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Common Pitfalls in Conversion of Units in Chemical Engineering Calculations
Posted on June 17th, 2016 by Sasha Gurke in Chemical Manufacturing Excellence
Chemical engineers need to clearly understand units of measurement to be able to apply them in so-called pseudo-empirical equations correctly as well as to convert, express, document and communicate the units in correspondence, operating instructions and publications.
Pseudo-empirical equations, found in many chemical handbooks, are basically physical equations that in reality are empirical because they require units of measurement for computation. A special care should be exercised when computing with these equations to avoid potentially costly errors.
Fortunately, unit inconsistencies and incorrect conversions rarely cause incidents of significant magnitude. Nevertheless, they can lead to errors and inefficiencies in process design and operation. Unit conversion is inevitable due to diversity of units used in engineering work. Data, equations and other information in scientific and engineering literature are not all reported in consistent units. Units that are presented in design calculations, process information or other communications should be clearly documented.
A good example are well-known formulas for conversion of solution concentrations expressed in different units of measurement. For instance, Mathcad and similar software for engineering calculations would produce an answer with correct units of measurement and, incredibly, with plausible results while converting molarity (ratio of the solute to the volume of solution) of an aqueous NaCl solution to its molality (ratio of the solute to the mass of solution). The formulas for this conversion can be easily found in a number of chemical handbooks and on the web (see Fig. 1).
We can copy an equation for calculation of molality (L) based on molarity (M) from the table shown in Fig. 1. To calculate, we need to input additional values: molecular mass of NaCl (mp) and solution density (q). Copy, input and get … an incorrect answer (see the 2nd line of the calculations in Fig. 2).
In the table shown in Fig. 1, the variable K is defined as a mass percent without disclosing whether it is a mass of the solution or a mass of the solvent. Clearly, this can be an area of concern as this variable can mean different values depending on the audience that you are presenting to. An analysis of this table reveals that it is the mass of solution and not the solvent. However, other cases are not so apparent, leading to calculation errors. For example, in many analytical chemistry handbooks, solubility in water is given as a ratio of the mass of solute to the mass of solvent by default, without an explanation. There are lots of these “defaults”. Take a temperature for example. Here is a typical problem: the temperature at the inlet of a heat exchanger is given as 25°C, find the temperature at the outlet if the temperature of the heat-transfer fluid in the heat exchanger increases by 5°C. The answer is 30°C. However, if this problem is input into Mathcad as is, the answer will be paradoxically 25°С + 5°С = 303.15°С. The answer can be explained by remembering that 5°С equal 5K but 25°С is equal 298.15K. Most users understand this default (Celsius scale and degree centigrade), found in many handbooks, but computers don’t. Also, in these calculations, users should account for the year of the temperature scale, 1968 or 1990, in which the temperature is given.
The problem here is that the equations in Fig. 1 have been adopted for the convenience of manual computation by using non-basic (“chemical”) units of measurement: concentration, density (g/cm3 instead of kg/m3), molar mass (g/mol vs. kg/mol), mass (g vs. kg), volume (cm3 vs. dm3), etc. The formula for computation of molality from molarity can be, of course, used as empirical by adding required units of measurement to obtain the correct result. However, it is better to go back to the initial physical formula by removing the coefficients (1000 – see line 3 in Fig. 2), realizing that 1000 is the number of grams in a kilogram and the number of centimeters cube in a liter, etc.
As a result, most practicing chemists and chemical engineers, when they need to convert concentration from one unit to another, try to avoid the existing formulas like those shown in the table in Fig. 1. Instead, they calculate using ratios. These ratios are not required, however, if you use Mathcad with modified classical formulas. There you can input and solve an algebraic equation linking, for example, the amount and mass of the solute for different units of concentration. Mathcad has a symbolic math engine that allows computing with the symbols of variables instead of their numerical values. Mathcad calculations with formulas for conversion of solution concentration from one unit to other using algebraic equations are shown in Fig. 3. This is a true improvement on handbook formulas. One can see both the formulas used for calculation and the corresponding physical law-based equations from which they are derived!
Same results (Fig. 4) can be obtained by imputing relevant formulas online using Elsevier’s Knovel Interactive Equations ((https://app.knovel.com/ie/#welcome).
Knovel Interactive Equations are based on a proprietary web-enabled math engine that supports a rapidly growing collection of several hundred validated equations and working examples in several subject areas, including Chemistry and Chemical Engineering, Electronics and Semiconductors, General Engineering, Mechanics and Mechanical Engineering, Metals and Metallurgy and Oil and Gas. Users can browse or search the collection, use the built-in Equation Solver to calculate, and export calculations for reports or sharing knowledge. They can also create a worksheet from scratch by combining text, math, images, and plots. The application has easy one-click access to a toolbox containing math functions, engineering units, programming structures, and math symbols used in engineering formulas.
Reference literature contains a huge number of pseudo-empirical formulas similar to those shown in the figures above. Using these formulas without proper adjustment can lead to computational errors but their simplification or modification so that more convenient units can be used is no longer required when using plug-ins such as Knovel Interactive Equations.
The author would like to thank Profs. V. Ochkov and E. Nikulchev for their contribution to this post.
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Engineering Technical Fellow, Elsevier