The Density of Metals and Liquids

Transcription

1 The of Metals and Liquids Roger Sandwick and Thomas Moffett Jr., Plattsburgh State University, 007 Edited by E. J. Miller (Version Fall 008) I. Learning Objectives The scientist will be able to: 1. Use the top-loading balance, graduated cylinder, volumetric flask, and transfer volumetric pipet in a competent fashion.. To make serial dilutions for the study of the properties that vary by concentration of a dissolved material. 3. Articulate the differences between intensive and extensive properties. 4. Explain the concept of density. 5. Use density to convert between mass and volume of a material. 6. Explain the concepts of accuracy and precision in scientific measurements. 7. Use experimental data to calculate percent error and standard deviation. 8. Use experimental data to create a graph of solution property versus concentration. 9. Use a linear regression to determine the concentration of a solute from the property value of a solution. II. Introduction A) is defined as the mass of a substance per unit volume. For a discussion of density see Chapter 1 of Chemistry: Matter and Its Changes, pages 5 to 8. In the first part of this experiment, you will determine the density of an unknown cylinder of metal by dividing its mass (determined on a laboratory balance) by its volume (determined using the formula for volume from the length of a cylinder and its radius). This will be done in a team fashion where your lab bench partners constitute your team. In the second part of the experiment, you will again calculate the density of the same piece of metal using a volume obtained from difference in water levels in a graduate cylinder filled with water before and after immersing the cylinder. This procedure will be done again in a team fashion. Using two different methods, as described above, to make measurements on the same piece of metal, will allow you to compare the accuracy of the two methods. Having different people make the measurements on the same piece of metal will allow you to determine a real life standard deviation. We perform these procedures in this fashion so that you will learn how scientists compare the quality of measurements. The standard deviation represents the dispersion in a set of measurements of a property of an object. The dispersion is due to randomness of the process. The percent error, or percent difference from a known accepted value for a property, provides a measure of the accuracy of the methods.

2 You will identify the unknown piece of metal by comparing its measured density with values in Table 1. Once you have identified the piece of metal by choosing the metal whose density is closest to your measured value you will then calculate the percent error. Table 1. Densities of some metals (g/cm 3 ) Metal Metal Aluminum.70 Zinc 7.13 Lead Copper 8.96 Magnesium 1.74 Iron 7.87 In the third part of this experiment, you will create a standard curve of the % concentration by weight of a solute, sugar, versus its intensive property known as density. The creation of this curve requires several steps. The first of these involves the preparation a stock sugar solution. This solution will involve the dissolving of sugar in water so that you obtain a certain number of grams of sugar per 100 milliliters (ml) of solution. Your lab instructor will assign the actual value for the % concentration. You will receive a portion of your grade for this lab based on how close your measured density is to the theoretical density. Once the stock solution is prepared, it will be used to make a series of solutions that are progressively less concentrated. The density of each will be determined and plotted against its measured density. This type of plot is known as a standard curve. You will then be provided with a sugar solution of unknown concentration and asked to determine its concentration using the standard curve data. B) Intensive versus Extensive Properties Certain properties can be used to identify a material since they are unique characteristics of the material. These properties, called intensive properties, depend only on the identity of the material and not on the amount of material that you have. is an example of such a property. Extensive properties depend on the amount of material that you have. An example of such a property is volume. Metal cylinders such as those that you will use in Part A of this experiment, and solutions, such as those you will use in Part B, each have their own characteristic densities. Since density is an intensive property, we will use the measured densities to identify the material or its concentration. C) Preparing Solutions and Making Dilutions (This section will not be done as a team but must be completed individually) In the third part of the lab you will prepare a stock sugar solution by weighing out an amount of sugar equal to the percentages assigned by the instructor. You then will withdraw an aliquot (small sample) from the stock solution to prepare a more dilute solution. You will do this quantitatively by transferring 5.00 ml of stock sugar solution using a volumetric pipet. The amount will be transferred to a volumetric flask. Then you will add enough deionized water to create a final volume of ml. You can determine the concentration of the diluted sugar solution by use of the dilution formula: Page of 1

3 C 1 V 1 = C V (Equation 1) C 1 V 1 /V = C (Equation ) Here C 1 and V 1 are the stock concentration and volume (5.00 ml from the pipette) of the stock solution used, respectively; V is the final volume of the diluted solution (50.00 ml or size of the volumetric flask). C is the concentration of the new diluted solution. After preparing your first dilute solution, you will prepare a second more dilute solution from it and so in a like manner until you have a set of dilutions. By measuring the density of the various dilutions, you will be able to prepare a graph of density versus sugar concentrations (C s from Equation ). The graph will then be fitted with a line using a linear regression command within Excel. The regression data will be used to determine the alcohol content of an unknown dilute alcohol solution. The data are plotted using Excel (Review Lessons on Excel on the website for this experiment). An example of such a regression is shown in the Chart below on the left. Notice the equation for the least squares line in the upper right hand corner of the chart on the left. It is a product of the regression routine. In this equation, x represents % concentration by weight and y represents the density. v Concentration y = 0.05x R = v Concentration y = 0.05x R = Measured Percent Concentration Concentration Percent Concentration After plotting the concentration of the dilute solutions versus their measured density and making the graph as shown above, you will be given a sugar solution with an unknown concentration and be asked to determine its concentration. This done by determining its density and using the graphical data determined for the diluted sugar solutions. The concentration of the unknown solution can be determined in two ways: graphically as shown with the dotted lines in the chart on the right by moving from the measured density to the regression line and then straight down to the x-axis or concentration of sugar; or, by using the information from the linear regression line (for this example it is ((y-0.84)/.05 = x = concentration). The latter method is required for full credit. Page 3 of 1

4 D) Error and the Experimenter Chemists deal with numbers and physical quantities almost everyday. As examples, chemists may need to know how much heat is given off in a particular reaction; how distant two atoms are from each other in some molecule; or want to measure the difference in volume of a gas before and after it is heated. The uncertainties in the numbers with which the chemist deals are also important. Scientists should always tell others how reliable a particular number is that they have measured. There are various ways of signifying uncertainty or reliability. At this point in your career as a scientist, it may be difficult to grasp the physical significance of the uncertainty in a particular measurement. Hopefully, after using some of the various ways in which scientists communicate uncertainty and error, you will understand the importance of this in your scientific work. The main terms related to error are: precision, accuracy, standard deviation, and percent error. To understand accuracy and precision, refer to Figure 1. As can be seen in the left portion of Figure 1, all of the measurements, i.e., where darts landed, were close together. If these had been real measurement, then you would have what is known in science as good precision. However, since you missed the bulls eye you would not have very good accuracy. On the other hand, you could have the darts spread out as in the top-center portion of the figure. Then you would have poor precision because the dart landings were not close together but the average point would be about a bull s eye. So you would have good accuracy but since the darts were spread out, your precision would be poor. The bottom center is of course the ideal situation; good accuracy and good precision. The drawing on the right side indicates a very bad day. Figure 1. Visual display of accuracy versus precision. Good Accuracy Poor Precision Ouch Less Ouch Poor Accuracy Good Precision Good Accuracy Good Precision Poor Accuracy Poor Precision Page 4 of 1

5 Scientists communicate precision and accuracy using mathematical quantities. The easiest one to understand is the measurement of percent error. The calculation for this is shown in equation 3. It is a measure of how far off you are from the accepted value. Percent error calculation: % error = (experimental value - accepted value) x 100 (Equation 3) accepted value The way that scientists communicate the precision of their measurements is through the use of standard deviation. The way that standard deviation is calculated will be shown with the aid of Table below. Table. "Made-up" set of data Run(i) Measurement Absolute Deviation (x-xi) (xi) (x-xi) lbs 0.5 x x x x x x x x 10 - The Average value is equal to the sum of all of the measurements divided by the number of measurements or: x + x + x + x + + x n Average = where n is the number of measurements (Equation 4) n where the x s represent the values for the individual measurements. Average for the made-up data = = Standard Deviation = ( x 1 Ave.) + ( x Ave.) + ( x Ave.) + + ( x Ave.) 3 n (Equation 5) n 1 Standard Deviation for the made-up data = ( ) + ( ) + ( ) ( ) = = = ± 0.6 A small standard deviation indicates better precision in a set of measured numbers. When you move to your more advanced classes, you will learn about the 95% confidence interval. This is based on the standard deviation and gives a more meaningful message about the precision relative to an average value. Page 5 of 1

6 II. Experimental Procedure (Review the Lesson, Introduction to the Laboratory and Keeping a Laboratory Notebook, for this laboratory prior to the lab period) 1) of Solids a) Volume from Dimensions (All of the individuals at a single bench should do a and b of the of Solids as a team please share your data with each other before you leave the laboratory) (1) Obtain a piece of unknown metal from the side bench. Weigh it on the toploading balance (Review and study the Document on Angel: Demonstration on the Use of Laboratory Balances prior to the lab) to as many significant digits as possible and then measure its dimensions with a ruler. Pass the cylinder to the next member of your team. () The next person should INDEPENDENTLY repeat step 1 of this section. (3) When the second person on the team has completed the measurements, it should be passed to the third person and so on until each member of the team (your bench mates) have completed the measurements. (4) All members of the team or bench should share their data at this point see Table 1 in Section III of this document for a sample data table. (5) Calculate the density of the metal for each set of measurements (the volume of a cylinder is πr h). Calculate the average density and the standard deviation for the set of measurements (you may use your calculator to do this if it has this function). b) Volume by Displacement (All of the individuals at a single bench should do this section as a team please share your data with each other before you leave the laboratory) (1) Determine the volume of your unknown piece of metal by carefully sliding it into a graduated cylinder (Don t drop it in since it could break the graduate cylinder) that is filled with a known volume of water (be sure there is enough water to completely cover the metal piece). The difference in volumes before and after adding the metal is the volume of the metal piece. Pass the cylinder to the next person on your team. () Repeat step 1 with different initial volumes of water. Make sure the metal piece is dry before each run. (3) When the second person on the team has completed the measurements, it should be passed to the third person and so on until all members of the team (your bench mates) have completed the measurements. (4) All members of the team or benchmates should share their data at this point see Table in Section III of this document for a sample data table. Page 6 of 1

7 (5) Calculate the density of the metal for each run using the average weight from Volume by Dimensions and the volumes determined here. Calculate the standard deviation for this approach. ) of Liquids a) Creating a Standard Curve (Review the Lessons: Demonstration on Use of Pipets and Demonstration of the Use of Volumetric Flasks, for this laboratory.) (1) Obtain a concentration of sugar (weight percent) to use for this part of the experiment. Record it in your data section. () On a piece of creased weighing paper weigh out a number grams of sugar equal to the number for the percent weight that you were given. Make sure to weigh the paper first. You need not spend time getting the sugar amount to the exactly equal the number you were given as long as you know the gross weight of the paper and the sugar. You need to be within 0.3 g of the number given by your instructor. (3) Transfer this solid to a ml volumetric flask that has about 50 ml of deionized water (DI) in its bottom. With the edge of the weighing paper in the lip of the volumetric flask, pour the solid in and then rinse the paper with a small amount of DI from a squirt bottle. Make sure that the wash water goes into the flask. Swirl the flask to dissolve the sugar. Once the sugar dissolves, fill the flask up to the calibration mark with DI water, place parafilm over the top of the flask, invert it with your palm over the parafilm, and shake. Calculate the concentration of this stock solution. Label this flask Solution A. Also add the appropriate NFPA diamond and numbers as well as the name of the chemical, the weight percentage of the dissolved solid, your name, and the date. (4) Rinse a 5.00 ml pipette with Solution A. Pipette 5.00 ml of Solution A into a second ml volumetric flask. Fill the volumetric to the mark with DI water. Cover, invert and shake as before. Calculate the concentration and label this flask Solution B. Add the information on a label as in the immediately preceding step. (5) Rinse the 5.00 ml pipette with Solution B. Pipette a 5.00 ml of solution B into a third ml volumetric flask. Fill the volumetric to the mark with DI water. Cover, invert and shake as before. Calculate the concentration and label it Solution C. Add the additional information from step 3 of this procedure. (6) Rinse the 5.00 ml pipette with Solution C. Pipette 5.00 ml of Solution C into a fourth ml volumetric flask. Fill the volumetric to the mark with DI water. Cover, invert, and shake. Calculate the concentration and label it Solution D. (7) Rinse your ml pipette with the stock sugar solution solution. Pipette ml of the solution into a dry, pre-weighed beaker. Determine the density of the solution. Record the value in your notebook. Page 7 of 1

8 Calculate the percent error of the density for the stock solution. The true value for the density of your stock solution can be obtained by substituting your theoretical concentration number based on weight of sugar into the following equation: True = [1.784 x 10-5 (Wt. Percent) x 10-3 (Wt. Percent) ] (g/cm 3 ) (8) Repeat step 7 for each of your solutions B to D and also for the DI water. This will provide you with five densities: stock sugar solution as well as solutions B to D and pure DI water. (9) Using Excel (Review Lesson: Using Excel to graph data from an experiment before doing this laboratory) prepare a graph of the concentration of the sugar solutions (y value) versus their densities (x value). Use the line generator function to get the least squares information for the line (i.e., do a linear regression using Excel). Record the Pearson coefficient as well as the least squares data. Print your graph and tape or paste it into your notebook. 3) Determining the of an Unknown a) From your instructor, obtain a 0 ml sample of dilute sugar solution with an unknown concentration. Record the identifying information from the unknown. b) After rinsing the ml pipet with the solution of unknown concentration, pipette a sample of the unknown into a dry small beaker (with known mass). c) Determine the density: by weighing the beaker with the sample; subtracting the weight of the empty beaker from the total gross weight of the beaker and sample; and, dividing the net weight from the difference by ml. d) Determine the concentration of the solution using the least squares data from the preceding section and record it in your notebook. Show the calculations using the line data from the linear regression. e) Dump the unknown from the beaker back into its original container. Dry the beaker. Repeat steps b to d four times in total. III. Data Recording and Analysis 1) Sample data Tables: For your noebook, you should set-up appropriate data tables for each experiment. You will need to think about this in order to do it effectively. Presenting data is a key part of good scientific work. For this experiment, samples of what the data tables should look like are provided below. Page 8 of 1

9 of Solids Person s Name Table 1. of a Solid Using a Ruler to Measure Dimensions Person s Weight Diameter Length Volume Average Weight Average Standard Deviation Observations: Person s Name Table. of Unknown Metal by Displacement Final Reading Initial Reading Volume * *Use average weight from part a. Average Standard Deviation Observations: Identity of the Metal it is) Percent Error in (assuming it is the metal you think Page 9 of 1

10 and Concentration of Sugar Solutions (10.00 ml of solution used) Table 3. Preparation of Stock Sugar Solution Weight Percent Sugar Solution Assigned Gross Weight of Sugar and Paper Weight of Paper Alone Weight of Sugar Volume of Solution Prepared Concentration of Stock Sugar Solution* * Grams of solute/volume of solution (ml) x 100 = % Concentration Table 4. Densities of Sugar Solutions (All samples have ml volumes) Solution Concentration Mass Stock Solution A B C D Pure DI Water 0% Table 5. Linear Regression Information Slope Intercept Pearson Coefficient Page 10 of 1

11 Table 6. Concentration of Unknown Sugar Solution Run 1 3 Weight ml Concentration Unknown Designation Marking Average for the Unknown Sugar Solution Standard Deviation Average Concentration of Sugar Solution from Graph ********************************************************** ) In your notebook make sure that you record all measurements with the appropriate number of significant digits and units (Review Lesson: Uncertainty and Significant Figures before the laboratory). Indicate the equipment used for a particular measurement. Show all calculations and make observations. IV. Prelab Questions A) What is the concentration of a solution that is prepared by taking 10.00mL of a 15% solution and diluting it to 500 ml? Show work in your laboratory notebook. B) What value should be recorded from the measurement in the diagram below? ml 1 ml C) What volume of 5% solution is needed to make 500 ml of a 10% diluted solution? D) Define accuracy, precision, standard deviation and percent error. E) Why should you make sure that the balance has all zeroes and the tare is all the way to zero before you weigh anything. Be explicit in your answer. Page 11 of 1

12 Post Lab Questions A) In part 3, which variable is the independent variable and which is the dependent variable? B) Which method of determining volume of the cylinder is more accurate? Explain why. C) Calculate the mass of soda in a two-liter bottle (d = 1.07 g/ml). D) A sample of lead has a mass of 85 g, how much water would the lead displace? E) Determine the density of a 3.5 g metal sample that displaces 8.39 ml of water. F) A student measures the density of a solution to be 1.36 g/ml. Determine the percent error if the accepted density was 1.5 g/ml. References K. I. Peterson, Measuring the of a Sugar Solution, J. Chem. Ed., 85, 008, Page 1 of 1