The Problem of “Chemistry” Units and
its Solution in Mathcad
http://twt.mpei.ac.ru/ochkov/v_ochkov.htm
Russian Version of the article
System SI is
legitimated almost everywhere. Chemical engineers cannot express hardness of
water in meq/L as this unit is outlawed. Demands of SI system forbid us to say,
“concentration of calcium in the solution is 1 eq/L”. But it is also forbidden to say, “Concentration
of calcium in the solution is 1 mole/L”. One must define what concentration, molar or
demal, is meant; i.e. define the base unit in the solution, calcium ions or
charges of calcium ions. Preterition can result in serious mistake: charges of
calcium ions are twice times as large as calcium ions themselves. For example,
if molar concentration of calcium in solution is 1 mole/L, demal (equivalent) –
2 mole/L. Old method (out of date but holding their positions) of uncovering is
to use two groups of units, similar in their physical - chemical essence but
different (as a rule) in value, mole (or, rather, g-mol, mg-mol, gram-molecule
and others) and equivalents (g.eq., mg.eq., and so on).
System SI abolished
units with equivalent ending and upholds moles and another way to point a base
unit in concentration defining. Its demands that permit moles and exclude
equivalents transfer concrete definition of the base unit from units to the
name of physical (or, rather, chemical, physical – chemical) value.
The author
wants to show that up-to-date computer mathematical programs supporting
physical quantities and their units, Mathcad, Maple, and Derive, cause a new
impulse to the problem of “moles – equivalents” and finally solve it.
As shown in
Figure 1 variable Cm holding molar concentration is entered into a
Worksheet. One can choose Unit from Insert menu to enter the variables with
assigned built-in units of volume (L, liter) and quantity of substance (moles).
User units
can be also defined in Mathcad including russified (see Figure 3, 4, 5, and 6).
Figure 2 shows Maple Help page with description of substance quantity unit. One
can assume that here is a mistake (after Freud): under the title Units only one
unit is listed. Probably, the equivalents were meant to be (g.eq. and others)
but only mole is kept recalling SI demands.
But Mathcad
is the most advanced in the field having the features
that let us solve the inveterate “chemical – metrological” problem easily
connected with “banishment” the equivalents from calculations. Further Mathcad
worksheets with characteristic “concentration” problems show these features.
Two variables, different (mmole/L, meq/L) but with similar name, are defined in
the worksheet based on condition that the same unit must express both the molar
and the equivalent concentration. The method, which is impossible from
conventional programming viewpoint, is applied using style of variables (see
Figure 3).
After
defining the variables one can solve the following water – chemical problem.
It is given
composition of natural water: concentration of basic ions expressed in mg/L.
Find hardness (total, carbonate, noncarbonate) and alcalinity.
To recur to
the problem of concentration units, the number of ions (molarity) and ion
charges (normality) must be expressed in one unit of substance quantity, mole,
not in two different units (in spelling not in essence), mole and equivalent,
as before. Mathcad worksheet has one feature to solve the problem easily; it is
possible to have different
variables but with similar name for concentration units (see Figure 3). There
are two variables in our calculation: mmole/L for the univalent ions and
mmole/L for bivalent ions. That let us type equivalent concentrations
(expressed in meq/L earlier, see area 5), in mmole/L too using only molar
concentrations (Figure 4 shows area 6 where variables with default units are
typed). The kernel of the calculation is that a user changes default unit of
the result, mole/m3, for mmole/L in the area 5, different for
alcalinity (the valence of bicarbonate ion is 1) and hardness (the valence of
calcium and magnesium is 2). The ‘2’ is present evidently in the reaction when
water being heated scales with precipitation of calcium carbonate and magnesium
hydroxide and simultaneous removing of carbon dioxide.
Ña2+ + 2 HCO3- → CaCO3↓
+ CO2↑+ H2O (1)
Mg2+ + 2
HCO3- → Mg(OH)2↓ + 2 CO2↑ (2)
Comment.
Anions of the weak acids (usually carbonic acid in natural water) give
alcalinity that is not alkali yet but so to speak future alkali produced when
the water is boiled.
Na+ +
HCO3- → NaOH + CO2↑ (3)
Alkalinity
of natural water is an important protective factor, which define buffering of a
solution; if an acid or an alkali is added into water, pH of a solution is
nearly constant due to displacement of carbonate equilibrium. Very pure water
(for example, in Baikal Lake or rainwater) without buffering is very sensitive
to the contaminations (sulfur or/and nitric oxides) that result to sharp
decreasing of pH value and serious environmental consequences.
Computer
calculating systems supporting physical quantities let us reconsider strict
requirements of SI concerning units. Moreover, Maple has not only built-in
units allowed temporarily in calculations but even out-of-date and peculiar
units settled down in some scientific and engineering fields and rejected hard
by SI.
Specialists
are believed to grasp themselves what units are better to use in calculations.
Dictates are not appropriate; only recommendations are taken into
consideration.
Figure 5
shows converting of concentrations with “illegal”, but as with meq/L, widely
used equivalent unit – normality. A reader can notice also that the result
shown in Figure 4 was duplicated in different units (legal and out-of-date).
The author works at Department of Technology of
Water and Fuel (http://twt.mpei.ac.ru) of
Moscow Power Engineering Institute (www.mpei.ru).
The department often receives requisitions from different places of Russia. The
problem is: if the boiler-house use water with certain hardness will the
boilers operate. If hardness is expressed in meq/L it is clear but some doubts
are cast if it is in mmole/L (that is seldom). The right value can be twice as
much as written. An alternative version can have serious consequences – a
frozen settlement in winter.