the force of attrac-tion and the number of unpaired electrons. Thisnumber is easily established for ions such as Cu2+,Ni2+, and Cr3+, whose electronic configurations d9,d8, and d3, respectively, are associated with 1, 2,and 3 unpaired electrons. In the d4–d7 ions thisnumber depends on the ligands attached to themand its coordination, as discussed above for theiron compounds. The theory of magnetochemistry(1) indicates that the force of attraction is propor-tional to N(N + 2) (N is the number of unpairedelectrons). Thus we can establish a scale of the

snoituloScinagronIemoSforoivaheBcitengamaraP.2elbaT

noituloS∆m

)g(∆m /n

)lom/g(

lCeF 3� H6 2 )retawfoLm5nig0.2(O � 22.0 7.92

lCeF 3� H6 2 )retawfoLm5nig0.1(O � 11.0 7.92

OSnM 4�H2 )retawfoLm5nig0.1(O � 61.0 0.72

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tlaS∆m

)g( WMn

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snips

lCeF 3� H6 2O � 59.0 3.072 1.11 6.58 052,51 5

OSnM 4�H2O � 62.1 0.961 7.71 2.17 002,41 5

OSeF 4� H7 2O � 15.0 1.872 8.01 2.74 002,11 4

lCoC 2� H6 2O � 74.0 9.732 6.21 3.73 017,9 3

OS(rCK 4)2� H21 2O � 71.0 0.994 0.6 2.82 022,6 3

OSiN 4� H7 2O � 22.0 9.082 5.01 9.02 003,4 2

K3 )NC(eF[ 6] � 80.0 3.923 0.9 9.8 092,2 1

OSuC 4� H5 2O � 90.0 7.942 2.21 4.7 075,1 1

K4 )NC(eF[ 6]� H3 2O 00.0 4.224 1.7 0 � 271 0

HN( 4)2 rC 2O7 00.0 0.252 0.21 0 83 0

lCuC 00.0 0.99 8.03 0 � 04 0aXm = magnetic susceptibility.

Figure 3. The different splitting of the d orbitals of Fe2+ and Fe3+

in strong and weak ligand fields accounts for the observed differ-ences in the paramagnetism of these compounds.

Fe3+

Fe3+

Fe2+

Fe2+

FeCl3

Fe(CN)64-

FeSO4

Fe(CN)63-

Figure 2. A lever made of aluminium and held by a spatula allowsmultiplying the small force that Alnico or ferrite magnets exert onparamagnetic substances.

In the Classroom

JChemEd.chem.wisc.edu • Vol. 75 No. 1 January 1998 • Journal of Chemical Education 63

force of attraction as shown in Table 3.The values of ∆m/n in Table 1 show that the attraction

for iron(III) chloride is about 12 times greater than for cop-per sulfate, as the scale of force in Table 3 suggests. Thescale also predicts that in MnSO4�H2O(s), Mn2+ has 5 un-paired electrons, owing to its d5 electronic configuration ina weak field. If we plot the force of attraction per mole ver-sus the number N of unpaired electrons of the compoundslisted in Table 1, where N has been established as discussedabove, the fit to a polynomial of second degree by the leastsquares method gives 2.2(N2

+ 1.9N + 0.3), with a standarddeviation of 1.3, very close to the k(N2+2N) polynomial pre-dicted by the theory (Fig. 4). The linear correlation between∆m/n and the known values of molar magnetic susceptibility(3), with a standard deviation of 1.7, is shown in Figure 5.

Unlike paramagnetism, diamagnetism is a generalproperty of all substances. The force of repulsion by a dia-magnetic sample introduced in a magnetic field is muchweaker, but this setup also allows demonstrating the dia-magnetism of solid bismuth, the most diamagnetic element.If a sample of bismuth is brought over the magnet, an in-crease of weight is observed because of the repulsion force.For example, with a 300-g sample of bismuth, an increaseof weight of nearly 1 g has been measured; but with a testtube filled with 10 g of ground bismuth, the increase is only0.08 g. The diamagnetism of aluminium could not been ob-served.

Acknowledgments

I thank the reviewers for their valuable suggestionsabout the quantitative treatment. I also thank Lluis Nadal

Figure 4. Plot of weight decrease per mole versus number of un-paired spins of compounds listed in Table 1. The data fit to a poly-nomial 2.2(N 2 + 1.9N + 0.3), (SD 1.3), close to the k(N 2 + 2N)polynomial predicted by theory.

Figure 5. Linear correlation (standard deviation 1.7) between theweight decrease by mole and the molar susceptibility for com-pounds listed in Table 1.

neewtebpihsnoitaleR.3elbaTsnortcelEderiapnUforebmuN

(N (noitcarttAfoecroFdna) F )

N N (N )2+ F a

0 0 0

1 3 1

2 8 7.2

3 51 5

4 42 8

5 53 7.11aMeasured in arbitrary units.

for some samples and for his wise comments.

Notes

1. I have used a set of three cylindrical neodymium magnetsof 22 mm diameter and 10 mm height. The magnetic field of a singlemagnet is 0.29 T, but by putting 3 magnets together it increases to0.43 T. CAUTION: these magnets are very powerful and must behandled far from any sensitive material such as computer hardwareor software. (I demagnetized my credit cards by handling the mag-nets too close to my pocket!). When they are pulled apart, theforce is so strong that they can easily pinch your fingers. In previ-ous experiments I used smaller neodymium magnets with a simi-lar magnetic field (12 mm diameter and 7 mm height), but sincethe diameter of the test tubes is 15 mm, the use of bigger mag-nets allows all the sample to be kept inside the magnetic field andthe force is almost twice the force of the small magnets. Further-more, with bigger magnets the accurate centering of the test tubeover the magnet is not a noticeable factor. As the magnetic field de-creases quickly with distance, the force must be bigger if the sub-stance is well packed in the tube; but some experiments with dif-ferent ground samples have shown that this effect is not notice-able if the substances already have a small grain size (as mostcommercial reagents do). The use of test tubes is recommendedover Petri dishes or watch glasses because it permits a biggerdistance between the metallic pieces of the clamp that holds themand the magnet.

2. With our balance there is an interaction between the mag-netic field of the magnet and the mechanism of the balance. There-fore it is necessary to put a wooden or plastic block between themagnet and the balance plate.

3. The Alnico and ferrite magnets in our laboratory have muchsmaller magnetic fields than the neodymium ones. An Alnico mag-net (cylindrical, 12-mm diameter and 50-mm length) has a mag-netic field of 0.11 T; a ferrite one (prismatic, 39×10×20 mm) hasa magnetic field of 0.08 T.

4. The samples are stored in stoppered test tubes. The resultsare very reproducible (within 0.02 g) along successive monthsusing the same magnets, except for hygroscopic salts such asiron(III) chloride.

Literature Cited

1. Porterfield, W. W. Inorganic Chemistry—A Unified Approach,2nd ed.; Academic: San Diego, 1993; pp 579–587.

2. Shriver, D. F.; Atkins P. W.; Langford C. H. Inorganic Chemis-try, 2nd ed.; Oxford University: Oxford, 1994; Chapter 6.

3. König, E. In Landolt–Börnstein Numerical Data and FunctionalRelationship in Science and Technology, New Series, Vol. 2,Group II: Atomic and Molecular Physics; Hellwege, K. K.;Hellwege, A. M., Eds.; Springer: Berlin, 1966; pp 24–379.