The Densities of Solids and Solutions

Transcription

1 The Densities of Solids and Solutions Objectives The objectives of this laboratory are as follows: To determine the density of an unknown metal using the technique of water displacement and use this value to identify the metal, To determine the density of a de-gassed soda via graphical analysis, To determine the density of distilled water using different types of volumetric glassware in order to compare the precision of this glassware, To use a common spreadsheet program, Microsoft Excel, to perform graphical analysis of experimental data. Background Density is a fundamental physical property of matter. Physical properties are characteristics of a substance that can be observed or measured without changing its chemical identity. Other physical properties include melting point and solubility. In general, since different substances have unique densities, determining the density of an unknown substance can help identify it. Density is also an intensive property of matter. An intensive property is one that does not depend of the amount of matter present. In other words, a substance will have the same density whether its quantity is large or small. An extensive property, in contrast, is one that does depend on the amount of matter present. Density is specifically defined as the ratio of a substance s mass to its volume: Density Mass Volume The S.I. unit of density is kg/m 3, but in chemistry it is more often expressed in units of g/cm 3 for solids, and g/ml for liquids and solutions. Note that while both mass and volume are extensive, since density is a ratio of these properties, density is intensive. In Parts A and B of this lab, novel techniques will be employed to determine the density of a solid and the density of a solution to a high degree of precision. In Part C of this lab, a study of density values will be conducted in order to explore the concept of precision and the statistical nature of experimental data. Graphical Analysis: In Parts B and C of this lab, the experimental data collected will be graphically analyzed, both to provide a visual image of the data (and any trends therein) and to yield important physical values (density). The spreadsheet program Microsoft Excel will be used for this purpose. Students should already have explored the graphing capabilities of Excel in a separate exercise, and those skills learned will be applied here. The Densities of Solids and Solutions Page 1 of 6

2 Part A: In this section of the lab, the density of an unknown metal will be determined and the metal identified using this experimental value. Although a simple approach is used, this method can yield density results accurate to 0.1%. Using a capped glass vial, the following series of four mass measurements will be obtained: (A) empty vial (B) vial + metal (C) vial + metal + water (D) vial + water The difference in masses A and B yields the mass of the metal sample. The volume of the metal may be obtained by taking the difference between the water volumes in C and D (technique of water displacement Archimedes Principle). However, these water volumes must first be calculated using the water masses and the known density of water (see table below). Finally, density can be calculated using the metal mass and metal volume. Density of Liquid Water Measured for a Range of Temperatures (obtained from the CRC Handbook of Chemistry and Physics, 53 rd edition) Temperature (C) Density (g/ml) In order to identify the unknown metal, the experimentally determined density must be compared to the true (accepted) densities of several known metals. The percent error between this experimental value (EV) and the true density value (TV) of the metal will also be calculated. EV TV Percent Error = 100 TV A more accurate experimental value will yield a lower percent error (< 5% is desirable) than a less accurate value. The Densities of Solids and Solutions Page 2 of 6

3 Part B: In this section of the lab, the density of a de-gassed soda will be determined via graphical analysis of a series of mass and volume data. A de-gassed soda is soda with the gaseous carbon dioxide removed, typically by gently heating and stirring an open container of soda over several days. Using a buret to dispense precise solution volumes, the masses of several increasingly larger volumes of a de-gassed soda will be measured. This collected mass and volume data will then be plotted on a graph of Soda Mass versus Soda Volume using Microsoft Excel. A best-fit line will be applied to the plotted data (via linear regression), and the equation of the line obtained. Best-fit line Mass y x Volume Best-fit line equation: y = mx + b where b = y-intercept and m = slope The y-intercept (b) is the point where the line crosses the y-axis. In this experiment, the value of b should be equal to zero. This is because if there is no volume, the mass must also be zero. However due to random experimental error, the best-fit line might not pass exactly through the origin, but it should be quite close. The slope of the line (m) is the change in the y-axis values (y) divided by the change in x-axis values (x): m y x y x 1 1 y x 2 2 However according to the graph, since y is actually the change in mass (mass), and x is actually the change in volume (volume), the slope of the best-fit line will yield the density of the soda: y m x mass volume density The Densities of Solids and Solutions Page 3 of 6

4 Part C: In this final section of the, lab datasets of water density values will be experimentally obtained, and then analyzed in order to explore the concept of precision and the statistical nature of experimental data. Specifically, the density of distilled water will be calculated using measurements obtained from three different types of volumetric glassware (VG): a 50-mL buret, a 100-mL graduated cylinder and a 10-mL volumetric pipet. Measurements performed by each pair of students in the entire class will be pooled so that a large ensemble of density values is acquired for each type of glassware used. The three density datasets will be displayed in a scatter plot, as shown below: Density VG 1 VG 2 VG 3 Volumetric Glassware (VG) Used The datasets will be analyzed for outliers, which will be removed if identified. Recall that when measurements in a dataset are closely examined, occasionally one or more values may appear not to fit in with the others. These points are called outliers values that occur far outside the range defined by the rest of the measurements. One rough criterion for identifying an outlier is that it lies beyond two standard deviations from the average value. Such values may be legitimately excluded from a dataset, as they can skew results to a great extent. Finally, simple statistical analyses of the three datasets will be performed, including calculations of average density and standard deviation. An average value ( x ) is defined as the sum () of each of the measurements (x i ) divided by the number of measurements (N): x N x i Standard deviation () is defined as: ( x i x) N 1 2 Standard deviation indicates the degree to which a set of measurements deviate from the average value. Datasets with a large amount of scatter will have a higher standard deviation and are associated with less precise measurements compared to datasets with little scatter (greater reproducibility). Thus, using these results, the precision of the measurements obtained using the three types of volumetric glassware can be compared. The Densities of Solids and Solutions Page 4 of 6

5 Procedure Chemicals/Materials Unknown metal sample, de-gassed soda, distilled water Equipment 10-mL volumetric pipet and pipet bulb*, 50-mL buret*, buret stand, 50-mL Erlenmeyer flask*, 100-mL graduated cylinder, 100-mL beaker, 50-mL beaker, small funnel, electronic balance, capped glass vial, thermometer, wash bottle *Items with an asterisk may have be checked out from the stockroom Part A: The Density of an Unknown Metal 1. Obtain a capped glass vial and an unknown metal sample from your instructor. The cap on the vial should have a small hole pierced through it. This hole will allow air and excess water to be expelled from the vial. Record the ID Code of the metal on your report form. 2. All mass measurements are to be performed on an electronic balance, and should be recorded on your report form. Use the same electronic balance for the entire series of measurements to reduce systematic error. 3. First, weigh the empty, dry capped vial. Then add the entire sample of your unknown metal to the vial, and weigh it again (with cap). 4. Now fill the vial (with the metal still in it) to the brim with distilled water. Gently tap the vial to remove any air that might be trapped between the metal pieces. Place the cap on firmly, pressing out excess water. No air bubbles should be visible under the cap. Wipe off any drops of water on the outside of the vial, and then weigh it. 5. Next, remove the metal from the vial and then fill it to the brim with distilled water only. Place the cap on firmly, wipe off excess water, and weigh. Again, no air bubbles should be visible under the cap. 6. Finally, using your thermometer, measure and record the temperature of the water in the vial. When finished, dry the metal sample and vial, and return them to your instructor. Part B: The Density of a De-gassed Soda 1. A buret will be used to dispense precise volumes of the soda used. The buret should first be rinsed with distilled water, and then rinsed with a small quantity of the soda before filling it with the soda. Use the small funnel when adding soda to the buret. 2. Add approximately 60 ml of the supplied de-gassed soda to a medium 100-mL beaker. Fill the buret with this soda (after rinsing), secure it firmly in place with the buret clamp, and record the initial buret reading to the correct number of significant figures. Make sure that the buret tip is charged with soda before recording this measurement. The Densities of Solids and Solutions Page 5 of 6

6 3. Weigh a small dry 50-mL Erlenmeyer flask on an electronic balance, and record this mass. Then drain approximately 5 ml of the soda from the buret into this flask, and record the new buret reading. Now measure and record the combined mass of the flask and soda. 4. Do not pour the soda out of the Erlenmeyer flask!! Next, add an additional 5 ml of soda to the flask from the buret. Again, measure and record the new buret reading and the new combined mass of the flask and beverage. 5. Repeat Step 4 (preceding step) four more times. You will obtain a total of six measurements involving increasing larger samples of soda, and you will have used ml of the soda when you are finished. The soda may then be disposed of down the sink. Part C: The Precision of Volumetric Glassware 1. All glassware should be thoroughly rinsed with distilled water before use. Pay special attention to significant figures in your recorded measurements. 2. Add approximately 60 ml of distilled water to a medium sized 100-mL beaker. 3. Weigh a small dry 50-mL beaker on an electronic balance, and record this mass. You will use this same beaker for Steps 3, 4 and Graduated Cylinder: Fill the 100-mL graduated cylinder with slightly more than 10 ml of distilled water, then record the actual volume used to the correct number of significant figures. Carefully transfer the distilled water into the small pre-weighed beaker, and measure the combined mass. When finished, empty the distilled water out of the small beaker, then carefully dry it. 5. Volumetric Pipet: Your instructor will demonstrate the correct use of the volumetric pipet and pipet bulb at the beginning of the lab session. Use the volumetric pipet to transfer precisely ml of distilled water from the supply in the medium beaker into the small pre-weighed beaker. Record the volume used and the combined mass of the beaker and water. Note that the pipet measures volume to 2 decimal places. Again, empty the water out of the small beaker when finished, then carefully dry it. 6. Buret: Fill the buret with all the remaining distilled water in your medium beaker and note the initial buret reading to the correct number of significant figures. Make sure that the buret tip is charged with distilled water before recording this measurement. Then drain slightly more than 10 ml of the water from the buret into the small pre-weighed beaker. Record the actual volume used (= final initial buret reading) and the combined mass of the beaker and water. 7. For each of the three sets of data collected (using the graduated cylinder, volumetric pipet and buret), calculate the density of distilled water to the correct number of significant figures. Then share your three density values with all the students in your lab section, and record the results of the entire class on your report form. You should have at least twelve density values for each type of volumetric glassware used in this part of the lab. The Densities of Solids and Solutions Page 6 of 6