The
Determination of the Pyruvic Acid Content
of Garlic Tissue Homogenates

Results
(continued)

The
relationship between molar concentration
and light absorption is governed by the
Beer-Lambert
law.
This can be conveniently expressed as,

log_{10} (I_{o} /
I) = ε c l or ε = A
/ c l

where,
log_{10} (I_{o} / I)
is the absorbance of the solution, (A_{M} )
c is the concentration of the solute (mol dm^{-3})
l is the path length of the sample (cm)
ε is the molar absorptivity (10^{-2} m^{2} mol^{-1})

Since
path length ( l ) and molar absorptivity
( ε ) are constants, the expression
predicts a linear relationship between
absorbance ( A_{M} ) and concentration
(c) (Figure1).

Figure
1. The linear relationship predicted
by Beer-Lambert's law

In
order to asses the extent of the linear
relationship between the known concentrations
of sodium pyruvate (c) and the corresponding
absorbance values (A_{W}), the
Pearson product moment correlation coefficient
( r ) was calculated
The r value of the regression line is given by the following formula:

A
value of r = 0.980 for the two sets of
data indicates a high positive correlation.
If the correlation coefficient is calculated
for successive data sets then it will
be seen that the values decline consistently
as concentration increases and suggests
that the loss of linearity is a result
of increasing solute-solvent interactions
that are not accounted for by the Beer-Lambert
law rather than practical errors such
as inaccurate preparation of standard
solutions or temperature effects. Subsequent
trendline analysis shows that a polynomial
curve fits the data accurately. The function
of the calibration curve shown in Figure
2 is a polynomial of the form,

y
= b+c_{1}x+c_{2}x^{2}+c_{3}x^{3}+c_{4}x^{4}………c_{8}x^{8}

which
when calculated and applied to the data
in Table 1 results in perfect positive
correlation ( r = 1.0).

Figure
2 Calibration curve of pyruvic acid

In
order to accurately determine the concentrations
of pyruvic acid from absorbance measurements
of unknown samples (P_{C} and
P_{T})
the function y = f(x) of the calibration
curve was calculated
as a 9th order polynomial and applied.
The results are shown in Tables
2 and 3. Because of the progressive
loss of linearity above 0.3 μM/ml
the use of the calibration curve has
been limited to values between 0 - 0.4 μM/ml.
This is a workable range for the measurements
recorded during this experiment.