Chapter 1 Determination of the Density of Metals 2011 by H. Patterson This unit introduces the student to basic laboratory procedures, physical properties of matter, and units, Students work independently. Educational Objectives The student will become familiar with: The intensive property density and its units. The use of the analytical balance, the metric ruler and the buret. The techniques of accurate measurement and the determination of experimental error and standard deviation. Safety Goggles and proper shoes must be worn. Lab Notebook Content (25% of lab grade) Prior to lab, your notebook should include the title, date, the purpose of the lab and the required data tables. This will provide you with experience in record keeping and proper notebook set up. Your instructor may require that you write an experimental procedure and provide other information. Data and observations are to be recorded in the lab notebook as you perform the experiment. Calculations must be workout in detail in the lab notebook at the end of the experiment. Pre-Lab Exercise Tabulate densities and names for the following metals: Al, Cu, Fe, and Zn in your lab notebook. Include a reference for the source of data, i.e. CRC, Aldrich chemical web site, your chemistry textbook etc.
Required Data for Density of Metals The follow data tables should be copied into your notebook prior to lab. Table 1: Density of aluminum based on dimensional analysis. Mass of aluminum sample: Dimensions of aluminum sample: Length Diameter Volume of aluminum sample: Density of aluminum sample: (based on dimensional analysis) Trial 1 Trial 2 Trial 3 Trial 4 Units Table 2: Density of aluminum based on the displacement of water. Mass of aluminum sample : Final volume of the water in the buret. (V f ) Initial volume of the water in the buret. (V 0 ) Volume of water dispensed from the buret: V B =(V f - V 0 ) Volume of water level on graduated cylinder: V GC Volume of aluminum sample: Density of aluminum sample: Trial 1 Trial 2 Trial 3 Trial 4 Units Table 3: Density of a metal. Metal number: Trial 1 Trial 2 Trial 3 Trial 4 Units Mass of metal : Volume of metal: Density of metal:
Expected Results (75% of lab grade) You will turn in the following results and others as directed by your instructor. This content must also be in your notebook. The average density of aluminum bar based on displacement of water. The percent relative error, in your experimental value for the density of aluminum based on displacement of water. The average density of aluminum bar based on dimensional analysis. The percent relative error, in your experimental value for the density of aluminum based on dimensional analysis. A description of the unknown metal bar The average density of an unknown metal found by either dimensional analysis or displacement of water (student choice). The code number for the metal. The presumptive identity of the metal. Introduction The density of matter is the mass per unit volume in the sample. The units of density are grams per cubic centimeter (g/cm 3 ), used to describe the density of solids and grams per milliliter (g/ml), used to describe the density of liquids. Density = Mass Volume Densities vary with temperature and atmospheric pressure. Most materials expand when heated and thus their densities decrease with increasing temperature. Literature values for density are determined and reported at 20 C. The temperature is always specified when a density is reported. The density of an element or compound is a characteristic physical property and, therefore, is useful in identifying the substance. Unlike liquids and, especially, gases, the densities of most solids are not greatly influenced by small changes in the temperature or pressure. However, the density of a solid may depend somewhat on the method of sample preparation (i.e., whether it has been rolled, cast, or powdered). Volume is the amount of space occupied by matter. To determine the volume of a regularly shaped object, one may either measure its dimensions or determine the volume of water it displaces. To determine the dimensions of a cylinder, one measures the radius and the length and calculates the volume as: A solid that has a regular shape may be measured and dimensional analysis used to determine its volume as follows:
Cubic solid Volume = (edge) 3 Rectangular solid Volume = Length x width x height Cylindrical solid Volume = x(radius) 2 x height 4 Spherical solid Volume = (radius) 3 3 Volume (of a cylinder) = π r 2 h Where: = 3.14159, the ratio of the circumference to the diameter of a circle. r = the radius of the cylinder h = the length of the cylinder Alternately, the volume of any solid may be determined by measuring the volume of water it displaces. This method requires that a known volume of water, at a known temperature be added to a graduated cylinder. The solid is placed in the graduated cylinder and the apparent volume of water in the cylinder is read at the bottom of the meniscus in the graduated cylinder. The difference in the two volumes is the volume of the solid. When the density and the mass of a substance are known, equation (1) may be solved to find the volume occupied by that quantity of the substance.
Volume = Mass Density Error is the difference between the measured value of the quantity and its true value. Good Lab Practice Always set up the calculations for an experiment in your lab notebook using dimensional analysis before you put any numbers in your calculator. Error = True value- measured value Absolute Error is the absolute value of the Error. Absolute Error = True value- measured value Relative Percent Error is the quotient of the Absolute Error divided by the true value. Relative Percent Error = Absolute Error x100 True value Precision The most common way to specify the precision of a set of measurements is the standard deviation, s, which for a small number of measurements is: 1/2 S = n Σ (x i - x avg ) 2 i=1 (n-1) Where: x i is the individual result x avg is the average n is the total number of measurements
Procedures Procedure 1: Density based on dimensions. Obtain an aluminum cylinder from the instructor. Determine and record the mass of the aluminum sample. Measure the dimensions (length and diameter) using the metric ruler. Record this data in your notebook in a chart. Make up to five sets of measurements as directed by your instructor. (Be sure to use the same balance each time and include the units and correct significant figures.) Procedure 2: Density based on the displacement of water. Determine and record the mass of the aluminum sample. Two students may share a buret stand. Fill the buret with distilled water and secure it to a buret stand and. Open the stopcock and allow water to flow to remove any air bubbles. Let the buret stand for 2 minutes to allow water to drain down the sides. Place the aluminum sample in a PLASTIC graduated cylinder. Record the initial volume of the water in the buret (T i ). Dispense about enough water into the graduated cylinder to cover the metal. Record the final volume of the water in the buret (T f ) Calculate the volume of water dispensed from the buret (T f - T i ). Good Lab Practice Always use the same lab balance for measurements during a particular experiment. Good Lab Practice Always fill a buret by holding it in the sink. Never fill the buret when it is clamped above your eye level; chemicals could splash down in your eyes. After you have dispensed an aliquot don t fill the buret t up again unless less than 15 ml of reagent remains. Read the volume of water level on graduated cylinder; this is the apparent volume. The difference between the apparent volume and the volume dispensed from the buret is the volume aluminum cylinder. Determination of the Density of Unknown Samples (optional activity): Obtain an unknown metal sample (a cylinder or block) from the instructor. Determine and record the mass of the sample. Choose a method, (either dimensional analysis or displacement of water) and find the volume of the sample. At the end of the lab period, your lab notebook should have: all the Prelab material, all the experimental data in neat tables, all calculations with correct units and the answers to the post lab questions.
Required Calculations. Calculated the volume of the aluminum bar by displacement: V Al = V B -V GC Where: V Al = volume of the aluminum bar V B = volume of water dispensed from the buret V GC = volume of water level on graduated cylinder Calculate the volume of the aluminum bar: Volume = πr 2 h Calculate the relative percent error in each measurement: Relative Percent Error = Absolute Error x100 True value
Name: Date: Day: M T W R F S Time: Name of lab partner (if any): Attach notebook sheets to this page. Summary Report and Grading for Density of Metals Suggested Grading Possible points Points Earned Notebook Title, Purpose,Procedure-5; record keeping-10 Observations and Data tables-5 15 Lab technique set up-5;afe handling of chemicals-5;safe handling of equipment-5 10 The average density of aluminum based on the displacement of water is: 10 The percent error in measurements displacement of water is: 10 The average density of aluminum based on dimensional analysis is: 10 The percent error in measurements density by dimensional analysis: 10 The code number of the unknown metal is: 5 The density of unknown metal is: 10 Cleaning up your area, check out. 5 Safety: goggles, clothes and shoes 5 Prelab quiz (10 to 25 points) 10 TOTAL 100 1. Based on your data, which method yielded a more accurate result? Explain why. 2. Based on your data, which method yielded a more precise result? Explain why. End of Experiment.