Quantifying human error in visual endpoint detection during acid-base titration: An instructional study using independent student datasets

Visual indicators remain common in introductory analytical chemistry laboratories, but they also introduce subjectivity during endpoint recognition. In this study, human-observed endpoint variability was quantified by merging two independent student-generated triplicate datasets for the standardization of sodium hydroxide against 0.1000 M hydrochloric acid. Across six titrations, calculated NaOH molarity values ranged from 0.0996 to 0.1081 M, with a combined mean of 0.1041 M, standard deviation of 0.0035 M, relative standard deviation of 3.36%, and a 95% confidence interval of 0.1004-0.1078 M. Dataset-specific means were 0.1047 M and 0.1035 M, and no statistically significant difference was detected between the two small instructional datasets (Welch t-test, p = 0.732). The results demonstrate that visually judged endpoints can produce measurable trial-to-trial variability even when the same stoichiometric framework is followed. This manuscript therefore offers a classroom-ready model for teaching precision, bias, uncertainty, observer effects, and the analytical advantages of more objective endpoint detection.