CHE105L Laboratory Manual PDF

1. Scientific Method: Accuracy and precision Introduction Precision and accuracy are crucial concepts in the laboratory. They determine how reliable and valid an experiment is. Many people confuse these two terms, but they have distinct meanings in the scientific method. Precision is a measurement...

1. Scientific Method: Accuracy and precision Introduction Precision and accuracy are crucial concepts in the laboratory. They determine how reliable and valid an experiment is. Many people confuse these two terms, but they have distinct meanings in the scientific method. Precision is a measurement of reproducibility and how close the measurements are to each other. The measurements do not have to be accurate to have a high precision. Accuracy on the other hand is defined by how close the measurement is to the true value. The true value can be a theoretical value that is determined by calculation or a reference value from a table or book. Fig.1 shows a visualization of the principle of accuracy and precision. Figure 3 Visualization of the concept of accuracy and precision. CHE105L Laboratory Manual Fall 2024 Page 13 of 66 Relative and percentage error is often used to determine the Accuracy of the measured values from the actual value by the following equation. 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 − 𝑎𝑐𝑡𝑢𝑎𝑙 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑒𝑟𝑟𝑜𝑟 = 𝑎𝑐𝑡𝑢𝑎𝑙 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 − 𝑎𝑐𝑡𝑢𝑎𝑙 %𝑒𝑟𝑟𝑜𝑟 = ∗ 100 𝑎𝑐𝑡𝑢𝑎𝑙 The two parentheses-like symbols   in the percentage error equation are the absolute value bars that remove any negative values from the difference of  Experimental-Actual. Example: ∣8−10∣=∣−2∣=2 The standard deviation of a set of measurements determines the Precision. The standard can be described as the amount of dispersion of a set of values. A low standard deviation (SD) indicates that the values have a lower dispersion and are closer to the average value. 𝑖𝑥𝑖 𝑎𝑣𝑎𝑟𝑎𝑔𝑒 = 𝑥 = 𝑛 The following equation can calculate the SD. n-1 is the degree of freedom of the system. 𝑑2 𝑆𝐷 = 𝑠 = ↔ 𝑑 = 𝑥𝑖 − 𝑥 𝑛−1 CHE105L Laboratory Manual Fall 2024 Page 14 of 66 Standard deviation can be calculated following the steps below 1. Find the average (x̄): by summing the measurements (xi) and dividing by the number of measurements (n). 𝑖𝑥𝑖 𝑎𝑣𝑎𝑟𝑎𝑔𝑒 = 𝑥 = 𝑛 2. Calculate the deviation (d): by subtracting the average from each measurement. d = x̄ - xi 3. Calculate the square of the deviation (d2): square each of these deviations to get d2 4. Calculate the sum of the square deviation:  d2 = d21 + d22 + d23 ….. 5. Calculate the standard deviation using the equation below 𝑑2 𝑆𝐷 = 𝑠 = ↔ 𝑑 = 𝑥𝑖 − 𝑥 𝑛−1 CHE105L Laboratory Manual Fall 2024 Page 15 of 66 Sample calculations A test object has been weighed on different balances. The measured data and the calculated statistical values are presented in the table below. Balance number Mass (g) = xi d = x̄ - xi d2 1 10.21 -0.03 0.0009 2 10.23 -0.01 0.0001 3 10.20 -0.04 0.0016 4 10.22 -0.02 0.0004 5 10.29 0.05 0.0025 6 10.25 0.01 0.0001 7 10.30 0.06 0.0036 The average is calculated by the following equation: i xi 71.70 x= = = 10.243 n 7 The s can then be calculated by the following equation: 𝑑2 0.009 𝑠= = = 0.0390 𝑛−1 7−1 The standard deviation is typically shown as ±s, which describes the range where 95 % of all results can be found. That concludes that the results should be shown as 10.243 g ± 0.039. CHE105L Laboratory Manual Fall 2024 Page 16 of 66 Procedure 1. Accuracy and precision of the weighing balances A. Obtain unknown material from the instructor. The Identification number of your unknown you can find on your working bench. B. Weigh the unknown with the two different balances and record your data (repeat 6 times) for each balance. C. Ask your instructor for the actual value of your unknown by checking the identification number that you have with the numbers on the board (to get the actual weight of the unknown). D. Calculate the percentage error by calculating the average (mean) of your readings of the weight of the unknown object. E. Calculate the percentage error of both balances and write your conclusion in the report. F. Calculate the standard deviation of each balance and write your conclusion in the report. 2. Accuracy and Precision of different volume measuring techniques. A. Weigh the small empty beaker (or a conical flask) that is placed on your bench with the analytical balance. Record the weight of the empty beaker. B. Add 10 ml of deionized water measured with a graduated cylinder into the beaker. C. Weigh the beaker with the water. Record the weight. And then discard the water D. Repeat step A-C 3 times. E. Empty the beaker and re-weigh the beaker. F. Add 10 ml of deionized water measured by a volumetric transfer pipette to the beaker. G. Weigh the beaker with water. Record the weight. Discard the water after each reading H. Repeat steps E-G 3 times. I. Calculate the percentage error and the standard deviation (s), of each data set. CHE105L Laboratory Manual Fall 2024 Page 17 of 66