MEASURING VOLUME & MASS In this laboratory you will have the opportunity to apply your measuring skills in gathering data, processing it, and interpreting the results. For this experiment you will: 1) measure the volume and mass of samples of minerals, 2) plot the data on a graph, and 3) determine the slope of the line that represents the density of the minerals. PART I: MEASURING VOLUME USING A GRADUATED CYLINDER On each of the 100mL and 250 ml graduated cylinders there are markings (graduations) that indicate the volumes along the length of the cylinder. Notice there are two sets of graduations on each cylinder, a graduation for larger volumes and smaller volumes. The smallest graduations on the 100 ml graduated cylinder are in increments of 1 ml and the larger graduations are in increments of 10 ml. 50 70 50 The smallest graduations on the 250 ml graduated cylinder are in increments of 2 ml and the larger graduations are in increments of 20 ml. Numbers that express measurements always contain one or more digits we are certain of, plus one that is estimated. All of these digits, the certain ones and the estimated one, are considered to be reasonably reliable, and are called significant figures. For example, the readings of 36.0 ml for both graduated cylinders above each contain three significant figures, the first two of which are certain, and the last of which is estimated. 50 100 When the meniscus of the liquid lies somewhere in between graduations, the volume of liquid must be estimated. As a rule, the volumes between the smallest graduations can be further graduated into 10 parts so that the accuracy of the 100 ml graduated cylinder can be estimated to the nearest 0.1 ml and the 250 ml cylinder can be estimated to the nearest 0.2 ml. Therefore the liquid in the 100 ml graduated cylinder could be recorded as 43.4 or 43.5 or 43.6 ml and the liquid in the 250 ml graduated cylinder could be recorded as 92.8 or 93.0 or 93.2 ml. Partially fill each of the two graduated cylinders with water and determine the volumes. To do this, place the cylinder on the table and stoop down so your eye is level with the water level. You will notice that the water looks curved in the cylinder. To get an accurate reading, read the bottom of the curve (meniscus). Record the volumes of the water below and let your instructor check your results. Volume of water in 100 ml cylinder ml L Volume of water in 250 ml cylinder ml L Turn to Check Your Understanding at the end of this lab and record the volumes of liquids in the graduated cylinders. Measuring Volume & Mass 1
PART II: MEASURING MASS USING A TRIPLE BEAM BALANCE Mass is a measure of the quantity of material the object contains. Measuring mass is done by comparing the mass of an unknown object to the mass of a known object. A beam balance has known masses (riders) which can be moved along the beams to determine the mass of an unknown object on the pan. Each of the beams has its own graduations. The mass of the unknown object is simply the sum of the readings on all three beams. To start, move all of the riders to zero (far left.) Notice that the riders for the 100 g and 10 g beams must fit into notches, while the 1 g rider slides between graduations. On the far right of the balance is a zero-scale which indicates when the known masses are equal to the unknown mass. When all of the riders are on zero, the balance arm should be even with the zero-scale indicator. Notice that the 1 g beam is graduated into 0.1 g graduations. Similar to the graduated cylinder, the masses of objects must be estimated to one more decimal place than the smallest graduation, or 0.01 grams. This is done by making 10 imaginary graduations between these graduations and estimating to the nearest 0.01 g. Determine the mass of your pencil using the triple-beam balance and record your results below. Have your instructor check your results. Your answer should be recorded to the nearest 0.01 g (13.56 g, for example.) Mass of pencil = grams kilograms Turn to Check Your Understanding at the end of this lab and record the masses as displayed on the balances. PART III: DETERMINING THE DENSITY OF MINERALS Minerals are solids that form naturally within the earth through the process of crystallization. Minerals differ from one another in a variety of ways, but because minerals have specific chemical and physical compositions, they have uniform consistency and a specific density. This physical property allows us to identify minerals by determing their mass/volume ratios and comparing the results with known values. In this portion of the laboratory the density of two common minerals will be determined from plotting mass and volume data. The identity of the minerals will be determined by comparing the experimental results with a table of known values. Take one piece of a mineral and determine its mass and record this in the data table provided. Fill the overflow can with water and allow the water to drain from the spout into a beaker. Find the volume of the mineral by placing it in the overflow cup and collecting the water in the 100 ml graduated cylinder. Record this volume in the data table. Take a second piece of mineral and determine its mass. In the data table add the mass of the second piece to the mass of your first sample of mineral. Place the second sample in the overflow cup and collect the volume of water displaced by the mineral into the graduated cylinder. Record the total volume of the first and second sample. Repeat this procedure three more times for a total of five samples. Measuring Volume & Mass 2
Y - axis Mineral Appearance: Mass (g) Volume (ml) Sample 1 Sample 1 + 2 Sample 1 + 2 + 3 Sample 1 + 2 + 3 + 4 Sample 1 + 2 + 3 + 4 + 5 Collect the mass and volume data for the second mineral. Mineral Appearance: Mass (g) Volume (ml) Sample 1 Sample 1 + 2 Sample 1 + 2 + 3 Sample 1 + 2 + 3 + 4 Sample 1 + 2 + 3 + 4 + 5 PART IV: GRAPHING A BEST-FIT LINE AND DETERMINING SLOPE The best-fit line represents the data (measurements) collected during an experiment when the points are unlikely to fall on the line because of experimental errors made in performing the experiment. When drawing a best-fit line, assume that half of the errors would result in numbers greater than the true value, and half of the errors would be less than the true value. Thus the best-fit line generally has the same number of data points above and below it. The following graph is an example of best-fit line: Best-Fit Straight Line 3 units of Rise Rise 3 units Slope = = = 1.5 Run 2 units 2 units of Run X - axis Measuring Volume & Mass 3
DETERMINING THE SLOPE OF A LINE Since the slope of a line is a mathematical relationship, it is not satisfactory to say one line is "quite steep or "not so steep". It is necessary to know as accurately as possible how much the line is slanted from the horizontal. In order to do this the amount of vertical "Rise" for a given amount of horizontal "Run" of the line must be determined. The slope, therefore, is obtained by constructing a right triangle at any segment of the line, determining the Rise and Run on the vertical and horizontal axes, and then finding the ratio of the Rise to the Run for that segment of the line. If, for example, we find that for any given segment of the line there is a rise of 3 units for every 2 units of horizontal distance, then the slope of the line is 1.5. The graph below is a best-fit plot of mass and volume data of four samples of a mineral. The slope of the line is determined using two points located on the best-fit line, not data points. The slope of the line (density of the mineral) is the ratio of the mass and volume (M / V). 200 (65, 200) Volume (ml) Mass (g) 15.8 48.98 32.0 105. 50.0 149.37 66.4 190.26 1 Mass (g) 1 1 120 100 (46, 1) Change in mass (Y) = 200.00 g 1.00 g =.00 g Change in volume (X) = 65.0 ml 46.0 ml = 19.0 ml Slope (Y / X) =.00 g / 19.0 ml = 3.16 g / ml To determine the volume for 100.00g of the mineral, a set of perpendicular lines that intersect at the bestfit line are drawn. For this mineral, the sample would occupy a volume of 32.0 ml. 20 0 10 20 50 70 Volume (ml) Graph your data for both minerals with volume on the X-axis and mass on the Y-axis. Draw a best-fit line for each mineral and determine their densities from the slope of their lines. Label the axes, include units, and add an appropriate title for the graph. Measuring Volume & Mass 4
POSTLAB QUESTIONS 1. Prepare a statement that relates the steepness of the graph with the densities of the two minerals. 2. Why is a best-fit line drawn between the points rather than connecting the dots? 3. Attach your graph that includes the work for determining the densities of the minerals. 4. Use the following table and determine the identity of each mineral. Density (g/ml) Borax 1.7 Pyrite 5.0 Quartz 2.65 Hematite 5.26 Talc 2.8 Copper 8.9 Mica 3.0 Gold 19.3 5. From your graph determine the volume of a 65.00 g sample of each mineral. (Show your work on your graph using the procedure described on page 4.) 6. From your graph determine the mass of a 50.0 ml sample of mineral. (Show your work on your graph using the procedure descibed on page 4.) 7. If you had.0 ml of each mineral, which mineral would have the greater mass? 8. If you had.00 g of each mineral, which mineral would occupy the greatest volume? Measuring Volume & Mass 5
Check Your Understanding Cylinder #1: ml Cylinder #2: ml 100 20 Cylinder #3: ml Cylinder #4: ml 200 70 1 1 Measuring Volume & Mass 6
Check Your Understanding Balance 1: g Balance 2: g Balance 3: g Balance 4: g Measuring Volume & Mass 7