Optimizing the Experimental Procedure

Optimizing the Experimental Procedure

In the presence of H₂O₂ and H₂SO₄, solutions of vanadium form a reddish brown color that is believed to be a compound with the general formula (VO)₂(SO₄)₃. Since the intensity of the color depends on the concentration of vanadium, the ab- sorbance of the solution at a wavelength of 450 nm can be used for the quantitative analysis of vanadium. The intensity of the color, however, also depends on the amount of H₂O₂ and H₂SO₄ present. In particular, a large excess of H₂O₂ is known to decrease the solution’s absorbance as it changes from a reddish brown to a yel- lowish color.

Developing a standard method for vanadium based on its reaction with H₂O₂ and H₂SO₄ requires that their respective concentrations be optimized to give a max- imum absorbance. Using terminology adapted by statisticians, the absorbance of the solution is called the response. Hydrogen peroxide and sulfuric acid are factors whose concentrations, or factor levels, determine the system’s response. Optimiza- tion involves finding the best combination of factor levels. Usually we desire a max- imum response, such as maximum absorbance in the quantitative analysis for vana- dium as (VO)₂(SO₄)₃. In other situations, such as minimizing percent error, we seek a minimum response.