EXPERIMENT #5 Physical Properties and Measurement: Density

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1 OBJECTIVES: EXPERIMENT #5 Physical Properties and Measurement: Density Determine the density of a liquid, a regular solid, and/or an irregular solid Determine the volume of the regular solid by calculation and displacement Plot mass versus volume and calculate the slope of the resulting straight line graph Demonstrate proper use of a laboratory balance, pipet, and graduate cylinder BACKGROUND: Some properties of matter are dependent on the amount of substance we are dealing with; such properties are called extensive properties. Mass and volume are extensive properties. Other properties of matter are independent of the amount of substance we are dealing with; such properties are called intensive properties. Concentration and density are intensive properties. Density is the ratio of mass to volume. It is defined mathematically as density mass volume d where the letters d, m, and V represent density, mass, and volume, respectively. Determination of the density requires measuring the mass and volume of the same sample at a specified temperature. The mass of material is easily determined by weighing a sample on a balance. The shape of a sample may be regular or irregular. Two methods are available for finding the volume of a regular solid. Its volume can be found by direct measurement or by displacement when immersed in an appropriate liquid (provided the solid is not soluble in the liquid). The volume in this latter instance equals the volume of the liquid the solid displaced. Formulas for calculating of the volume of solids with regular geometry are given in TABLE I. Irregular solids require use of the displacement method for volume determination. Density determinations must be made at well defined values of temperature and pressure for precise work. Volume measurements for liquids can be made with pipets, graduated cylinders, pycnometers, etc. The pycnometer is a special piece of calibrated volumetric glassware used for measuring the density of liquids and solids to a very high precision. The unit of density for liquids and solids is g/ml (g/cc, g/cm 3 ); for gases it is g/l. Inorganic and organic liquid density values generally range from less than one to almost three for 1,1,2,2-tetrabromoethane ( g/ml). However, mercury has a density of g/cm 3, and osmium has a density of 22.5 g/cc. The most common substance, water, has a maximum density of g/cm 3 at 4 C. TABLE I: Formulas for the Volumes of Some Regular Solids m v Geometry right parallelepiped Formula V = lwh sphere V =(1/6) d 3 = (4/3) r 3 cylinder V = ( /4)hd 2 = r 2 h cube V= l 3 37 P a g e

2 EXPERIMENT #5 DENSITY PROCEDURE: (Work individually.) 1. Density of a Liquid. After obtaining the mass, c, of a 50 ml Erlenmeyer flask, add ml of the liquid sample to the flask using a volumetric pipet (marked TD -- to deliver). Use a suction bulb to fill the pipet. Write the code number or letter of the liquid sample on TABLE II. Weigh the flask and sample together and enter this value, c + s, under Trial I in TABLE II. Obtain the mass of the sample, s, by subtraction (third line, Trial 1). Add another ml of sample to the flask and weigh it to find the mass of the new volume (20.00 ml). Repeat the above process to find the values for Trials 3 and 4. Complete TABLE III. Use this data to make a graph (see 3 below) of mass versus volume for the liquid and find its density at room temperature from the slope of the line. 2. Density of a Solid. Using four different sizes of cylinders made from the same material, find the diameters and heights of each one with a vernier caliper. You should be able to read the caliper to at least the nearest tenth of a millimeter. Record the values in TABLE IV. Also record the code for the cylinder material in the data sheet. Weigh each cylinder and record its mass on the appropriate blank in TABLES IV and V. The values recorded should be consistent with the precision of the measuring instrument. Use the data in TABLE IV to calculate the density of each cylinder and the average density. Next, add about 40 ml of water to a graduate cylinder and record the volume to the nearest 0.5 ml. Carefully lower the first cylinder of the set into the water in the graduate cylinder. Determine the displacement volume by difference [(volume of H2O + cylinder) - volume of H2O = volume of cylinder]. Find the volume of the remaining cylinders in this way. There should be a tenth s place for these volumes. Use the data in TABLE V to make a graph and find the density of the metal cylinder form the graph (See 3 below.). 3. Preparing the Line Graph. Graph the data collected in TABLES III and V on graph paper. The graph paper to use should contain10 grids to the cm or half-inch, and is available on the instructor s web site. Use the entire piece of paper and distribute the data points over the entire coordinate space (See FIGURE I.). Place a title on each graph and label each axis. Use a straight edge to draw the axes and the graph. Draw the best straight line through your data points, including as many of the points as possible. See your instructor if you need assistance in making your graphs. SHOW SLOPE CALCULATIONS FOR THE LIQUID AND SOLID ON THE GRAPHS. 4. Calculation of the Slope. One of the properties of a straight line graph is its slope. If the straight line passes through the points P1(x1, y1) and P2(x2, y2), the slope of the line is given by y slope m x 2 2 y x 1 1 y x 1 1 y x 2 2 change in y rise Δy change in x run Δx where the letter "m" stands for the value of the slope. 38 P a g e

3 EXPERIMENT #5 DENSITY FIGURE I is a graph of mass, in grams, versus volume, in cc, for mercury. We can calculate the slope of this line by using any two points lying on the line. Let us use P1 and P2 as these points. To obtain coordinates for P1 and P2 in FIGURE I extend the perpendiculars (dashed lines) from the axes so that these dashed lines intersect each other at a point on the straight line. One usually sites P1 and P2 near each end of the line. (Use the experimental data points to calculate the value of the slope of the line only if the points clearly lie on the line.) The coordinates of the data points are not normally listed on the graph, but are compiled in a table similar to TABLES III or V in the experiment. The value of the slope from using points P1 and P2 in FIGURE I is calculated as follows: 13.5g 68.0g 54.5g 3 m 13.6g/cm cm 5.00cm 4.00cm 39 P a g e

4 EXPERIMENT #5 DENSITY FIGURE I: Mass-Volume Ratio for Mercury 40 P a g e

5 NAME Section Date DATA AND CALCULATIONS: Density TABLE II: Mass and Volume Measurements for the Liquid Sample Trial ml Trial ml Trial ml Trial ml Mass of flask and liquid (c + s) Mass of flask (c) Mass of liquid* Liquid Sample *Also record these mass values in Table III Would you use the calibration marks on the flask to make exact measurements? TABLE III: Mass, Volume, and Density Values for the Liquid Sample Trial Mass of Sample, g Volume of Sample, ml Density, g/ml Average Slope of Graph 41 P a g e

6 TABLE IV: Total Mass and Calculated Volume Measurements for a Solid Cylinder Number Diameter, mm Height, mm Diameter, cm Height, cm Mass*, g Calculated Volume, cc Density, g/cc Average Material Chosen *Also record in Table V. TABLE V: Displacement Volume of Right Cylinder and Its Density Cylinder Number Mass, g Final Volume of Water Initial Volume of Water Displacement Volume, ml Density, g/ml Average Slope of Graph 42 P a g e

NAME Section Date ADDITIONAL ASSIGNMENT I: Density 1. What is the volume, in ml, of the cylinder in the drawing below. Use a metric ruler with millimeter graduations.

7 NAME Section Date ADDITIONAL ASSIGNMENT I: Density 1. What is the volume, in ml, of the cylinder in the drawing below. Use a metric ruler with millimeter graduations. The calculation should be consistent with the precision of the measuring instrument. diameter = height = Volume = 2. If the cylinder in the figure above weighed g, calculate its density in g/ml. 43 P a g e

8 3. A graduated cylinder is filled to a volume of 35.3 ml with water. An irregularly shaped solid weighing 58.1 g is placed in the cylinder. The water level rose to 71.6 ml. What is the density of the solid? 4. Calculate the mass of a gold sphere of radius 10.0 cm (the density of gold = 19.3 g/cm 3 ); 44 P a g e

9 NAME Section Date ADDITIONAL ASSIGNMENT II: Density 1. Calculate the mass of a cube of platinum of edge length mm. The density of platinum = 21.4 g/cm 3 ); 2. Calculate the mass of 50.0 ml of ethanol (the density of ethanol = g/cm 3 ). 45 P a g e

10 3. Osmium (Os) is the densest element known (density = g/cm 3 ). Calculate the mass in pounds and kilograms of an Os sphere cm in diameter (about the size of a grapefruit). 46 P a g e

Microscopic Measurement

Microscopic Measurement Estimating Specimen Size : The area of the slide that you see when you look through a microscope is called the " field of view ". If you know the diameter of your field of view,