Stoichiometry of Calcium Medicines

In the Classroom edited by

Resources for Student Assessment

Thomas A. Holme University of Wisconsin–Milwaukee Milwaukee, WI 53201

Stoichiometry of Calcium Medicines Gabriel Pinto Departamento de Ingeniería Química Industrial y del Medio Ambiente, E.T.S. de Ingenieros Industriales, Universidad Politécnica de Madrid, 28006 Madrid, Spain; [email protected]

Modern-day students will better appreciate chemistry concepts if these concepts are applied to compounds that are found in everyday lives. The idea of using a familiar context with chemistry is common but not usually found in textbooks. Thus chemistry instructors are always looking for examples of how chemical phenomena affect our lives (1–4) and for novel problems that will stimulate students’ interest once they have mastered the more routine skills. To this end, this article represents a continuation of a research program intended to help firstyear undergraduate-level and high school-level instructors include connections between students’ daily experience and chemical principles taught in the classroom (5–18). Here I use the topic of calcium supplements to provide a context in which to review most of the core content of general chemistry, namely, stoichiometry, concentration units, hydration of salts, inorganic and organic salts, physiological importance of elements, resonance in ions, geometry of polyatomic ions, and isomerism. The topics are included in questions to the students about calcium supplements. Calcium and Physiology Calcium is the fifth element in abundance in the human body (19, 20). It makes up about 1.5–2.0% of the total body weight. Most of the body’s calcium is stored in the bone structure giving the bones their strength and density. In fact, if calcium is not taken in through the diet in adequate quantities, it must be drawn from the body’s reserves found in bones. With loss of bone density, skeletal strength cannot be maintained and fractures can then occur with minimal stress. Eggshell is largely crystalline calcium carbonate. The calcium comes partly from the hen’s bones, and when necessary the hen can mobilize 10 percent of her bones for this purpose in a day (21). In addition to its major function in building and maintaining bones and teeth, calcium is also necessary for important biological and metabolic contributions including enzyme activation, effects in all types of muscle, nerve transmission, regulation of the heartbeat, and as an essential component in the blood clotting process (22, 23). Calcium requirements are difficult to quantify. The body requires calcium throughout life but especially during periods of growth, pregnancy, and lactation. About 700 mg daily has been deemed sufficient to meet the requirements of most adults, although for adolescents a little more is required (19). Calcium deficiency in children may cause rickets, slow growth, or, more likely, continued body growth but with abnormal development of bones, resulting in bowed legs and other bone deformities. Deficiency in adults may lead to os-

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teomalacia (often called adult rickets). A calcium deficiency contributes to the development of osteoporosis (a metabolic disorder that can be defined as a reduction in the quantity of bone). The translation of osteoporosis is “porous bones”. In several chemistry books (24, 25) there are impressive color micrographs showing healthy bone tissue and bone that has suffered calcium loss through osteoporosis. As quoted before, a decrease in bone density leads to increased risk for the development of fractures. In general, the best sources of calcium are milk, dairy products such as cheese, fish (salmon and sardines with bones), beans, and dark green vegetables (broccoli, collard greens, and so forth). There are different calcium salts commercially available for use in food and dietary supplements: inorganic salts, such as calcium carbonate or phosphate, and organic salts such as calcium citrate, lactate, gluconate, or lactategluconate. Calcium phosphate is less expensive than calcium citrate but more expensive than carbonate (19). The cost is one of the reasons, besides medical and pharmaceutical issues, for the use of the various calcium salts. Vitamin D is often added to the tablets to stimulate intestinal absorption of calcium ion and to enhance the bone building process. The role of vitamin D in calcium absorption is discussed in several references (26, 27). The prospective user of a calcium supplement is faced by a bewildering selection of supplements. Thus the assignment is based around the identification of the compounds available as calcium supplements and a comparison of the actual masses of calcium contained in each standard dosage. Additional readings can be undertaken using print (28, 29) or Internet resources. Questions for Students

Question 1 The information leaflet for several medicines and medicinal sourcebooks (28, 29) indicate that a quantity (per tablet, per envelope, or per spoonful) of different compounds are equivalent to a certain quantity of elemental calcium (third column of the Table 1). Check by stoichiometric calculations the values of equivalences given. Question 2 In the information about a medicine the manufacturer indicates that there are 800 mg of calcium phosphate, 200 mg of calcium carbonate, and 5 mg of calcium fluoride per tablet. According to the information, these quantities are equivalent to 393 mg of calcium ion and 2.43 mg of fluoride ion. Check these equivalences.

Vol. 82 No. 10 October 2005

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Journal of Chemical Education

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Question 3 According to the prospectus of a medicine recommended for deficiency of vitamins and mineral salts, each tablet has, among other substances, 90 mg of calcium as calcium phosphate and 70 mg of phosphorus, also as calcium phosphate. By considering these data, check that the indicated “calcium phosphate” is not Ca3(PO4)2. Note that sometimes in pharmacology, the term “tricalcium phosphate” is the term reserved for this formula, whereas the term “calcium phosphate” is reserved for an acid salt of the phosphate. If this is the case here, indicate whether it is calcium hydrogen phosphate or the calcium dihydrogen phosphate. Question 4 Based on the information supplied on the packaging, the composition of each effervescent tablet of a supplement (medicine J in Table 1) for the treatment of decalcification shows that, among other compounds, it contains 2.94 g of calcium lactategluconate and 0.30 g of calcium carbonate, both altogether equivalent to 500 mg of calcium ions. Deduce from these data a composition of calcium lactategluconate provided the gluconate usually forms a monohydrate.

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Answers to Questions

Answer 1 Students should be familiar with the chemical formulas of all the common anions. The formulas of lactate, gluconate, and pidolate, a pharmaceutical name of 2-pyrrolidone-5-

N O

H

Figure 1. Structure of pidolate, a pharmaceutical name of 2pyrrolidone-5-carboxylate.

carboxylate (Figure 1), can be found in texts, handbooks, and Internet sources. In the medicine A in Table 1, taken as an example, the stoichiometric calculation involves the expression:

1.250 × 103 mg CaCO3

×

5

1.001 × 10 mg mol CaCO 3

Question 5 Following from the previous question, determine the number of stereoisomers of the lactate and gluconate anions. Question 6 Identify the calcium salts from in the previous questions where the bonding of the anions can be explained in terms of resonance structures.

O

O

1 mol Ca 1 mol CaCO3 (1)

4

×

4.008 × 10 mg Ca = 500.5 mg Ca mol Ca

Table 1 shows a comparison of the cited calcium ion content together with that found from mole calculations for the other proposed medicines. In most cases the calculated values are close to those indicated by the manufacturers, but there are differences that range from ᎑3% to 7%, assuming the numbers provided by the manufacturers are precise. This exercise could also be used to discuss significant figures and precision. For example, in eq 1 there are four significant figures in the data and four significant figures in the answer; however, the answer is more precise that the initial data provided by the manufacturer (500 mg Ca).

Table 1. Masses of Calcium for Selected Medicines Medicine

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Mass of Elemental Ca/mg

Ca Salt

via Manufacturer

via Stoichiometry

A

1250 mg calcium carbonate

500

500.5

B


500

505

C


600

601

D


1000

1001

E

3.3 g calcium phosphate

1.2 x 103

1280

F

A spoonful (=15 mL) of solution with 1671 mg calcium phosphate per 100 mL

100

97

G


125

122

H


180

180

I

3750 mg calcium pidolate

500

508

J

2.94 g calcium lactategluconate and 0.30 g of calcium carbonate

500

500


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Answer 2 The stoichiometric calculations are in this case more complex than in the previous one and are given by the following equations: 8.00 × 102 mg Ca 3 (PO 4 )2 5

3.103 × 10 mg mol Ca 3 (PO 4 )2

×

3 mol Ca 1 mol Ca 3 (PO 4 )2

4.008 × 10 4 mg Ca × = 310.0 mg Ca mol Ca 2.00 × 10 2 mg CaCO3 5

1.001 × 10 mg mol CaCO3 ×

×

1 mol Ca mol CaCO3

2.94 g Ca lactategluconate

4.008 × 10 4 mg Ca = 80.1 mg Ca mol Ca

5 mg CaF2 4

7.81 × 10 mg mol CaF2

×

(2)

(3)

7.81 × 10 mg mol CaF2 ×

×

(4)

2 mol F 1 mol CaF2

1.900 × 10 4 mg F = 2 mg F mol F

(5)

The answer is given with one significant digit to agree with the precision of the data. It is not correct, as stated by the manufacturer, to give a more precise result than the initial data.

Answer 3 With the indicated data, the ratio Ca:P, in moles, is 1:1. This shows that it is not Ca3(PO4)2 but Ca(HPO4). This is an example of pharmaceutical terminology not matching that of inorganic chemistry.

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×

(1 + x ) mol Ca 1 mol Ca lactategluconate

40.08 g Ca mol Ca

(6)

= 0.38 g Ca

From these relations we obtain x = 0.665 or 3 lactate to 2 gluconate. Thus, the formula of the calcium lactategluconate is Ca5C42H74O46⭈2H2O.

The calculation of calcium content (393 mg Ca) matches the listed value (393 mg Ca). Note that the calcium content was rounded to agree with the lack of decimal places in the quantity of calcium fluoride; however, the answers in equations 2–4 were not rounded as these are intermediate calculations. The CaF2 is equivalent to 2 mg of fluoride, similar to the value given by the manufacturer, in accordance with the calculations from the equation: 4

( 218.22 + 448.38 x ) g mol Ca lactategluconate ×

1 mol Ca 1 mol CaF2

4.008 × 10 4 mg Ca × = 2.6 mg Ca mol Ca

5 mg CaF2

Answer 4 The composition of calcium lactategluconate is deduced using two calcium salts. The molecular formula of the first salt, calcium lactate, is Ca(CH3CHOHCOO)2 (218.22 g兾mol) and the molecular formula of the second salt, calcium gluconate monohydrate, is Ca(HOCH2(CHOH)4COO)2⭈H2O (448.38 g兾mol). Assuming the ratio of salts in calcium lactategluconate is 1 mole of lactate to x mole of gluconate, calcium lactategluconate has a molar mass of (218.22 + 448.38x) g兾mol and contains 40.08(1 + x) g of Ca. Taking into account that 0.30 g of CaCO3 are equivalent to 120 mg of Ca, we know that 2.94 g of this lactate and gluconate mixture contains 0.38 g Ca (500 − 120 = 380 mg). With these data we can deduce the expression:

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Answer 5 Stereoisomers are species that are identical in atomic constitution and bonding, but differ in the three-dimensional arrangement of the atoms. The lactate anion has a chiral carbon and therefore has two configurations. As it is well known (30) the maximum number of stereoisomers of a molecule with n chiral or asymmetrical carbons is 2n. The gluconate anion, having four chiral centers, thus possesses 16 stereoisomers. The trivial generic names of all isomeric acids (Dseries), traced to corresponding monoses (hexoses) are: allonic, altronic, galactonic, gluconic, gulonic, idonic, mannonic (mannitic), and tallonic acids. With corresponding L-acids they present all 16 stereoisomers. Answer 6 The structures of both phosphate and carbonate anions can be drawn as resonance forms. The combinations of the resonance forms provide average X⫺O bond orders of 1.25 and 1.33 respectively. The anions 2-pyrrolidone-5-carboxilate (pidolate), gluconate, and lactate also present resonance in the carboxylate group, providing a C⫺O bond order of 1.50 in this group. Summary By using the context of over-the-counter calcium supplements, core chemical calculations can be made more interesting and challenging. Such contexts enable students to realize the relevance of chemistry outside of the classroom surroundings.


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Acknowledgments Geoff Rayner-Canham, Sir Wilfred Grenfell College, Canada, is thanked for helpful comments on the manuscript. The author would like to gratefully recognize the support provided by the Escuela Técnica Superior de Ingenieros Industriales (Universidad Politécnica de Madrid) under the Project 4A, Apoyo al Aprendizaje Activo de los Alumnos (Support for Students’ Active Learning). The author is also grateful to the reviewers and editors for valuable suggestions. This article is dedicated to my father, Ramiro Pinto, the doctor who encouraged my interest in medicinal chemistry. Literature Cited


20. 21. 22.

23.

1. Roesky, Herbert W.; Möckel, Klaus. Chemical Curiosities; VCH: Weinheim, Germany, 1996. 2. Barker, G. K. J. Chem. Educ. 2000, 77, 1300. 3. Erné, B. H. J. Chem. Educ. 2000, 77, 1309. 4. Jones, M. B.; Miller, C. R. J. Chem. Educ. 2001, 78, 484. 5. Zubizarreta, J. I.; Pinto, G. Chem. Eng. Educ. 1995, 29, 96. 6. Pinto, G. J. Chem. Educ. 1998, 75, 725. 7. Pinto, G. Educ. Chem. 2000, 37, 71. 8. Pinto, G. Educ. Chem. 2001, 38, 150. 9. Pinto, G. Anuario Latinoam. Educ. Quím. 2002–2003, 16, 200–204. 10. Pinto, G.; Rohrig, B. J. Chem. Educ. 2003, 80, 41. 11. Pinto, G. Educ. Chem. 2003, 40, 11. 12. Pinto, G. Educ. Chem. 2003, 40, 80.

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Pinto, G. Anales Real Soc. Esp. Quím. 2003, 99, 44. Pinto, G. Anuario Latinoam. Educ. Quím. 2003–2004, 17, 54. Pinto, G.; Esín, A. J. Chem. Educ. 2004, 81, 532. Pinto, G. Anales Real Soc. Esp. Quím. 2004, 100, 37. Pinto, G. J. Chem. Educ. 2005, 82, 1321–1324. Pinto, G. Educ. Chem. 2005, 42, 108. GlaxoSmithKline Calcium Information Home Page. http:// www.calciuminfo.com/index.aspx (accessed Aug 2005). Seaborg, G. T.; Valens, E. G. Elements of the Universe; E. P. Dutton & Co: New York, 1958. Taylor, G. C. Scientific American 1970, Mar, 89. Wilkins, R. G.; Wilkins, P. The Role of Calcium and Comparable Cations in Animal Behaviour; Royal Society of Chemistry: London, 2003. Rayner-Canham, G. Descriptive Inorganic Chemistry, 2nd ed.; W. H. Freeman & Company: New York, 2000. Jones, L.; Atkins, P. Chemistry: Molecules, Matter and Change; W. H. Freeman & Company: New York, 2000; p 330. Kelter, P. B.; Carr, J. D.; Scott, A. Chemistry: A World of Choice, 2nd ed.; McGraw-Hill: Boston, 2003; p 557. Compston, J. E. Clinical Endocrinology 1995, 43, 393. Bilke, D. D. Rheumatic Disease Clinics of North America 1994, 20, 759. Vademécum Internacional; Peisker, V., Ed.; Medicom S. A. Ediciones Médicas: Madrid, 1999. New Guide to Medicines and Drugs; Henry, J. A., Page, M., Eds.; The British Medical Association: London, 2003. Solomons, G. Fundamentals of Organic Chemistry, 5th ed.; Wiley: New York, 1996.


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Stoichiometry of Calcium Medicines

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