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

log₁₀ (I_o / I)  =  ε c l  or  ε  =  A / c l

where, log₁₀ (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 m² 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).

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+c₁x+c₂x²+c₃x³+c₄x⁴………c₈x⁸

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.

Results are shown in Table 4.