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Question: In a separation of phenols by reverse phase high performance liquid chromatography a group of environmental chemistry students were asked to examine which factors are important and to optimize the separation of 11 pollutants (phenol derivatives). Several factors are known to have an effect. 1). Proportion of methanol in the mobile phase (methanol: water). 2). Conc. of citric acid in the mobile phase 3). Conc. of acetic acid in the mobile phase. All variables are quantitative. The response is the chromatographic response function (CRF), a summation of the individual resolutions between pairs of peaks. Thus if the peaks are separated at the base line and the degree of peak tailings is small, the CRF will have a high value. In factorial design with the factors at two levels, it is usual to assign – and + to indicate the level of the factor. The – represents the low level and the + the high level. The levels used in the experiment were:P a g e | 4 The results Factors - + Acetic acid conc. (mol/dm3) 0.004 0.01 Methanol conc. (%) 70 80 Citric acid conc. (g/dm3) 2 6 Run Factors/Interactions CRF value 1 1 65 2 a 64.5 3 b 66 4 ab 65.7 5 c 64.3 6 ac 63.8 7 bc 66.9 8 abc 66.7 Use Yates method to find if any of the main effects are significant and provide your interpretations and conclusions
Yates' method is a statistical approach used to analyze the results of factorial design experiments. For your experiment, we are considering three factors: Acetic acid concentration, Methanol concentration, and Citric acid concentration and a function CRF Value. First, let me explain how to arrange your data using Yates' method. 1. Arrange your experimental CRF values according to the order of the experiments. In your case, the order of the experimental runs are a, b, ab, c, ac, bc, abc which corresponds to CRF values 64.5, 66, 65.7, 64.3, 63.8, 66.9, and 66.7 respectively. 2. Now, construct the study order by starting with ‘a’ and systematically adding each variable in alphabetical order. For each addition, reflect and jumble the order. Study order: a, b, ab, c, ac, bc, abc 3. The differences for Yates’ order are then calculated by subtracting each pair of results from the previous column. This is done pairwise, starting from the top of the column. The calculation details depends on the complete data. Next, Analysis of Variance (ANOVA) can be used to determine the significance of the variables. If a variable’s influence on the system response (CRF) is statistically significant, the p-value resulting from ANOVA will be less than 0.05. From a practical standpoint, if a factor does show significance, it means that controlling or changing that factor can have a sizable impact on the outcome of your experiment. Remember, this analysis provides mathematical evidence of the extent of impressiveness of each factor. However, interpreting the impact of these factors on the whole system and making an ultimate decision should be based not only on this statistical evidence, but also on the scientific judgement and expertise in the field of Chemistry or more specifically Environmental Chemistry in your case. And finally, it's always necessary to perform further confirmation experiments to validate the findings from factorial experiments. NOTE: The exact calculations couldn't be provided as there are missing data points. Typically, we should have eight runs for a three factor two-level factorial design. In your provided data, there's missing the first run with all factors at low level (-). Please make sure you have all the accurate data before starting your calculations.
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