A number of methods have been developed to determine the composition of a binary mixture spectrophotometrically. Most of these are directed at mixtures where one component can be isolated from the other or they require a Beer’s law experiment to measure the molar absorptivity of each of the substances in the mixture. Vernier consultant, Walter Rohr, came across an article published in the February 1989 Journal of Chem Ed that described a method of resolving mixtures with overlapping spectra without determining molar absorptivities or complicated mathematics. The method developed by Blanco called Multi-Wavelength Linear Regression Analysis, or MLRA, allows the composition of a binary mixture with overlapping spectra to be resolved with only three measurements—the absorbance of a standard solution for each component, and the unknown mixture itself.
Walt applied this method to the analysis of the metals in a United States five-cent coin. To this end, Walt used a Vernier Spectrometer to capture the absorption spectra of a nickel standard solution, a copper standard solution, and solution containing part of a U.S. five-cent coin. (See Figure 1.)
Figure 1 – Absorbance spectra of nickel, copper and nickel coin
Using the Vernier Logger Pro software, Walt created calculated columns for the ratios A(copper)/A(nickel) and A(coin)/A(nickel) as prescribed by the MLRA procedure. Walt plotted the resulting data and determined the equation for the line of best fit. (See Figure 2.)
Figure 2 – Linear regression analysis of absorbance ratios
The MLRA procedure comes down to this—the concentration of the copper in the coin solution will equal the slope times the concentration of the copper standard solution. Likewise, the concentration of the nickel in the coin solution equals the intercept times the concentration of the nickel standard solution.
Walt’s results indicate the coin contains 75.8% Cu and 25.7% Ni. The U.S. mint claims a nickel coin is composed of 75% copper and 25% nickel. Walt’s data are within acceptable limits of error for absorption spectroscopy, especially considering that both of the metal standards he used were of unknown purity.
Walt has also used this technique to analyze red food dye (a mixture of red # 3 and red #40), and Pína Colada Kool-Aid (a mixture of yellow #5 and yellow #6).
Download Walt’s full write up of this activity (271 KB PDF)