# Accuracy and Precision of Laboratory Glassware: Determining the Density of Water

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3 measuring devices based on laboratory data. Our quantitative measure of accuracy is called percent error. Percent Error (Experimental Value - Theoretical Value) Theoretical Value x 100 So, for each measuring device, using the averages calculated previously, we can calculate a percent error. If you use the values from Device A: Percent Error x % The lower the percent error is, the more accurate the measuring device is. In this case the mean for Device A had a 16% error from the true value of the length of the metal rod. (Notice that when calculating percent error, we used some extra significant figures from our calculation of the mean. This is done to minimize rounding errors; errors that come from rounding and then using a rounded number in the next calculation. Remember it s always best to round only when you need to report a number, as in a table. If you need to use a calculated number in another calculation, use the unrounded number.) Device A Device B Device C Percent Error 16% 0.5% 0.5% You re probably wondering why the percent error for device A has two significant figures while the others only have one. If you look at the formula for percent error, you will notice that the first step is subtraction. Thus, we must use the addition/subtraction rule. So, for device A, when we take (unrounded average) and subtract 1.23 we get Since the numbers that are being subtracted each has two sig figs after the decimal point, based on the addition/subtraction rule, the answer can only have two sig figs after the decimal point: Then, once we divide the answer by 1.23 and multiply by 100 (an exact number), we have a number with two sig figs, divided by a number with three sig figs. Based on the multiplication/division rule, our answer can only have two sig figs. The same logic gives only one sig fig for device A and B (do the calculations step by step to see for yourself). Precision is a measure of how close repeated measurements are to each other. Like accuracy, we can describe precision in qualitative terms (such as high precision and low precision). So, which measuring device is best to use? We want a device that is both accurate and precise. Based on our experimental data, using the percent error we calculated, we can see that Devices B and C have better accuracy than A. Therefore, we will need to look at the precision of these devices in order to make our final selection. Looking at the measurements, we can see that Device B has a higher degree of precision (lower standard deviation) than C. Therefore, Device B has the best combination of accuracy and precision. GCC CHM151LL: Accuracy and Precision of 2013 GCC Page 3 of 9

5 **Lab Notebook** In your lab notebook, create a separate data table for each piece of glassware used. Be sure to label and title each table so you can easily identify the information contained in each one. (For example, the table for the 150 ml beaker might look like the following: Table 1. Volumes and masses for 150 ml beaker Mass of empty beaker: Temperature of water: Trial Mass of beaker with water Mass of water Volume of water Density Procedure: Part I 1. Obtain approximately 100mL of de-ionized in a 250mL beaker. Place the beaker on a folded piece of paper towel on the bench. Place a thermometer in the water. Record the temperature after there is no change in temperature for at least ten minutes. This water will be used for all of the experiments. Find the CRC Handbook of Chemistry and Physics located in your laboratory. Using the CRC Handbook, look-up and record the following information: The density of water at the exact temperature you measured (notice that the units in the book are kg m -3, which is the same as kg/m 3. You will need to convert to g/ml. Show this work in your lab notebook. Remember 1mL = 1cm 3 ). You will also need to record the following values from the CRC Handbook to answer postlab questions: o The density of water ten degrees higher than the temperature you measured. o The temperature at which the density of water is the highest. 2. Obtain one of the pieces of glassware listed the Table 2. Ensure that it is dry and determine its empty mass using an analytical balance. Make sure all of the doors of the balance are closed, as air currents in the lab can affect the balance. Record its mass in the Data Table. Remove the glassware from the balance. Table 2. Laboratory glassware manufactured to contain specific volumes Type of glassware 150mL beaker 100mL graduated cylinder Volume of de-ionized water to add 50mL 50mL GCC CHM151LL: Accuracy and Precision of 2013 GCC Page 5 of 9

6 50mL volumetric flask* Kitchen measuring cup** 50mL 50mL 10 ml graduated cylinder 10mL * can only measure a single volume ** actually made of plastic 3. From the 250mL beaker, transfer a little less than the volume of water listed for the glassware from Table 2. Use a plastic disposable pipette to add the water drop-wise until the bottom of the meniscus is on the line that corresponds to the volume listed in Table 2. If too much water was added, remove the extra water using the plastic disposable pipette. Wipe down the outside and bottom of the beaker in case any water was spilled during the transfer. 4. Using the same balance as before, record the mass of the glassware with the added water. 5. Pour the water from the glassware back into the 250mL beaker and repeat steps 3-4 two more times with the same piece of glassware. You should have a total of three trials. You will use the empty mass from step 2 for all three trials. 6. You will then repeat the process (three trials each) with each piece of glassware listed in Table 2. Procedure: Part II The proper use of a pipette is a skill that takes time and practice to perfect. Therefore, you should perform at least three practice runs of filling the pipette and delivering the water back to the 250mL beaker. For the glassware in Table 3, the glassware will be used to transfer water to a beaker for weighing. 1. Obtain a dry 50mL beaker and determine the mass of the dry, empty container. 2. Obtain the glassware listed in Table 3. For each type of glassware, deliver the indicated volume to the 50mL beaker. For the buret, record initial and final buret readings in a table along with the amount of water delivered to the beaker. Weigh the beaker with the water. 3. Repeat the process so that you have three trials with each type of glassware. Table 3. Laboratory glassware manufactured to deliver specific volumes Type of glassware 50mL buret 10mL volumetric pipette* Volume of de-ionized water to dispense 10mL 10mL * can only measure a single volume GCC CHM151LL: Accuracy and Precision of 2013 GCC Page 6 of 9

7 Calculations Complete your data tables by calculating the mass of water for each trial. Using this value, calculate the density of water in units of grams per milliliter (g/ml) for each trial using the formula for density (density = mass/volume). **Lab Notebook** Next create a Summary Table that summarizes the percent error for each piece of glassware. List the glassware in order of the smallest percent error (best) to the largest percent error (worst). Summary Table Rank based on % error Glassware % Error GCC CHM151LL: Accuracy and Precision of 2013 GCC Page 7 of 9

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