Accuracy and Precision of Laboratory Glassware (Adapted from GCC CHM151LL Laboratory Manual , NSF-PACT Collection of Laboratory Activities, & TAMU Math Skills Review ) 1.0 INTRODUCTION 1.1 Objectives After completing this experiment, the student will be able to: Use various volumetric glassware. Use the density formula. Determine which volumetric glassware contains or delivers the most accurate volume. Determine the percent error. 1.2 Background During the semester in the general chemistry lab, you will encounter various pieces of laboratory glassware. Some of these pieces (e.g. beakers, Erlenmeyer Flasks) are used primarily to hold liquids during experiments. Upon closer inspection, you will also notice that they have graduations on the side to measure volumes. Both glassware mentioned above can measure volumes. Why do we have so many pieces of glassware if they all do the same basic job of measuring volumes? Laboratory glassware can generally be divided into two main types based on how they measure volumes: those that are manufactured to contain certain volumes those that are manufactured to deliver certain volumes The first thing to realize is that there is no such thing as a perfect measurement. Even when using expensive lab equipment there is some degree of uncertainty in measurement. The general rule of thumb is you can estimate one more digit past the smallest division on the measuring device. If you look at a 10 mL graduated cylinder, for example, the smallest graduation is tenth of a milliliter (0.1 mL). That means when you read the volume, you can estimate to the hundredths place (0.01 mL). You must use the bottom of the meniscus to determine the volume in the 10 mL graduated cylinder. Since the smallest division (graduation) is a tenth of a milliliter, we can estimate to a hundredth of a milliliter (0.01). Some glassware such as volumetric flasks and volumetric pipets only have a single line to indicate volume. They are made to measure just one specific volume. In the case of the glassware used in general chemistry lab, both the 10 mL volumetric pipet and 50 mL volumetric flask will have two significant figures (sig figs) after the decimal point (i.e. 10.00 mL and 50.00 mL), for a total of four significant figures each. For the 150 mL beaker assume that 50. mL has two sig figs (it will not be obvious based on the volume markings). 1.3 Recording and Analyzing Lab Data If a metal rod has a known length of 1.23 cm and you measure its length using three different measuring devices (A, B, and C), you obtain the following data. 0 1 2 3 4 Data Table: Measured Lengths of Device A, B, and C Data Table: Measured Lengths of Device A, B, and C Data Table: Measured Lengths of Device A, B, and C Data Table: Measured Lengths of Device A, B, and C NaN NaN Device A (cm) Device B (cm) Device C (cm) Device C (cm) Trial 1 1.43 1.24 1.19 1.19 Trial 2 1.43 1.23 1.23 1.23 Trial 3 1.43 1.25 1.22 1.22 Trial 4 1.42 1.22 1.26 1.26 The first thing we want to do is to find an average from our multiple trials. As you may know, there are different types of averages. The types you may have heard about in your math classes are most likely mean , median , and mode . Many times, when we say “average” or “simple average” we are actually referring specifically to the mean . A mean is calculated as follows: add all of the values together and divide by the number of values. For example, for device A: The “2” is underlined in the unrounded answer above because based on the addition and division rules, when the answer is rounded, it should have three significant figures. If I want to use the unrounded number for another calculation in the future, the underline will remind me of the significant figures that number actually has. The “4” that is in the denominator of the equation is an exact number and therefore has an infinite number of significant figures. Using the same formula, we can then calculate a mean for the other measuring devices: 0 1 2 3 4 Data Table: Average Lengths of Device A, B, and C Data Table: Average Lengths of Device A, B, and C Data Table: Average Lengths of Device A, B, and C Data Table: Average Lengths of Device A, B, and C NaN NaN Device A (cm) Device B (cm) Device C (cm) Device C (cm) Average 1.43 1.24 1.23 1.23 How do we describe how “good” these measuring devices are based on our measurements and means? There are two ways we can describe these measurements – by their accuracy and precision . Accuracy is a measure of how close your measured value is to the true value or other standard. Although sometimes we use qualitative (verbal) words to describe the accuracy (such as good accuracy and bad accuracy), a quantitative (numerical) measure is more useful when comparing measuring devices based on laboratory data. Our quantitative measure of accuracy is called percent error . So, for each measuring device, using the averages calculated previously, we can calculate a percent error (remember the known length of the rod is 1.23 cm). If you use the values from Device A: The lower the percent error, the more accurate is the measuring device. 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.) 0 1 2 3 4 Data Table: Average Lengths of Device A, B, and C Data Table: Average Lengths of Device A, B, and C Data Table: Average Lengths of Device A, B, and C Data Table: Average Lengths of Device A, B, and C NaN NaN Device A (cm) Device B (cm) Device C (cm) Device C (cm) Percent Error 16% 0.5% 0.5% 0.5% The percent error for device A has two significant figures. Look at the formula for percent error. The first step is subtraction. Use the addition/subtraction rule for the numerator. For device A, take 1.4 2 75 (unrounded average) and subtract 1.23 to calculate 0.1975 as a result. The numbers that are being subtracted each have two significant figures after the decimal point. Based on the addition/subtraction rule, the numerator can only have two sig figs after the decimal point: 0.1 9 75. Once we divide the answer by 1.23 and multiply by 100 (an exact number), the result is a number with two sig figs, divided by a number with three sig figs. Based on the multiplication/division rule, the final answer can only have two sig figs. The same logic yields only one significant figure for the percent error for devices 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) or quantitative terms. Precision is usually expressed in terms of the deviation of a set of results from the arithmetic mean of the set. The standard deviation (S) is a measure of how precise the average is, that is, how well the individual numbers agree with each other. The relative standard deviation (RSD) is often times more convenient. It is expressed in percent and is obtained by dividing the standard deviation by the mean, and multiplying by 100 to express as a percentage. So, for each measuring device, using the averages calculated previously, we can calculate a standard deviation and relative standard deviation (remember the known length of the rod is 1.23 cm). If you use the values from Device A: Our final result for Device A can be written as 1.43 ± 0.005 or 1.43 ± 0.4% The lower the standard deviation and RSD are, the more precise the measuring device is. 0 1 2 3 4 Data Table: Average Lengths of Device A, B, and C Data Table: Average Lengths of Device A, B, and C Data Table: Average Lengths of Device A, B, and C Data Table: Average Lengths of Device A, B, and C NaN NaN Device A (cm) Device B (cm) Device C (cm) Device C (cm) RSD 0.4% 1% 2% 2% 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. Errors in general chemistry are classified as systematic (determinate) and random (indeterminate). A systematic error is caused by a defect in the analytical method or by an improperly functioning instrument or analyst. A procedure that suffers from a systematic error is always going to give a mean value that is different from the true value. The measured value is described as being biased high or low when a systematic error is present. Systematic errors can be avoided. Sources of systematic errors include spectral interferences, chemical standards, glassware, and analytical balances where an improper calibration or use will result in a systematic error. For example, a dirty glass pipet will always deliver less than the intended volume of liquid. Random errors are unavoidable. They are unavoidable due to the fact that every physical measurement has limitation, i.e., some uncertainty. Using utmost care, the chemist can only obtain a weight to the uncertainty of the balance or deliver a volume to the uncertainty of the glassware. For example, most four-place analytical balances are accurate to ± 0.0001 grams. Therefore, with care, a chemist can measure a 1.0000 gram weight (true value) to an accuracy of ± 0.0001 grams where a value of 0.9999 to 1.0001 grams would be within the random error of measurement. A truly random error is just as likely to be positive as negative, making the average of several measurements more reliable than any single measurement. 1.4 Using Burets and Pipets Using a buret Filling the buret: Close the stopcock. Use the beaker of water and a funnel to fill the buret about 1 mL above the “0” mark. Place a container under the buret tip and open the stopcock slowly. The buret tip should fill with solution, leaving no air bubbles. If the tip does not fill with solution, ask the instructor for help. Continue to let out solution until the liquid level is at “0” or below. Reading the buret: Record the volume by noting the bottom of the meniscus. (Be sure that the meniscus is at eye level). If this reading is exactly “0,” record 0.00 mL. Otherwise, count the number of markings between each number, and estimate to the nearest 0.01 mL. Using a pipet Identify and move a receiving container close to the pipet to minimize time and distance the pipet needs to travel. Do not pipet by mouth. Different pipet bulb styles are available. Some work differently. These instructions are for pipet bulbs that provide suction and do not form full seals on the top of the pipet. Place the pipet bulb loosely on the top of the pipet. Place it just far enough on the pipet to get an air-tight seal. Position the tip of the pipet below the liquid level in the beaker. Apply suction and fill the pipet well above the calibration line (etched or marked above the wide center section of the pipet). Take care not to get liquid into the pipet pump. Slide the bulb off the pipet while quickly sliding your index finger or thumb over the top of the pipet. Move your finger slightly and rotate the pipet to allow the liquid level to drop to the calibration line on the pipet. Stop the flow, and move the tip of the pipet into a position over the receiving container. Remove your finger and allow most of the liquid to drain out. Then hold the tip of the pipet against the inside of the container for about 10 seconds to allow more liquid to drain. Do not remove the small amount of liquid remaining in the tip. Pipets are calibrated to retain this amount. 2.0 SAFETY PRECAUTIONS AND WASTE DISPOSAL Goggles are not required for this experiment. Be careful not to spill water on the balances. Water can go down the drain. If glass should break, do not pick it up with bare hands. Use a dust pan and broom and wear leather gloves. 3.0 CHEMICALS AND SolutionS 0 1 2 3 Chemical Concentration Approximate Amount Notes Laboratory water Pure 100 mL Be sure to use laboratory water 4.0 GLASSWARE AND APPARATUS 0 1 250 mL beaker 50 mL beaker 150 mL beaker 10 mL graduated cylinder 100 mL graduate cylinder 50 mL buret 50 mL volumetric flask 10 mL graduated pipet Thermometer Balance 5.0 PROCEDURE 5.1 GLASSWARE MEANT TO CONTAIN SPECIFIC VOLUMES Obtain approximately 100 mL of laboratory water in a 250 mL 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. Look-up and record the following information using the CRC Handbook of Chemistry and Physics located in your laboratory or the excerpt available on Canvas. The density of water at the exact temperature measured. The density of water ten degrees higher than the temperature measured. The temperature at which the density of water is the highest. When using the CRC Handbook of Chemistry and Physics notice that the units are kg∙m -3 , which is the same as kg/m 3 . You will need to convert to g/mL. Remember 1mL = 1cm 3 . When using the excerpt available on Canvas, whole degrees are listed down the left hand side of the table, while tenths of a degree are listed across the top. First, find the whole degree by searching down the left hand column until you reach your desired whole number. Then slide across that row until you reach the column corresponding to your tenth of a degree. Obtain one of the pieces of glassware listed below. Use a top-loading balance as directed by the instructor (if using a balance with doors, make sure all of the doors of the balance are closed, as air currents in the lab can affect the readings). Ensure that the glassware is dry and determine its empty mass. Record its mass in the Data Recording Sheet. Remove the glassware from the balance. 150 mL beaker 25 mL graduated cylinder 50 mL volumetric flask 50 mL beaker 10 mL graduated cylinder From the 250 mL beaker, transfer a little less than the volume of water listed for the glassware below, one piece of glassware at a time. Use a plastic disposable pipet to add the water drop-wise until the bottom of the meniscus is on the line that corresponds to the desired volume. If too much water was added, remove the extra water using the plastic disposable pipet. Wipe down the outside and bottom of the glassware in case any water was spilled during the transfer. 150 mL beaker – 50 mL laboratory water 25 mL graduated cylinder – 12 mL laboratory water 50 mL volumetric flask – 50 mL laboratory water 50 mL beaker – 10 mL laboratory water 10 mL graduated cylinder – 10 mL laboratory water Using the same balance as before, record the mass of the glassware with the added water. Record its mass in the Data Recording Sheet. Pour the water from the glassware back into the 250 mL beaker and repeat steps 3-4 two more times with the same piece of glassware. You should have a total of three trials for each piece of glassware. You will use the empty mass from step 2 for all three trials. You will then repeat the process (three trials each) with each piece of glassware listed. 5.2 GLASSWARE MEANT TO DELIVER SPECIFIC VOLUMES The proper use of a pipet is a skill that takes time and practice. Try at least three practice runs of filling the pipet and delivering the water back to the 250 mL beaker. For the glassware listed below, the glassware will be used to transfer water to a beaker for weighing. 50 mL buret 10 mL volumetric or graduated pipet Obtain a dry 50 mL beaker and determine its mass. For each type of glassware, deliver 10.00 mL to the 50 mL beaker. For the buret, record initial and final buret readings in a table along with the amount of water delivered to the beaker. Using the same balance as before, record the mass of the beaker with the added water. Record its mass. Repeat the process so that you have three trials with both the buret and the pipet. 6.0 DATA RECORDING SHEET 0 1 2 3 4 Last Name First Name NaN Partner Name(s) Date Table 1. Volumes and masses for 150 mL beaker Mass of empty beaker: _____________________Temperature of water: _______ Volume of water: ______________Theoretical density of water: ______________ 0 1 2 3 Trial Mass of beaker with water (g) Mass of water (g) Calculated Density (g/mL) 1 NaN NaN NaN 2 NaN NaN NaN 3 NaN NaN NaN Table 2. Volumes and masses for 25 mL graduated cylinder Mass of empty cylinder: _____________________Temperature of water: ______ Volume of water: _________________Theoretical density of water: ___________ 0 1 2 3 Trial Mass of cylinder with water (g) Mass of water (g) Calculated Density (g/mL) 1 NaN NaN NaN 2 NaN NaN NaN 3 NaN NaN NaN Table 3. Volumes and masses for 50 mL volumetric flask Mass of empty flask: _____________________Temperature of water: _________ Volume of water: ___________________Theoretical density of water: _________ 0 1 2 3 Trial Mass of flask with water (g) Mass of water (g) Calculated Density (g/mL) 1 NaN NaN NaN 2 NaN NaN NaN 3 NaN NaN NaN Table 4. Volumes and masses for 50 mL beaker Mass of empty beaker: _____________________Temperature of water: _______ Volume of water: __________________Theoretical density of water: __________ 0 1 2 3 Trial Mass of beaker with water (g) Mass of water (g) Calculated Density (g/mL) 1 NaN NaN NaN 2 NaN NaN NaN 3 NaN NaN NaN Table 5. Volumes and masses for 10 mL graduated cylinder Mass of empty cylinder: _____________________Temperature of water: ______ Volume of water: __________________Theoretical density of water: __________ 0 1 2 3 Trial Mass of cylinder with water (g) Mass of water (g) Calculated Density (g/mL) 1 NaN NaN NaN 2 NaN NaN NaN 3 NaN NaN NaN Table 6. Volumes and masses for 50 mL buret Mass of empty beaker: _____________________Temperature of water: _______ Volume of water:___________________Theoretical density of water: __________ 0 1 2 3 4 5 6 Trial Initial buret reading (mL) Final buret reading (mL) Volume of water (mL) Mass of beaker with water (g) Mass of water (g) Calculated Density (g/mL) 1 NaN NaN NaN NaN NaN NaN 2 NaN NaN NaN NaN NaN NaN 3 NaN NaN NaN NaN NaN NaN Table 7. Volumes and masses for 10 mL pipet Mass of empty beaker: _____________________Temperature of water: _______ Volume of water: __________________Theoretical density of water: __________ 0 1 2 3 Trial Mass of beaker with water (g) Mass of water (g) Calculated Density (g/mL) 1 NaN NaN NaN 2 NaN NaN NaN 3 NaN NaN NaN 7.0 CALCULATIONS For each calculation show your work for at least one piece of glassware. Calculate the mass of water for each trial by subtracting the mass of the empty glassware from the mass of the glassware with water. Remember to record the value in your data table with the appropriate number of significant figures and to retain all of the digits for further calculations. Using the mass of water and volume of water for each trial, calculate the density of water in units of grams per milliliter (g/mL) for each trial using the formula for density (density = mass/volume). Remember to record the value in your data table with the appropriate number of significant figures and to retain all of the digits for further calculations. Calculate the average density of water using the measured values for each piece of glassware. Record the value in the summary table with the appropriate number of significant figures and to retain all of the digits for further calculations. Calculate the percent error for each piece of glassware using the average and theoretical values for the density of water with equation 1. Record the value in the summary table. Calculate the standard deviation for each piece of glassware using the calculated densities for each trial, average density, and equation 2. Calculate the relative standard deviation for each piece of glassware using the calculated densities for each trial, average density, and equation 3. Record the value in the summary table. Table 8. Summary of glassware accuracy and precision 0 1 2 3 4 Glassware Average density (g/mL) Theoretical density (g/mL) Percent Error RSD 150 mL beaker NaN NaN NaN NaN 25 mL grad. cylinder NaN NaN NaN NaN 50 mL volumetric flask NaN NaN NaN NaN 50 mL beaker NaN NaN NaN NaN 10 mL grad. cylinder NaN NaN NaN NaN 50 mL buret NaN NaN NaN NaN 10 mL pipet NaN NaN NaN NaN 8.0 POST-LAB QUESTIONS List the glassware in order of the smallest percent error (best) to the largest percent error (worst). Which piece of laboratory glassware is the most accurate? least accurate? Explain. List the glassware in order of the smallest relative standard deviation (best) to the largest relative standard deviation (worst). Which piece of laboratory glassware is the most precise? least precise? Explain. What effects will a difference in temperature cause? For each of the following situations, determine which type of glassware would be most appropriate. (150 mL beaker, 10 mL pipet, 50 mL buret, 100 mL volumetric flask, 100 mL graduated cylinder) Each will be used only once. Note: When working with laboratory glassware, scientists choose the glassware that is appropriate while also efficient for the experiment. For example, if an experiment calls for using approximate volumes, it would be a waste of time to set up a buret. A lab calls for adding enough water to dissolve 5 g of NaCl to make a total of 100.00 mL of solution. A lab calls for adding very small amounts of liquid A to solution B until a color change is detected. The amount of liquid A added must be recorded. A lab calls for adding approximately 50 mL of water to a solution. A lab calls for adding 50.0 mL of water to a solution. A lab calls for delivering 10.00 mL of solution Z to an Erlenmeyer flask. For each of the following situations during the density of water experiment, determine if the mistake would give a false high, false low, or unchanged density for water. Also indicate if the error is systematic or random error. For each situation, assume everything else in the experiment is done correctly. Note: It may be helpful to try some hypothetical calculations. When weighing a volumetric flask full of water, a student does not notice that the outside of the flask is wet. € HIGH € LOW € UNCHANGED ◊ SYSTEMATIC ◊ RANDOM Explanation: Before placing an empty 10 mL graduated cylinder on the balance to get its mass, a student does not notice that the balance reads “-1.4444g”. When the student weighs the full 10 mL graduated cylinder later in the experiment, she correctly sets the balance to “0.0000g.” € HIGH € LOW € UNCHANGED ◊ SYSTEMATIC ◊ RANDOM Explanation: A student accidentally used the hot water faucet to deliver water to a piece of glassware. (Use the densities you recorded from the CRC Handbook during the lab in your explanation to received complete credit). € HIGH € LOW € UNCHANGED ◊ SYSTEMATIC ◊ RANDOM Explanation: In lab, your group used something called “laboratory” water to find the density of water. Explain what laboratory water is and why your group did not use tap water instead. Would you expect the density of tap water to be higher, lower or the same as the density of laboratory water? Explain your answer. Why is it important to know the accuracy and precision of glassware?