Alcohol Gauging and Blending Calculations
Data for the density of ethanol-water mixtures is very widely used in industry and several methods of storing and presenting this data are used, each with its own advantages and disadvantages. The most flexible, powerful and accurate method is to use an ethanol density calculator application like AlcoDens. This allows the density to be calculated as a function of both the strength and temperature of the mixture.
A computer program can work with ethanol density in many different units of measurement, and AlcoDens includes kg/m³, g/cm³, kg/liter, g/liter, lb/ft³, lb/US gallon, lb/Imp gallon and SG relative to water at 60°F. If the ethanol density is known in any of these units AlcoDens can be used to determine the strength of the ethanol-water mixture over the range of temperatures from -20°C to 100°C (-4°F to 212°F). AlcoDens can also be used in reverse mode, i.e. if you know the strength you can work back to the ethanol density. The strength or concentration of an ethanol-water mixture can be expressed in several different ways. The most usual methods are alcohol percentage by volume (%ABV), alcohol percentage by mass (%Mass), molar percentage and alcohol proof. All of these options are included in AlcoDens, which makes it possible to convert between these different strength options as well as determining the density over the full strength range from 0% to 100% (0 to 200 Proof).
This screenshot shows the AlcoDens ethanol density calculator in action. It can calculate the density for a known strength, or determine the strength for a known density. Click on the "Home" option in the menu above to get more details on AlcoDens and to download a free trial copy.
The relationship between ethanol density and strength can also be shown on a graph (see below). An advantage of using a graphical representation is that the "big picture" behavior is seen very easily. It is immediately clear from the graph below that the relationship between the mixture composition, expressed in %ABV terms, and the ethanol density is not linear. This non-linearity is caused by the shrinkage that occurs when ethanol and water are mixed. The non-linearity is not obvious when using a computer program or tabulated data to determine the ethanol density, even though the density vs composition behavior is accurately represented.
Unfortunately the graphical method of representing the ethanol density has several disadvantages. Unless the graph is very big it is impossible to read the data accurately. Also, each graph can only display the data in one unit of measurement (eg kg/m³) and for one type of concentration. Multiple temperatures can be accommodated by drawing more than one curve on each graph, but this results in interpolation being required for values between the displayed temperatures.
Plotting a graph makes the non-linear relationship between ethanol density and strength obvious. This non-linearity is the reason for the inaccuracy of simple proportion-based methods for ethanol blending calculations (eg Pearson's Square).
Another alternative for presenting ethanol density data is to use a table. A small excerpt from such a table is shown below. A table allows the ethanol density data to be given with much greater precision than when shown in a graph. The disadvantage of tables of density data is that huge tables are required to cover the practical ranges of temperatures, concentrations and ethanol densities with sufficient accuracy. This results in book-sized publications like the Practical Alcohol Tables or else partial tables like the American TTB Tables which give full accuracy at only one temperature and then require correction factors to be applied for other temperatures.
Tables of ethanol density have the same disadvantage as graphs in that they usually include only one set of units. In order to cover other sets of units for the density and strength data the entire table has to be reproduced.
In times gone by, detailed tables of ethanol density were the only way to achieve sufficient accuracy to satisfy trade and tax regulations. Fortunately we now have computer programs like AlcoDens that allow us to easily achieve the required accuracy.
Tables of ethanol density data achieve high precision at the published combinations of strength and temperature. But in order to achieve similar precision between the published points it is necessary for the tables to include very closely spaced data points so that simple interpolation methods remain accurate. This results in tables that are useably accurate being very large. (Note that the example given here is a small extract only.)
Ethanol density data is frequently used in the alcoholic beverage and industrial chemical industries. The most common use of this data is in determining the strength of ethanol-water mixtures. Measuring the density of the ethanol sample is much quicker, and requires much less expensive equipment, than using chromatographs or wet chemistry methods and the measured density is easily converted to a strength.
Knowing the relationship between ethanol density and strength also allows conversion between the different methods of expressing the strength of ethanol-water blends. These conversions are frequently required because plant and process design calculations require the strengths to be expressed in mass or molar terms, but for historical reasons most trade is done in volumetric strength terms (eg % ABV or proof).
In the alcoholic beverage industry the potable ethanol is purified by distilling it to a strength of approximately 95 % ABV. This allows the impurities to be removed efficiently, but the product cannot be consumed at these high concentrations and it is necessary to dilute the ethanol down to a safe level. In most countries the tax on potable ethanol is at least an order of magnitude higher than the production cost of the ethanol and this makes it very important to be able to blend the high strength spirit very accurately with water - you don't want to be caught cheating the tax man, but you also don't want to pay him more than his share.
As was shown above where the ethanol density data was presented as a graph, the relationship between ethanol density and strength is not linear. This greatly complicates the blending calculations and they can only be done properly if accurate ethanol density data is available. When less accurate methods are used it results in time-consuming trial and error methods being used to achieve the correct blend strength.
The most common method for measuring the density of ethanol-water blends is with an hydrometer - often called an alcoholmeter when it is calibrated with a proof or % ABV scale. Although the basic hydrometer was invented about 1500 years ago it is still used in many distilleries and laboratories around the world. They are relatively cheap and can be made very accurate by making the stem narrow and covering only a small range of density. An hydrometer is calibrated for a specific temperature, but if the relationship between ethanol density and temperature is known it is possible to correct the hydrometer reading when it is used at other temperatures.