CLINICAL LAB SCIENEC

CHAPTER 9: LABORATORY MATHEMATICS 209
Logarithms (Negative or Inverse)
Logarithms are not used often in today’s laboratory, but certain elements of
these mathematical functions are common in laboratory practice, although they
are not fully understood by many laboratory workers. An example of a common
laboratory calculation using logs of a number is the determination of the pH of
a solution (acidity or alkalinity). The pH of a solution is based on the numbers of
hydrogen ions (H + ) in the solution. Keep in mind that a neutral solution would
have a pH of 7.0, while an acid solution would have a pH less than 7.0 and an
alkaline solution would have a pH greater than 7.0. The character of a log (number
to the left of the decimal) may be positive or negative, and the mantissa is
the part of the logarithm to the right of the decimal point. Log tables are in the
appendix of this book, or may be derived from a calculator with that function.
A sample calculation of the pH of a solution is as follows:
Where “X” = log of 2.61 and
“N” = 5 (derived from the superscript of -5),
the equation for determining the pH of a given solution is:
pH = x – log N
The hydrogen ion concentration of a solution is 2.61 10 –5
From a logarithm table, N is equal to (0.4166) and x 5.
Therefore, the pH for the solution given is:
pH 5 – 0.4166 4.5834 (round to 4.58)
Laboratory and Scientific Systems of Measurement
Basically, two systems of measurement are used in the world today. One is the
English system, which the United States has used since the country was established.
The second is the metric system, which is much more accurate for scientific
work than the English system for specific measurements of all types. The
English system was based on the average anatomical features of the human body.
For instance, a yard was the distance from the nose to the end of an outstretched
hand, a foot was the length of a bare foot, and an inch was the length of one bone
in the finger. Because there are size differences between individuals, the amount
of material measured would vary with the size of the individual. Although this
system has been standardized, it remains difficult to use.
The International System of Units (SI) was developed in 1960 and is used in
science and for many procedures performed by the clinical laboratory. SI is an
advanced, more extensive measurement system based on the metric system. Built
on the convenience of the number 10, SI is derived from the meter-kilogram-second
system rather than the centimeter-gram-second system, where some variations in
units were present.
SI measurements are precise and reproducible measurements that provide consistency
in the diagnosing of diseases in patients as well as in the preparation of
quality control functions. Units of measurement are created as scientific advances
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