Introduction to Measurement and Error Analysis: Measuring the Density of a Solution

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1 Introduction to Measurement and Error Analysis: Measuring the Density of a Solution Introduction: Most of us are familiar with the refreshing soft drink Coca-Cola, commonly known as Coke. The formula for Coke was devised in the 1880 s by Dr. John Pemberton of Atlanta, and remained a secret for many years. Not long ago. the secret formula ( 7X ) was revealed by a researcher searching through Coca-Cola Company archives. Of course, the main ingredients are water and sugar, and the density of Coke is primarily due to its sugar content. Because of this, Diet Coke is significantly less dense than regular Coke. Indeed, cans of Diet Coke will float in a tub of water while the same cans of Coke will sink. Density is defined as mass per unit volume in our case, in g/ml and you will thus have to measure both the mass and volume of a given sample of Coke. You will use several different methods to do so. Then, the data from all the students in the lab will be compared so you can determine the best possible experimental value for the density of Coke. In addition, you can evaluate the several experimental techniques in terms of their precision and accuracy. Waste Disposal All of the substances used in this experiment are non-toxic and may be rinsed down the drain. Using the Balances Before you weigh an object, there are certain considerations you must follow: Any object to be weighed must be at room temperature; air currents from hot or cold objects will affect the measurement. Chemicals must be held on weighing paper, or in a beaker. Never place any chemicals directly on the balance. Don t forget to weigh the empty container (or tare the balance) so you can find the weight of the chemicals alone. Clean up any spills carefully and promptly. Both the top-loading digital balance and the digital analytical balance are similar in operation. The top-loading balance is less precise (only to ±0.1 g) but can weigh heavy objects and is very sturdy. The analytical balance is much more precise (to ± g) but is more delicate and can only weigh relatively light objects. Top loading balances that measure ±0.01g and ±0.001g will be used in labs. Both balances have a large button labeled zero which is used to turn on and tare the balance. The balance is tared when it reads zero grams. You can tare the balance with an empty pan (this is called zeroing the balance) or you can tare it with an object on the pan (such as an empty beaker that you intend to fill with a chemical). The power button and the zero buttons are the only two you will need to use on the balance. Analytical Balance

2 Procedure: Part 1: Density Determination Using a Beaker The purpose of a beaker is to obtain and hold chemicals, but in this lab we are going to use it to measure the volume of a liquid. 1. Obtain an empty 50 or 100-mL beaker. Make sure the beaker is clean and dry. Go over to the balance. With the balance pan empty, close the doors and press the zero button to zero the balance. 2. Place the beaker on the balance pan. Record the mass of the beaker. 3. Remove the beaker from the balance pan and re-zero the balance. It is good etiquette to reset the balance to zero (with an empty pan) before leaving it. Return the test tube to the center bench. 5. Go over to the supply of Coke and add 25 ml of Coke to your beaker, simply using the marks on the side of the beaker to make your best estimate of this volume. If there is any fizzing, wait until the fizzing stops to measure the volume. Bring the beaker with Coke to the balance, zero the balance if necessary, and determine the mass of the beaker with the Coke. 6. Subtract the mass of the beaker from this in order to determine the mass of the Coke. Since you know that the volume is 25 ml, calculate the density of the Coke in g/ml. Part 2: Use of a Graduated Cylinder A graduated cylinder is the simplest general tool for measuring volume; simply fill it with the desired quantity of liquid and pour to dispense. Always make readings from liquid level, recording the volume measurement at the bottom of the meniscus. 1. Using a 250-mL beaker, collect about 150 ml of Coke. You will use this for the rest of your density measurements. 2. Use a 50-mL graduated cylinder to obtain 25.0 ml of Coke. Again, make sure there is no fizzing before you take your reading. Record your measurement and uncertainty. 3. Rinse and dry a small beaker and determine its mass. Add the Coke and determine the new mass. 4. Use your data to calculate the density of the Coke. Part 3: Use of the Buret The buret is generally used to dispense precisely any volume of solution. The stopcock at the end is used to control the flow of liquid from the buret; when the handle is in the horizontal position the stopcock is closed. The buret is filled from the top using a beaker or graduated cylinder and a funnel, taking care not to spill any liquid, and ensuring that the stopcock is closed before filling. Place a beaker under the tip and turn the stopcock swiftly in order to fill the tip with liquid. There must be no air bubbles in the buret tip. Before using any buret, it should be thoroughly rinsed with a small amount of the solution that is to be dispensed. Rinsing with distilled water before this rinse is necessary when exact concentrations are needed as in a titration. Do not try to align the liquid meniscus with the zero on the buret; rather, record the starting volume and subtract it from the final volume to obtain your net volume. Note that the numbers increase going down the buret.

3 1. Take your 50 or 100-mL beaker, rinse it, and dry it thoroughly. Determine its mass. 2. Using a buret, transfer ml of Coke to the beaker and measure the mass of the beaker with the Coke. Record your exact mass and volume 3. Calculate the density of Coke. Clean-Up: Clean all beakers and cylinders with fresh water. Dry and return them to where you got them. Drain and rinse the buret thoroughly first with tap water and then with distilled water. Clamp in an upright position with the stopcock open so that it may dry. 4. Record your density value for part 1, part 2, and part 3. with uncertainty on the board. Record all class data. Part 4: Preparation of a Standard Curve In order to determine the percentage of sugar present in a sample of Coke, you will need to compare your data to that obtained using sugar solutions of specific concentration. Prepare a graph of the following data. Solution Density (g/ml) % sugar % sugar % sugar % sugar % sugar Percentage of sugar should go on the x-axis and density on the y-axis. Include a best-fit line. Data (copy into your notebook): Part 1 Volume of Coke Using Beaker Density of Coke Using Beaker Measurement (+ uncertainty) Part 2 Volume of Coke Using Cylinder Density of Coke Using Cylinder Part 3 Volume of Coke Using Buret Density of Coke Using Buret

4 Class Data: (copy into your notebook) Group Density Using Beaker (Part 1) Density Using Cylinder (Part 2) Density Using Buret (Part 3) Class Average Calculations and Graphs: 1. Record the class data (density calculations) in your notebook. 2. Using the class data, perform a Q-test at 95% confidence level for each instrument to determine if any data should be thrown out. Show your work for one calculation. 3. From the remaining data, calculate the mean and the standard deviation for the data for all three instruments. Show your work for one calculation. 4. Perform a t-test at 95% confidence level and give the range for each instrument. 5. Use your standard curve to determine the percentage of sugar in Coca-Cola for all three instruments. Show your work on the graph and include the final answer. 6. If the actual density of coke is 1.03 ± 0.21g/mL * calculate the % error for each instrument Post-Lab Questions 1. Looking at the class data, which technique seems the most precise? The least precise? Support your answer with information from the error calculations performed. 2. Is this what you expected given the details of the measurement techniques? Explain. 3. You are asked to determine the density of 10 different solutions rapidly and accurately. Which technique would you use and why? 3. What is the difference between the error calculations performed or used in this lab? In what situations might you use one over another? Conclusion: Use your lab report format sheet to write a 2-3 paragraph conclusion about this experiment. Include information/answers which are pertinent to this lab.

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