Title: The Alcohol Dilution

Author: Valter TRAVAGLI

Affiliation: Dipartimento Farmaco Chimico Tecnologico, Università degli Studi di Siena, Via

Aldo Moro, 2 53100 Siena, Italy

Phone: + 39 0577 234317. Fax: + 39 0577 234333; e-mail: travagli@unisi.it

KEYWORDS: Alcohol; Vehicles; Solvents; Pharmaceutical calculations

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ABSTRACT

From a practical point of view, there are evidence that many chemists and pharmacists

encounter difficulties in performing dilution calculations even though they have high

knowledge in mathematics. However, the comprehension of the various logical steps to be

followed helps anyone to be able to carry out calculations with confidence. When this aspect

is of interest in economic and health terms, it becomes more important, too. Finally, such a

practical manner is well inserted in the sense of Total Quality Management principles at the

various formulation steps. The peculiarity of alcohol dilution was reputed as representative of

all these aspects with particular emphasis on hospital pharmacy.

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1. Introduction

The alcohol content in the beverages has a historic origin.1 The use of alcohol (synonims:

ethanol, ethyl alcohol, grain alcohol, methylcarbinol, Spiritus Vinis Rectificatus; CAS [64-17-

5]) is widespread and of great interest in pharmacy practice, too. This aspect is proved by

several works recently appeared in the literature dealing with binary mixtures of water and

alcohol.2,3

But apart from these aspects, industrial applications of alcohol dilution range from food

industry, biotechnology, cosmetics and chemical industry. In the latter case, of particular

importance is the pharmaceutical field.4-6 In fact, alcohol – absolute (i.e. anhydrous) or at

various aqueous dilution degrees – is typically used as a solvent in the phases of the new

chemical entities (NCE) synthesis or as vehicle in various processes and preparations.

Furthermore, the alcohol plays an important role during the preformulation stages, especially

for the analysis and the definition of the physicochemical properties of several components

that are of importance from a biological viewpoint. Finally, the pharmaceutical concern could

be of greater interest because it may be considered a valid example of the Total Quality

Management concept both in the industrial scale and in the view of convergence and

harmonisation among the major pharmacopoeias. The Quality-based requirements at

international level, like for example OSHA, ACGIH, ICH (see Glossary), also justify the

attention regarding limiting residual solvents levels in active substances, excipients and

medicinal products with relation to their hazardous characteristics and/or exposure limits.7,8

Ethanol is often present along with other substances in the formulation of compounds

destined to the hospital pharmacy. In this case, the amount of ethanol that is employed must

be suitable for the supplying and the cosolvent effect due to the presence of the ethanol itself

is exploited.

The legal issues (e.g. denatured, tax-paid, alcohol tax drawback) are not tackled here,

however it is well-known that the alcoholic grade in terms of Gay-Lussac scientific scale

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indicates the percentage by volume of alcohol in the binary hydroalcoholic mixture. In the

United States Pharmacopoeia (USP) there are tables reporting the unit values of percentage by

volume and by weight, along with the corresponding percentage by weight and by volume,

respectively. The corresponding specific gravity in air at the temperatures of 15.56 °C and

25°C are also reported.9 In the European Pharmacopoeia10, such a measure is spaced by

decimal in terms of alcoholic grade along with the corresponding %m/m and absolute density

(20). The latter has been officially recognized through a general formula by the European

Community Council, within the ruling of July 27th, 1976, as reported in Appendix A.11,12

In the Japanese Pharmacopoeia13 are present only the ethanol monographs where the ethanol

content is referred to a temperature of 15 °C.

It is interesting to note the difference in the standard value of temperature that is used for the

density measurement. At the regulatory level, a temperature of 15.56 °C is employed, which

derives from the value of temperature originally expressed in °F, and equal to 60 °F

(Fahrenheit Graphics API, 2000).14 Instead, the values of density presented in the EP Tables

above cited have been obtained for the more usual temperature of 20 °C, as indicated below.

In this paper, practical information of hydroalcoholic mixtures are focused with the aim to

highlight and deepen the main questions that arise with the use of ethanol and its dilution in

the pharmacy practice.15

2. Relevant alcohol properties

The dehydrated alcohol or, equivalently, absolute ethanol or 100° alcohol, does not exist in

nature but it must be obtained through appropriate industrial or laboratory procedures. It

presents a high level of hygroscopicity that causes the transformation of the alcohol into its

natural composition or azeotrope. The mixture of alcohol and water is a binary azeotrope,

having a distillate composition between 95° and 96°. This azeotrope is the common form

available on the market, from which it is possibile to obtain lower-grade solutions through

dilution. However, as regards dilution, when volumes of water and alcohol are mixed

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together, a rise in temperature and volumetric contraction of the resulting solution take place,

i.e. . Such volumetric contraction is about 3% (i.e., it can be

neglected only for not refined purposes). So, accurate methods of calculation are needed.

3. Calculations

3.1. Preparation of Alcohol Dilution Starting from Alcohol 95° and Water

Although there is no practical evidence of the volumetric additivity, the property of ponderal

additivity will be satisfied, obviously. Thus, the correct amount of alcohol characterized by a

certain grade and of water that are needed to obtain lower-grade, hydroalcoholic binary

mixtures can be computed by solving the well-known equation (Eq. 1):

Eq. 1

So, assume the preparation of 100L of alcohol 70% by volume starting from alcohol 95% by

volume or 92.41% by weight: consulting the alcoholometric tables of the European

Pharmacopoeia, we know that the alcohol 70° absolute density at 20 °C is equal to 885.56

kg/m3, corresponding to an alcohol 62.39% by weight. Therefore, we can write wconc = 62.39 ·

88.556 / 92.41 = 59.79 kg (or 73.69L considering its absolute density equal to 0.8114 g/mL).

Finally, assuming the specific gravity of water ≈ 1, we add 28.77L of purified water to obtain

100L (instead of theoretic 102.46L) .

Observe that, in the case of liquid substances, it is more convenient to express the obtained

results in terms of volume. According to the alcoholometric tables mentioned above, if the

density values are known, the corresponding volumetric values was trivially derived. As

already stated, the values in the Tables apply correctly to binary hydroalcoholic mixtures

only. Hence, if we need to obtain a solution of a certain compound in alcohol with different

grade from the azeotrope, the calculation must include alcohol and water only. The logical

sequence of steps to follow for the preparation of a hydroalcoholic solution - with a grade that

is known and lower than the one of the azeotrope - of a known compound available in a

known amount (in weight or in volume), whose resulting solution is characterized by its own

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known density are reported in Appendix B). Furthermore, as expected, it is possible to find

tables or internet platform useful – but not accurate - to calculate the amount of alcohol and

water to mix together to make a certain amount (in volume or in weight) of alcohol of various

dilutions.16,17

3.2. Determination of Alcoholic Grade of a Binary Alcohol/Water Mixture

Then, one may wonder how to determine the alcoholic grade of a binary, hydroalcoholic

solution that is obtained by combining equal volumes of water and alcohol. By using Eq.1, we

have (Eq. 2):

Eq. 2

By using alcohol not less than 94.9° and not more than 96.0° as evaluated at 15.56 °C and

consulting alcoholometric tables, the alcoholic grade ranges from 49.5 and 48.4. It is also

interesting to note that starting from an alcoholic grade of 96° and mixing equal volumes of

alcohol and water at the same temperature we obtained a grade higher than the half, as an

important consequence of the volumetric contraction that took place.18

Obviously, when the determination of the alcoholic gradation resulting from mixing alcohol

and water is the aim regardless the final volume of the solution, Eq. 2 is always applicable.

For example, if we mix 45.5L of alcohol 95° with 9.5L of water we obtain %w/w diluted = 73.5,

corresponding to alcohol 80 percent by volume.19

3.3. Determination of the Amount of Water for Diluting a given Volume of Alcohol

A further comment can address the practical issues related to alcohol dilution. It is common to

find tables that indicate the amount of water to add to a given volume of alcohol with a certain

grade, to obtain alcohol with a desired, lower grade. In this case, we can apply Eq. 1 in

volumetric terms, since it holds independently of the final volume of the binary,

hydroalcoholic solution that we want to obtain. By rewriting Eq. 1 in volumetric terms, we

have (Eq. 3):

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Eq. 3

From Eq. 3, the final volume of the hydroalcoholic solution resulting from the mixing and

that underwent the volumetric contraction, is given by (Eq. 4):

Eq. 4

Furthermore, knowing that multiplying the volume by its density value, the result obtained

represents the final weight of the diluted solution. Given this value, deriving the amount of

water that we need to add is straightforward (Eq. 5),

Eq. 5

or (Eq. 6)

Eq. 6

Then, fixing the volume of concentrated alcohol to 100 parts, Eq. 6 can be rewritten as (Eq. 7)

Eq. 7

This general equation, considering the %v/v of C2H5OH in alcohol equal to 94.9, the specific

gravity of alcohol 94.9°, and indicating d the specific gravity of the solution containing c in

the quality of the %v/vdilute of alcohol to be obtained, may also be written as the formula

represented in the USP.18

3.4. Mixing of Alcohol of Different Grades

Finally, in the Web it is possible to find questions like this: “How many liters of a 40%

alcohol solution must be mixed with 30 liters of a 70% solution to get a 60% solution?”. 20

Assuming no volume contraction and solving - eg applying alligation rule or by the stated

equation: 0.4x + 0.7·30 = 0.6 (30 + x) - we obtain the result of 15L. However, to respond

correctly, we have to consider: alcohol 40% by volume (with a specific gravity of 0.948)

corresponding to 33.30% by weight; alcohol 70% by volume (with a specific gravity of 0.886,

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as previously indicated) corresponding to 62.39% by weight; alcohol 60% by volume

corresponding to 52.09% by weight. Thus, we can write: 0.333x + 0.6239 · 26.58 = 0.5209 ·

(26.58 + x), with x = 14.53 L. This is the demonstration that only by mixing 14.5L of alcohol

40° with 30L of alcohol 70° we obtain the required alcohol 60° and, last but not least, an

amount of more than 1.5L of alcohol 40° every 100L of alcohol 60° to be prepared is saved.

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REFERENCES

1. Jensen WB. The origin of alcohol proof. J. Chem. Educ. 2004; 81: 1258

2. Yüksel A. Study of solvent composition effects on the protonation equilibria of various

anilines by multiple linear regression and factor analysis applied to the correlation between

protonation constants and solvatochromic parameters in ethanol-water mixed solvents. J

Solution Chem 2004 ; 33: 479-497

3. Herraez JV, Belda R. Viscous synergy of pure monoalcohol mixtures in water and its

relation to concentration. J Solution Chem 2004 ; 33: 117-129

4. Desai KGH, Kulkarni AR, Aminabhavi TM. Solubility of rofecoxib in the presence of

methanol, ethanol, and sodium lauryl sulfate at (298.15, 303.15, and 308.15) K. J Chem Eng

Data 2003; 48: 942-945

5. Owen SC Alcohol. In: Rowe RC, Sheskey PJ and Weller PJ (eds.) Handbook of

Pharmaceutical Excipients, 4th ed., Washington, DC, 2006 pp. 13-15.

6. Reilly WJ Jr. Pharmaceutical necessities. In: Hendrickson R (ed.) Remington: The Science

and Practice of Pharmacy, 21st ed., Philadelphia, PA, 2005 pp. 1080-1081

7. Young JA Ethyl alcohol. J Chem Educ 2004; 81: 1414

8. ICH Q3C Maintenance procedures for the guidance for industry Q3C impurities: residual

solvents. URL http://www.fda.gov/cder/audiences/iact/ICH_Q3C.htm Updated May, 7 2004

9. United States Pharmacopoeia 29 - National Formulary 24. USP Convention, Inc. Rockville,

MD, 2006 pp 3246-3247

10. European Pharmacopoeia, 5th Edition. Council of Europe. Strasbourg Cedex, F, 2004 pp.

519-530

11. Annex V – Federal Law on Weights and Measures. Available online

(http://www.trncpresidency.org/documents/text_annan_plan/AnIIIAt17_ANNEX_5_Alcohol

_Tables.pdf)

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12. Metrologische Reglementering. Available online

(http://mineco.fgov.be/organization_market/metrology/showole_nl.asp?cParam=9132)

13. Japanese Pharmacopoeia XIV Edition, English version. Society of Japanese

Pharmacopoeia, Yakuji Nippo's Publications, 2001 p. 914

14. Fahrenheit Graphics API - Wikipedia, the free encyclopedia. Available online

(http://en.wikipedia.org/wiki/Fahrenheit_graphics_API). Last modified 23 november 2004

15. Rees, JA, Smith, I., Smith, B. (eds.) Introduction to Pharmaceutical Calculation. London,

2001 pp. 61-89

16. Henley's Twentieth Century Book of Formulas, Processes and Trade Secrets. E-book

available online (http://www.librum.us/) 1912 p. 703

17. Dilution and Concentration. Available online (http://pharmcal.tripod.com/ch8.htm#alcdil)

18. United States Pharmacopoeia 29 - National Formulary 24. USP Convention, Inc.

Rockville, MD, 2006 p. 3268

19. United States Pharmacopoeia 29 - National Formulary 24. USP Convention, Inc.

Rockville, MD, 2006 p. 3107

20. Free Math On-Line Tutoring Services. Available online

(http://www.gomath.com/Questions/question.php?question=47231). Last accessed December

21, 2006

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GLOSSARY

ACGIH American Conference of Governmental Industrial Hygienist

API Active Principle Ingredient

CAS Chemical Abstract Service Registry Number

EP European Pharmacopoeia

NCE New Chemical Entity

ICH International Conference on Harmonisation of Technical Requirements for

Registration of Pharmaceuticals for Human Use

JP Japanese Pharmacopoeia

OSHA Occupational Safety and Health Administration

USP United States Pharmacopoeia

%v/v percentage of ethanol by volume

%m/m and %w/w percentage of ethanol by mass and percent weight to weight, respectively

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APPENDIXES

A) This formula is reported also in Annex V Federal Law on Weights and Measures -

Alcohol Tables - Federal Regulations of 2004, which holds for values of temperature ranging

between –20°C and +40°C (the explanation of this formula has been considered beyond the

aim of the present paper. However, see below if legend and numerical coefficients are

considered notable).

wheren = 5 m1 = 11 m2 = 10 m3 = 9 m4 = 4 m5 = 2

with the numerical coefficients A1= 9,982 012 300 · 10²

Ak [kg/m³]2 - 1,929 769 495 · 10² 3 3,891 238 958 · 10² 4 - 1,668 103 923 · 10³ 5 1,352 215 441 · 104 6 - 8,829 278 388 · 104 7 3,062 874 042 · 105 8 - 6,138 381 234 · 105 9 7,470 172 998 · 105 10 - 5,478 461 354 · 105 11 2,234 460 334 · 105 12 - 3,903 285 426 · 104

Bk 1 - 2,061 851 3 · 10-1 kg/ ( m³ · °C ) 2 - 5,268 254 2 · 10-3 kg/ ( m³ · °C² ) 3 3,613 001 3 · 10-5 kg/ ( m³ · °C³ ) 4 - 3,895 770 2 · 10-7 kg/ ( m³ · °C4 ) 5 7,169 354 0 · 10-9 kg/ ( m³ · °C5 )

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6 - 9,973 923 1 · 10-11 kg/ ( m³ · °C6 )

C1k kg/ ( m³ · °C ) 1 1,693 443 461 530 087 · 10-1 2 - 1,046 914 743 455 169 · 10¹ 3 7,196 353 469 546 523 · 10¹ 4 - 7,047 478 054 272 792 · 10² 5 3,924 090 430 035 045 · 10³ 6 - 1,210 164 659 068 747 · 104

7 2,248 646 550 400 788 · 104 8 - 2,605 562 982 188 164 · 104 9 1,852 373 922 069 467 · 104 10 - 7,420 201 433 430 137 · 10³ 11 1,285 617 841 998 974 · 10³

C2k kg/ ( m³ · °C2 ) 1 - 1,193 013 005 057 010 · 10-2 2 2,517 399 633 803 461 · 10-1 3 - 2,170 575 700 536 993 4 1,353 034 988 843 029 · 10¹ 5 - 5,029 988 758 547 014 · 10¹ 6 1,096 355 666 577 570 · 10² 7 - 1,422 753 946 421 155 · 10² 8 1,080 435 942 856 230 · 10² 9 - 4,414 153 236 817 392 · 10¹ 10 7,442 971 530 188 783

C3k k kg/ ( m³ · °C³ ) 1 - 6,802 995 733 503 803 · 10-4 2 1,876 837 790 289 664 · 10-2 3 - 2,002 561 813 734 156 · 10-1 4 1,022 992 996 719 220 5 - 2,895 696 483 903 638 6 4,810 060 584 300 675 7 - 4,672 147 440 794 683 8 2,458 043 105 903 461 9 - 5,411 227 621 436 812 · 10-1

C4k kg/ ( m³ · °C4 ) 1 4,075 376 675 622 027 · 10-6 2 - 8,763 058 573 471 110 · 10-6 3 6,515 031 360 099 368 · 10-6 4 - 1,515 784 836 987 210 · 10-6

C5k kg/ ( m³ · °C5 )

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1 - 2,788 074 354 782 409 · 10-8

2 1,345 612 883 493 354 · 10-8

B) Assume that 1.5 L of alcohol 65° containing an API at 7%w/v have to be prepared. The

final solution density, determined for example by pycnometric method, is assumed to be equal

to 1.05 g/mL. Based on these values, the weights of the final solution and that of the active

principle were 1.575 kg and 0.105 kg, respectively. Thus, the volume of the binary,

hydroalcoholic mixture corresponding to the desired amount of alcohol 65° is equal to 1.47

kg, value to be considered for the dilution calculations by solving Eq. 1, as previously

explained.

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