Experiment 2: THE DENSITY OF A SOLID UNKNOWN AND CALIBRATION WITH DATASTUDIO SOFTWARE Concepts: Density Equipment Calibration Approximate time required: 90 minutes for density 90 minutes for two thermometers EQUIPMENT NEEDED 50.00 ml volumetric flask wash bottle dropper base and support rod 250 ml beaker utility clamp slit two-hole stopper stirring rod aluminum foil thermometer safety goggles 5 ml pipette 125 ml Erlenmeyer flask rubber or cork stopper Science Workshop Interface temperature sensor CHEMICALS AND CONSUMABLES solid unknown distilled water ice PURPOSE The purpose of this laboratory activity is to explore the concept of density and to calibrate your laboratory thermometer by comparison with an accurate temperature sensor and calibrate your laboratory pipette. THEORY Density is a physical characteristic of substances that can be used to identify unknown pure substances. The density of an object is its mass per unit volume or: density mass volume
In addition, the density is a useful way to relate mass and volume. In the laboratory, it will sometimes be easier to measure out substances by mass rather than volume and other times by volume rather than mass. Knowing the density of an object will allow us to convert from one measurement to the other. Melting and freezing points can also be used to identify unknown pure substances. When a substance experiences a phase change, the temperature does not rise or fall during the phase change. For example, as energy is added, pure solid water (ice) at 0 C changes to liquid water at 0 C. When the substance reaches its melting (or freezing point), energy that is added (or removed) is used to generate the phase change instead of raising (or lowering) the temperature. The same concept applies to the liquid to gaseous phase change that occurs for water at 100 C at one atmosphere. The boiling point of water does vary with atmospheric pressure, but can be determined exactly from tabular data in the handbook of chemistry and physics if the pressure is found from a barometer. The freezing and boiling point temperatures will be precisely known and will serve as a reference for our calibration. A pipette is capable of very high precision and accuracy when used to measure volume properly. This experiment will allow you to practice your technique, and determine the accuracy of the pipette you are using. PROCEDURE Part I. Density of Solid Unknown 1. Zero the analytical balance and then weigh a clean, dry, 50.00 ml volumetric flask. Record all of the digits shown on the balance display. Do not round off. 2. Remove the flask from the balance and add your entire unknown from the vial to the flask. 3. Check to be sure that the balance still reads zero and then reweigh the flask and contents. To minimize errors due to small differences in balances, use the same balance to do all weighing during this experiment. 4. Remove the flask to your lab bench and add distilled water from your wash bottle to fill the flask about half way. 5. Swirl and tap the flask and contents to remove any large air bubbles. Your unknown may contain some entrapped air so removal of tiny bubbles on the surface of the unknown may be nearly impossible. 6. Add water up to the neck of the flask and then use a dropper to add distilled water to within a millimeter below where the meniscus would touch the calibration mark. 7. Use a piece of rolled paper towel to remove any drops from the neck of the flask that appear above the water line. 8. Use you dropper to very carefully add drops until the bottom of the meniscus is at the calibration mark without getting any water drops on the neck above the calibration mark. 9. Using the same balance as before, check the zero on the balance and then weigh the filled flask. 10. Empty your flask and its contents into the container provided at the de-ionized water sink. Rinse the flask three times with about 1/4 flask of distilled water. Place the rinsed flask on the tray provided.
11. Use your thermometer to take the temperature of the distilled water in your wash bottle and record it in the space indicated. Data #1 Mass of Empty Flask #2 Mass of flask and Sample #3 Mass of Flask, Sample and Water water temperature: Calculations: 1. Calculate the mass of the sample (#4) by subtracting the mass of the empty flask (#1) from the mass of flask and sample (#2). 2. Calculate the mass of water added (#5) by subtracting the mass of flask and sample (#2) from the mass of the flask, sample and water (#3). 3. Calculate the volume of water added (#6) by dividing the mass of water added (#5) by the density of water at room temperature. We will, for now, assume that the density of water at room temperature is 0.998203 g/ml. 4. Calculate the volume of your sample (#7) by subtracting the volume of water added (#6) from the capacity of the flask (50.00 ml). Take care to include the correct number of significant figures. 5. Calculate the density of your unknown by dividing the mass of sample (#4) by the volume of sample (#7). Take care to include the correct number of significant figures in your answer. Unknown Number: #4 Mass of Sample #5 Mass of Water added #6 Volume of Water added #7 Volume of Sample #8 Density of your Sample Show calculation set-up below result
Part II. Thermometer Calibration PART A: Computer Setup 1. Turn on the Science Workshop interface, and turn on the computer. 2. Connect the DIN plug of a Temperature Sensor into Analog Channel A of the interface. You can also connect another Temperature Sensor into Analog Channel B if needed for a lab mate. WARNING: Be sure to protect the temperature sensor probe s wire from direct heating by covering it with aluminum foil and keeping it away from fire. Follow all safety directives given by your teacher. 3. The file to open depends on the type of temperature sensor you will be using: If you have a temperature sensor with a box attached that says RTD, open the folder RTD on the desktop and then the file RTDVC002.ds If you have a temperature sensor that has a blue end (model CI-6605A), open the folder BLUE on the desktop and then the file BLUEVC002.ds If you have all black temperature sensor (model CI-6505B), open the folder BLACK on the desktop and then the file BLACKVC002.ds The document will open with two Digital temperature displays, one for Analog Channel A, and the other for Analog Channel B. Note: To bring a display to the top, click on its window or select the name of the display from the list at the end of the Display menu. 4. The Sampling Options... for this experiment have been set to 2 readings per second (2 Hz) PART B: Equipment Setup 1. Use a base and support rod, a utility clamp and a two-hole slit stopper to support the temperature sensor and thermometer. Be sure to wrap the sensor cable with aluminum foil and protect the cable from direct heating by keeping it far from the fire. 2. Place about 125 ml of ice and 75mL of water into a 250-mL beaker. 3. Gently lower the temperature sensor and thermometer into the ice water to about 1 cm from the bottom. Gently stir with a glass-stirring rod.
PART C Data Recording 1. Click the Start button to begin reading the temperature sensor data. The temperate sensors may take a few minutes to give accurate readings since like all electronic equipment they need to warm up. 2. When the temperature has stabilized at or near 0 C, accurately read the thermometer to the nearest 0.1 C and record the temperature sensor reading from the computer. Enter these numbers on the following data sheet. 3. Remove the ice cubes and place a total of 200 ml of cool (< 20 C) water into the beaker. 4. With a Bunsen burner, heat the water to about 20 C. Allow the system to come to thermal equilibrium for at least ONE minute. (i.e. take away the flame to let the temperature stabilize). Read the thermometer to the nearest 0.1 C and immediately read the digital display from the computer. Record both values in the data table below. 5. Repeat step 4 in 20 C degree intervals until the water reaches a gentle boil. 6. With the water gently boiling, accurately read the thermometer to the nearest 0.1 C and read the Digital display. Record both values in the data table below. 7. Have your instructor determine the corrected barometric pressure and determine the boiling point of water at this pressure. A table for the boiling point of water at various pressures is available in the CRC Handbook of Chemistry and Physics. Data Analysis Actual Temperature (T A ) of boiling water 1. Finding a correction factor for the temperature sensor. No instrument is 100 % perfect - even the computer temperature sensor. Consequently, we will first determine a correction factor for its reading using the properties of water. The actual temperature at the freezing point of water is 0 C and the actual temperature at the boiling point, T A (boiling point), is determined from the atmospheric pressure. If you are near sea level, the boiling point of water will be nearly 100 C. We can calculate a temperature correction factor (T C ) for the temperature sensor using T C = (0 C - T S (freezing point) ) + (T A (boiling point) - T S (boiling point) ) 2 where: T S (freezing point) is the sensor reading at the freezing point and T S (boiling point) is the sensor reading at the boiling point. Your T C = Note: T C may be positive or negative depending upon the temperature sensor. 2. The Actual Temperature, T A, can be found based on the temperature sensor readings and correction factor calculated above. T A = T S + T C
DATA TABLE: Temperature Calibration Thermometer Reading (T R ) Temperature Sensor (T s ) Temperature Correction (T c ) Actual Temperature (T A ) T A (Freezing) = 0 T A (Boiling) = On a piece of graph paper, draw a thermometer calibration graph of Actual Temperature (y) vs. Thermometer Reading (x). The data should cover the majority of the graph paper, the graph should have a title and the axis should be properly labeled. An example is printed on the next page. Alternately, you can make this graph in Excel 2007 using the following procedure: 1. Enter your six Thermometer readings in column A. Enter your six Actual temperatures in column B. Enter your numbers only (no units) and then highlight your data. 2. After entering all of your data, go to insert, then scatter. Several charts will appear. Select the top left one (no lines). Your graph should then appear. 3. Add a linear regression line by right clicking on one of the points of the graph. Select Add a trendline. Finally click on Display equation on chart 4. You can add titles and label your axis by selecting chart layout. 5. To print the graph, go to file, then print.
Part III. Correcting Unknown Density Now we will use your thermometer calibration graph to obtain a more accurate value for your unknown density. Show all your work for the calculations below or on the back of this sheet. Include units, label all quantities and show the equations you used. 1. Use your graph to find the actual temperature that corresponds to the temperature you recorded for the distilled water in your wash bottle. On your graph, pinpoint the temperature you recorded on the x-axis and find that temperature on the graph. Extrapolate this horizontally to the y-axis and record that value below. (Alternately, if you did your graph in Excel you can use the equation of the line) 2. Now find the exact density of water at this corrected temperature by using a table from the CRC Handbook of Chemistry and Physics. 3. Recalculate the density of your unknown by using this new density of water and record your corrected value below. Calculate the percent error between your two values by using the following formula: % error = corrected unknown density original unknown density x 100% corrected unknown density Corrected temperature of distilled water: Density of water at that temperature: Corrected unknown density: (from graph) (from CRC) % error in unknown density:
Part IV. Pipette Calibration 1. Fill a 250-mL beaker half full of de-ionized water and place your thermometer in it..2. Weigh a clean 125 ml Ehrlenmeyer flask with a solid rubber or cork stopper. Record the mass in the data table below. The stopper and flask together should not weigh more than 135 g. If they do, switch to a cork stopper or exchange your flask for a thin walled flask at the stockroom. 3. Take the 5.00 ml pipette in your locker and using the bulb, fill the pipette with deionized water and allow it to drain into the sink. If it does not drain cleanly (without hanging droplets of water on the inside), clean it with a hot soap solution. [Heat about 100 ml of de-ionized water to boiling. Turn off burner and remove the beaker from the ring stand. Add several drops of dish washing liquid and stir. Immerse the top of the pipette in the hot soap solution and apply the bulb to the tip. Vigorously pump the hot solution up and down the pipette for about a minute. Then rinse the pipette first with tap water and then with de-ionized water. Turn the pipette upright refill with de-ionized water and test for clean draining again. If there are still clinging droplets inside the pipette return it to the stockroom for ultrasonic cleaning or ask your instructor for help with more powerful cleaning methods. 4. Record the temperature of the de-ionized water in your beaker. 5. Refill the pipette to the mark and drain it into the Ehrlenmeyer flask. Stopper the flask and reweigh it on the same balance. Record the mass on the data page. 6. Pipette a second 5.00 ml portion of de-ionized water into the flask and reweigh. Record the mass. 7. Continue until you have pipetted five portions and weighed them. 8. From your temperature calibration curve, determine the actual temperature of the water in the flask. Look up the density of water at the actual temperature in the Handbook of Chemistry and Physics and record it on the data page. 9. Calculate the mass of each portion of water added. All masses should be about 5 g. 10. Divide each mass by the density of water to find the volume of each portion. All volumes should be about 5 ml. 11. Calculate the average volume after ignoring any values that are less than 4.75 ml or more than 5.25 ml. 12. Using method on the next page, calculate the standard deviation for the values that were not ignored.
Temperature of water pipetted into flask: Actual temperature of water in flask: Density of water at above temperature: (from graph) (from CRC) Data 1. Mass of empty flask & stopper 2. Mass of above + 5.00 ml of water 3. Mass of above + 5.00 ml more of water 4. Mass of above + 5.00 ml more of water 5. Mass of above + 5.00 ml more of water 6. Mass of above + 5.00 ml more of water Calculations Mass of first pipetted portion of water (2-1) Mass of second pipetted portion of water (3-2) Mass of third pipetted portion of water (4-3) Mass of fourth pipetted portion of water (5-4) Mass of fifth pipetted portion of water (6-5) Volume of first portion (Mass/density) Volume of second portion Volume of third portion Volume of fourth portion Volume of fifth portion Trial 1 Trial 2 (if needed) Average volume delivered by your pipette: ml The standard deviation is a method of expressing the precision of a given set of data. It represents the range into which 2/3 of all measured experimental values will fall when the experiment is repeated several times. A small standard deviation indicates very precise work and, providing there is not some systematic error (repeated non-random error due to poor apparatus or operating procedure,) it indicates the reliability of the results.
1. The average (mean) for your results from the previous page: ml 2. Calculate the deviation from the average for each individual result. Show your calculations. Individual Result Calculation Deviation ( show absolute value) Calculation of the standard deviation, σ (show your setup) Show your result (mean σ )
To find the standard deviation, one must first find the mean (average) of the results. This is found by adding together all the results and dividing the sum by the number of results. mean = (x 1 + x 2 + x n ) / n Then the deviation from the average for each result is calculated. d i = x i -mean The standard deviation,σ, is then calculated from the formula: d 1 2 + d 2 2 +.d n 2 σ = n-1 For example, if we have the following measurements for the volume of 5.00 ml of water: 5.0102 ml 4.9980 ml 5.0310 ml We would add them up and then divide by n = 3 to obtain an average: 5.0102 ml mean = 15.0392 ml / 3 = 5.0131 ml 4.9980 ml + 5.0310 ml 15.0392 ml Then, we calculate the deviation from the average by subtracting the mean from each measurement: d 1 = 5.0102 ml - 5.0131 ml = -.0029 ml d 2 = 4.9980 ml - 5.0131 ml = -.0151 ml d 3 = 5.0310 ml - 5.0131 ml =.0179 ml Finally, we square each of those deviations above, add them up, divide by n-1 (3-1) and then take the square root: (-.0029) 2 + (-.0151) 2 + (.0179) 2 = 0.0005568 = 0.0002784 = 0.0167 ml σ = (3-1) 2 The final results are often shown as: mean σ or 5.0131 0.0167 ml
Postlaboratory Assignment - Experiment 2 1. In Part I, if there are several large air bubbles trapped by your unknown, how will this affect the density of your unknown? Would it turn out higher or lower than the true value? Explain. Sometimes diagrams can help explain this better than words. 2. Luckily, in Part IV, you find that you have a small standard deviation in your series of measurements. Does this mean that you have a small random error or a small systematic error? Does it necessarily mean that you have precise results? Does it necessarily mean you have accurate results? Explain. 3. In Part I, if you do not remove all of the water from the neck of the flask above the 50.00 ml line, how will this affect the weight of #3, the mass of the flask, sample, and water? How will this affect the density of your unknown? Explain. 4. Take the density of your unknown that found in Part I, and convert it to the following units. SHOW WORK. a. pounds / ft 3 b. tons / yard 3 c. kilograms / liter
Name Prelaboratory Assignment Experiment 2 1. An unknown weighs 12.924 grams. This unknown is put into a 100.00 ml flask that weighs 35.9325 grams and then water is added to the calibration mark. The unknown, the flask, and the added water weigh 140.8321 g. What is the density of the unknown, assuming that the density of water is 0.998203 g/ml? 2. What two measuring devices are we calibrating in this experiment? 3. The following volumes were obtained for the calibration of a 10 ml pipet: 10.15 ml, 9.95 ml and 10.02 ml. Calculate the mean and the standard deviation.