Measurements & Common Glassware

Transcription

1 Experiment 2 Measurements & Common Glassware Purpose: The purpose of this experiment is to become familiar with using common laboratory glassware to obtain volumes of liquids and to determine the relative accuracy of the volumes obtained from these various pieces. The experiment includes an exercise to introduce the concepts of data graphing and linear regression analysis to quantify the relationship between two variables. Background: Laboratory experiments involve making measurements. It is impossible to make an exact measurement. No matter how sophisticated the instrument, errors cannot be avoided and all measured values have an uncertainty. Values reported as final results for use in scientific, commercial, medical, engineering activities have a well-defined uncertainty. In order to determine the best values to use for establishing standards set by the National Bureau of Standards, minimum contaminate levels for environmental regulations, medicine dosages, engineering formulas, and any number of other human activities requiring precise numbers, experiments must be very carefully designed to produce precise, accurate and statistically verifiable results. Appendix B gives a detailed overview of the rules governing accuracy and precision as applied to scientific measurements. Appendix C gives an overview of the basic statistical tools used to organize and interpret numerical data, especially the analysis of population characteristics by inference from sampling. The Experiment: In order to make measurements in the laboratory as accurate as possible, it is important that the student learn how to use common equipment correctly and to understand the relative accuracy of measurements made from the various pieces. The validity of any experiment depends on the reliability of the measurements. The equipment used in this experiment will be used in many of the experiments conducted in this course. In today s experiment, the accuracy of volume values obtained from commonly used laboratory glassware will be determined from the measured mass and temperature corrected density of the water samples. Mass measurements will be made on an electronic balance whose precision will be assessed. All mass measurements must be made on the same balance. Initial volume values will be obtained from a variety of glassware including: graduated cylinder, volumetric pipet, and a buret. The accuracy of using volumes obtained from reading the scale values on each piece will be determined by comparing a measured volume with the calculated

2 volume from the conversion factor relating volume, mass and density, which is assumed to be the true value. Error = Measured Value - Calculated Value Calculated Value 100 = % Error At room temperature one gram of water occupies about one milliliter of volume (that is the density of water = 1 g/ml or 1 g/cm 3 ). The density of water is temperature dependent and has been accurately determined in other laboratories. The relationship between density and temperature is quantified in the following relation: Density = ( ) * T Where: T is in o C and the density is in g/ml or g/cm 3 Approach: Density Values for Water at Typical Lab Temperatures Temperature ( o C) Density of Water (g/ml) Prepare a constant temperature reservoir of distilled water. Obtain a 3 measurement sample of the mass of the graduated cylinder and the 25 ml beaker. Determine the mean mass of each piece. Compute the standard deviation of the mean mass for each piece. Determine the mass of water in the graduated cylinder. Compute the volume of water from the mass and density. Determine the mass of water in the volumetric pipet. Compute the volume of water in the pipet from its mass and density. Compute the % error. Determine the mass of water in the buret. Compute the volume of water in the buret from its mass and density. Compute the % error. Pre-Lab Report & Notebook: Download from the department data base to your hard drive or flash drive a copy of the lab report template and the data summary tables for the Measurements experiment: Print the data summary tables and use them to record the laboratory results during class. Measurements; Graduate Cylinder; Pipet; Buret Prepare the Pre-lab report according to instructor s instructions.

3 Materials & Equipment: Equipment: Procedure: Electronic Balance Calculator Thermometer 250 ml Beaker 25 ml Beaker 25 ml Graduated Cylinder 10 ml Volumetric Pipet 50 ml Buret Water Source 1. Place about 250 ml of Distilled Water in a 250 ml beaker from the equipment drawer of the bench top 2. Place a thermometer in the water and record the temperature to the nearest 0.1 o C Note: All students using a given bench will use this single source of water for their measurements Mass of Graduated Cylinder and Beaker 3. Weigh a dry 25 ml graduated cylinder on the electronic balance 3 times to the nearest g. 4. Compute the mean of the cylinder masses. 5. Compute the standard deviation of the mass mean. 6. Repeat steps 1-3 for the 100 ml beaker. Graduated Cylinder Volumes 7. To the graduated cylinder, add about 10 ml distilled water from the constanttemperature water bath. 8. Record the volume in the cylinder to the nearest 0.1 ml. 9. Weigh the graduated cylinder containing the water to the nearest g. 10. Determine the mass of water in the cylinder by difference. 11. Compute the volume of water in the cylinder from its mass and density 12. Compute the error and % error of the measured volume using the computed volume as the true value.

4 Volumetric Pipet Volumes 13. Obtain a clean 10 ml volumetric pipet. 14. Squeeze a rubber bulb and place it over the top of the pipet. 15. Slowly release the pressure on the bulb and allow water from the constant temperature water bath to enter the pipet until the level is above the mark on the neck. 16. Quickly remove the bulb and slide the thumb of the other hand over the top of the pipet so that no water drains back into the beaker. 17. With the piper tip still over the beaker, carefully release the pressure on the thumb until the water begins to drip out of the tip. 18. Continue releasing water until the bottom of the meniscus rests on the mark (the thumb reasserts pressure on the pipet top. Note: This takes practice. 19. Place the pipet tip over the clean, dry, pre-weighed 25 ml beaker and release the water into the beaker. Note: Do not attempt to force all the water from the tip. These pipets are manufactured to deliver the exact amount. 20. Determine the mass of the water and beaker. 21. Compute the mass of water by difference. 22. Compute volume of water from its mass and density. 23. Compute the error and % error of the measured volume using the computed volume as the true value. Buret Volumes 24. Set up a clean buret and rinse with distilled water. 25. Fill the buret with distilled water from the constant temperature water bath. 26. Drain enough water through the tip to flush out any air bubbles. 27. Release enough water until the water level is below the 0.00 ml mark. 28. Note: it is not necessary to adjust the water level to the 0.00 ml mark. The volume of water to be delivered to the beaker is simply the net difference between two marks on the buret scale. 29. Record the staring volume level and drain about 10 ml from the buret into the same pre-weighed (and dried) 25 ml beaker used above. 30. Determine the measured volume from the beginning and ending scale values. 31. Determine the mass of the water in the beaker by difference. 32. Determine the volume of water delivered from its mass and density.

5 Celsius vs. Fahrenheit an exercise in graphing data and regression analysis: Many physical and chemical properties are linearly related to each other. As the numerical value of one property changes, there is a proportional change in the other property s value. A mathematical equation which expresses the linear relationship is: y = m x + b Where: x and y are the values of the two properties of interest. The slope, m, is the rate of change of the two variables m = y2 - y1 x2 - x1 The intercept, b, is the point where the line crosses the y-axis when the x-axis value is zero, 0. It is often helpful or necessary to visualize the linear relationship by graphing the values for x & y. As an example, consider the relationship between Celsius and Fahrenheit temperature scales. The data to be plotted on the graph is shown below. The data will be plotted along with the regression line and equation for the linear relationship using the graphics functions in the Microsoft Excel spreadsheet program. Degrees Celsius Fahrenheit Data Processing: Use the printed Pre-lab report as a notebook to record the results for each procedure in the results section of the applicable procedure. Enter the experimental and computational results into the printed Measurements table and attached to report If required by the instructor, transfer the results to the electronic tables and insert them into the electronic laboratory report.

6 Analysis and Conclusions: Analyze the results of the mass measurements made on the beaker and graduated cylinder relative to the accuracy of measurements made on the balance. How does the standard deviation of the mass mean compare to the stated accuracy of the balance ( 0.001g)? Based on these results, how many duplicate measurements of the mass of an object need be made in future experiments. Discuss the relative accuracy of volumes obtained from the graduated cylinder, volumetric pipet, and buret. Compare your results with the uncertainties listed for these pieces of glassware in Appendix B. Spreadsheet Processing: Create a scatter plot with trend line for Celsius vs Fahrenheit Open a new Excel document Select the A and B columns for line 1. In the Alignment box select the Merge and Center option Select Merge Cells Enter Degrees in the merged cell In line 2 enter Celsius into A column and Fahrenheit into B column In lines 3-8, enter the values under Celsius from the table into column A In lines 3-8 enter the values under Fahrenheit from the table into column B Select the 12 values from columns A and B, lines 3-8. Create the scatter plot Click on Insert from menu bar Click on the Scatter box (the scatter plot is created) Click anywhere on the chart Click on Chart Layout from the menu bar Click on the first icon in the box, which modifies the chart to accommodate the chart title, the Y-axis title and the X-axis title Right click on each of the title boxes and select edit to enter your titles Add a trend line (regression curve, equation, coefficient of determination (r 2 ) Click on Chart Tools icon above menu bar Click on Layout Click on Trendline Click on More Trendline Options Click on Linear Regression

7 Click on Display Equation on Chart Click on Display R-squared Value on Chart Select the equation box and move to upper left corner of chart The chart can be copied and pasted into the lab report.

8 Measurements Measuring Mass Mass of 25 ml Cylinder g g g Average: g Uncertainty g Std Deviation: g Mass of Small Beaker: g g g Average: g Uncertainty g Std Deviation: g Assessment of Precision:

9 Glassware Accuracy Temperature of Room Air: Temperature of Water: Density of Water (from table or show calculation): o C o C g/ml Show Calculations where applicable below Graduated Cylinder: Measured Vol. of H 2 O Mass of Cylinder + H 2 O Mass of Cylinder = Mass of H 2 O ml g g = g Calculated Vol. H 2 O Error Percent Error ml ml % Pipet: Measured Vol. of H 2 O Mass of Beaker + H 2 O Mass of Beaker = Mass of H 2 O ml g g = g Calculated Vol. of H 2 O Error Percent Error ml ml %

10 Buret: Final Vol. in Buret Initial Vol. in Buret Measured Vol. of H 2 O ml ml ml Mass of Beaker + H 2 O Mass of Beaker Mass of Water ml ml ml Calculated Vol. of H 2 O Error Percent Error ml ml % Assessment of Accuracy: