What is the Percent Sugar in Soda? An Investigation Using Density

Transcription

1 Lab 4 Name What is the Percent Sugar in Soda? An Investigation Using Density Pre-Lab Assignment This written pre-lab is worth 15% (3 points) of your lab report grade and must be turned in to your lab instructor before class begins. 1. Read the entire lab handout. 2. Make a list of all chemicals used in this lab (may be names or chemical formulas). 3. List the suspected safety hazards in today s lab AND the safety precautions that should be taken to protect yourself from these hazards. Put this list in a table: one column for safety hazards, one for related safety precautions. Additional general safety precautions may be listed after the table. 4. Write a brief summary (2-3 sentences each) of each experiment that will be performed today (two experiments). Experimental Questions How can density be used to identify an unknown metal? What is the percent sugar in soda? Learning goals Make precise measurements needed to determine the density of materials, including two different methods for measuring the volume of a solid. Identify an unknown substance using its density and physical appearance. Use reference books like the CRC to look up physical properties of various substances. Prepare a calibration curve and use it to determine the concentration of sugar in an unknown. Background Density is the relationship between the mass of an object and its volume. By measuring the physical properties of the mass and volume we will determine the density. The mass can be measured directly but the volume will be determined by several different methods. For the liquid we will determine the volume by using a graduated cylinder. For the solid we will use physical dimensions of length, width and height or diameter and height which will be used to calculate the volume. We will also use water displacement to calculate the volume by difference. As we have seen, substances can be categorized according to whether they are a mixture (heterogeneous or homogeneous) or a pure substance (element or compound). Regardless of the substance's nature, it can be characterized by its various physical properties: color, density, melting point, etc. As we know, different substances have different physical (and chemical) properties. Today we will be examining the properties of solutions, which are homogeneous mixtures. The density of a substance or object is defined as the ratio of its mass to volume: density mass volume Density is a particularly important physical property because it is extremely sensitive to the substance's environmental conditions and composition. This is illustrated by looking at the variation in the density of water (Figure 1) with temperature and the variation in the density of aqueous NaCl solutions (Figure 2) with composition Water Temperature [ o Density C] [g/ml] Figure 1 Aqueous NaCl at 20 o C % Salt By Weight Density [g/ml] Figure 2

2 General Chemistry Lab 4: What is the Percent Sugar in Soda? 2 As can be noted from the data, water has a maximum density of g/ml at 3.98 o C, and the density decreases as the temperature rises. This is expected since as the temperature rises the added thermal energy causes the molecules making up the sample to "bounce around" more, therefore requiring an increased volume, resulting in a lower density. It can also be noted, that unless we are performing high precision work, the density of water, near room temperature, can be taken as about 1.00 g/ml. Because the density is a distinguishing characteristic of a given substance, it can be helpful in identifying it. Consider solutions of table sugar in water. As the table sugar becomes more concentrated, the density of the solution increases. By knowing how the concentration affects the density, we can determine the table sugar concentration in a given sample by simply measuring its density. This basic procedure has several important industrial applications. Two common examples are the determination of electrolyte concentration in automobile batteries and the determination of antifreeze concentration in automobile cooling systems. Laboratory Techniques: Measurements in the Lab Mass Measurements In all cases, density measurements require an independent determination of the mass and volume for a sample of the substance under consideration. Mass measurements are quite easy. The pan balance was one of the earliest instruments employed by the medieval alchemists; and you may see the modern version of them in the lab called the triple beam balance. Most modern laboratories use electronic balances, NOT BECAUSE THEY ARE MORE ACCURATE, but because they are easier to use. You might see in the laboratory or in a balance room, electronic balances to precisions of the centigram (0.01g), milligram (0.001g) or on tenth of a milligram (0.0001g). Each is progressively more expensive (you pay for precision) but the last digit shown on any balance is considered to be a guess. Another useful feature of an electronic balance is the TARE or ZERO button that allows you to add an object (like weighing paper) and set that mass to zero. Your teacher will show you which balance to use; always remember these 5 rules: 1. WHATEVER BALANCE YOU USE, RECORD ALL OF THE NUMBERS SHOWN. Never take off digits because you think you do not need them. 2. ALWAYS USE THE SAME BALANCE if you are doing weights by difference. Even electronic balances can consistently read too high or too low. 3. NEVER PUT CHEMICALS OR WET OBJECTS DIRECTLY ON THE BALANCE Use a container or weighing paper (folded twice and opened). 4. NEVER PUT HOT OBJECTS ON THE BALANCE Hot objects create air currents near them that can affect the weight shown on the balance. 5. ALWAYS CLEAN THE BALANCE AFTER USE You will see a brush near the balance to remove solids and paper towels to remove liquids. Volume Measurements Volume by measuring physical dimensions For regular solids, a simple ruled measuring device (ruler, caliper, etc.) can be used to determine the geometric parameters of the solid, and these parameters can be used to determine the volume: Rectangular Solid Cylindrical Solid height diameter height length width For these regular solids, the volume is related to the geometric parameters by: Rectangular Solid Cylinder diameter Volume height width length Volume height 2 2

3 General Chemistry Lab 4: Density Determinations 3 Volume by liquid displacement using a graduated cylinder: To measure the volume of an irregular solid, we can submerge the solid in an appropriate liquid. Using a principle first enunciated by Archimedes in 212 B.C., the volume of the solid will equal the volume of the displaced liquid, provided the solid does not dissolve in, or react with, the liquid. This is a volume determination by difference. Be careful of putting heavy metal objects into glassware (glass can break). Math in volume calculations: When you are multiplying (or dividing) numbers with units the units are physically attached by multiplication and act like a number or variable in algebra. That means that they can cancel like common factors if the same unit is on the top and bottom of a division bar. They multiply and can be squared or cubed. The problem comes when student used squared terms. Usually a student does not have a problem with 3.0 cm* 2.0 cm = 6.0 cm 2. But they get mixed up with (5.0 cm) 2. Let us take this from two angles. First, algebraically, the power on the outside will square all the terms inside to give cm 2 or 25. cm 2. Secondly, sometimes it is better for students (and teachers also) to use the definition of square, two numbers multiplied by themselves, to rewrite the problem to 5.0 cm*5.0cm = 25. cm 2 to make the problem easier. A value of 7.2 cm 3 can be rewritten as 7.2 cm*cm*cm in a calculation problem to help you visually see that each cm must be canceled individually. Following is an example showing how you might do a cube of a conversion factor of inches to cm: 3 1in cm in cm or 1in cm 1in cm 1in cm note that each unit is cancelled individually. Preparation of a Calibration Curve In order to determine the percent sugar in soda, we must first establish the relationship between sugar concentration in water and solution density; i.e. we will use known concentrations of several sugar solutions to establish a calibration curve relating the measured density and concentration. Then we will measure the density of a soda whose sugar concentration is unknown. Use of the prepared calibration curve will allow us to establish the concentration of the soda. A calibration curve relates a measured quantity with the factors that influence the measured quantity. For example, suppose we measure the density of a sodium chloride (NaCl, table salt) solution in water, as its concentration is varied. Density is the measured quantity and the percentage by weight of NaCl in water is the factor which influences the density. Figure 3 shows some measured values of the density of NaCl as the % of NaCl is varied. % NaCl by weight in water Density [g/ml] Figure 3 We will now prepare a calibration curve for this data. This curve will allow us to use measured densities of unknown samples of salt solutions to determine the composition, % NaCl, of the solution. The desired graph will plot: i) % NaCl along the x-axis as it is the independent variable. The axis will run from 8% to 18%. This is done to maximize the region over which data points will be spread. The axis will be labeled "% NaCl". No additional units are needed. ii) Density along the y-axis as it is the dependent variable because the density depends on the percent of NaCl in the solution. The dependent variable is the measured value that changes when we change a variable in the experiment such as percent NaCl. The axis will run from 1.00 to The axis will be labeled "Density [g/ml]". The following points should be considered when preparing the calibration curve: i) The independent variable is plotted on the x-axis and the dependent variable is plotted on the y-axis. ii) Each axis should have a descriptive label. The label must include the units of measurement associated with that measurement. iii) The axis range for both the x-axis and y-axis should be selected to maximize the region of the graph over which the data points are spread. You must fill the entire graph with data points. It is not acceptable to fill only a small corner of the graph with data points. It should be noted that the axes do not need to start at the value zero. iv) The graph should be given a descriptive title. It is not acceptable to merely repeat the axis labels. For our example, "Density vs. % NaCl" is not an acceptable title. A more appropriate title would be "Density of Sodium Chloride

4 Density [g/ml] General Chemistry Lab 4: Density Determinations 4 Solutions". This title tells us something about the system being examined; i.e., it tells us the substance whose density is being measured. v) A "best fit" curve should be included; this will be a straight line for most of cases we will be examining. The data points should NOT be connected in a dot-to dot fashion. The "best fit" curve averages out the errors which infect our data. When making the best fit line with a ruler, align the ruler such that as many points are above the line as below the line and it does not necessarily go through any of the data points. With these points kept in mind, a calibration curve for our sodium chloride data is: Density of Sodium Chloride Solutions 1.14 An unknown has a density of 1.11 g/ml Use straight lines (horizontal then vertical) to find concentration. Notice you must guess at a #. A guess at 15.1% would be reasonable % salt (NaCl) in water At this point, the calibration curve can be used to determine the % NaCl for any solution whose density has been measured. For example, suppose the measured density of a sodium chloride solution is found to be 1.11 g/ml and we wish to know the % NaCl. Consulting the calibration curve, we see this density would correspond to a solution whose composition is ~ 15.1% NaCl. What we have just done is a graphical interpolation of known data. Interpolation is where you determine a value in the middle of a set of known values. Extrapolation is where you go outside of known values (below or above ) and try to predict a value. It is sometimes called forecasting. In the case above an extrapolation would looked for % salt solution less than 8% or greater than 20%. The trouble with extrapolation is that you may not know if the data follows the same trend or starts to curve in a new direction. The further from known values you go, the more likely that you may be wrong.

5 General Chemistry Lab 4: Density Determinations 5 Procedure My lab partner is: Experiment 1. Density of Unknown Metal (mass and volume data) 1. Obtain an unknown regular metallic solid. Make sure it will fit into the 50 ml plastic graduated cylinder. Record the sample number. Unknown Solid ID Observations Concerning Unknown (Include shape, color, luster, etc.): Luster = shininess or makes a kind of reflection. A property of most metals is that they can be polished smooth to reflect the light almost like a mirror. When some metals oxidize (tarnish, rust), they become dull and do not shine) 2. Weigh the unknown metal sample. If it is wet then dry it first. It can be put directly on the balance. Mass of unknown 3. Measure the geometric parameters of the solid in cm using a metric ruler. Then determine the volume by calculation using the mathematical equations on page 2. Note: depending on what the shape of your solid is you will be taking one of the two sets of measurement. If your solid looks more like a brick or box use the rectangular solid, if it looks like a cylinder then take the cylindrical solid measurements. Rectangular Solid Cylindrical Solid Ruler Ruler height OR diameter width height length Critical Thinking Question 1: How many significant figures did you record using the ruler? How did you choose your last digit? Data Analysis 1: Calculate the volume of the solid. Show the formula, then the numbers in the formula including units and significant digits. Make sure that the final answer has the right units and significant digits. V (ruler) =

6 General Chemistry Lab 4: Density Determinations 6 4. Measure the volume of the solid using the liquid displacement method described on page 3. i) In a 50 ml plastic graduated cylinder add ml of water to the cylinder. Record the volume with correct significant figures. ii) Gently slide the solid into the cylinder. Record the new volume with proper significant figures. Initial Volume Final Volume Displaced Volume Data Analysis 2: Calculate the density of the solid based on geometric parameters on page 2 and on liquid displacement. Include equation and units. Method I (Geometric Parameters) Density Calculation (Include equation and units): Method II (Liquid Displacement) Density Calculation (Include equation and units): 5. Your unknown metal is one of the metals listed in the table below. Use a CRC handbook or Merck Index to look up the densities and other physical properties for each metal. Metal Density [g/ml] Observable properties (Color, etc.) Aluminum Copper Zinc Data Analysis 3: What is the identity of your metal? Briefly explain how your data led to that conclusion. Unknown number Element Data Analysis 4: Calculate the percent error in density separately for both Method 1 and Method 2 (take the literature value as the true value). measured value - true value Percentage error is calculated as: %error x100% true value

7 General Chemistry Lab 4: Density Determinations 7 Experiment 2: Percent Sugar in Soda A. Preparation & Density of Table Sugar (Sucrose) Solutions 1. Each individual will make one sugar solution of a concentration assigned by your instructor. The class will later share data on these solutions, which will range in concentration from 0% sugar (water only) to 20% sugar (20 g sugar/100 ml solution). Put a piece of tape on each beaker that you prepare and label it with a number. Do not throw your solutions away until after you have graphed them (you may need to redo one). i) Tare a 150 ml beaker. (This means put the beaker on the balance and push the tare or zero button so that the balance should read zero.) ii) Measure out close to the desired amount of table sugar in the beaker (remember to clean any spills after you use it). Record the actual amount on your data sheet. Important concept: When you are asked to weigh, for example, 5 g it means come close but do not try to get 5 with only zeros after it. For example on a balance that reads to g then 4.951g or or or would all have been acceptable. The important part is that you record all the numbers from the balance and that you are close to 5 g. iii) Add ml of water to the beaker and stir with a glass stirring rod until all the sugar is dissolved. iv) Transfer the sugar solution into a 100 ml volumetric flask. Rinse the beaker and all glassware into the flask. Add water to the mark. Make sure the meniscus is at the 100 ml mark. Use your dropper if necessary. If you go over the mark, start over. Note that this volumetric flask has a precision of ml (5 significant figures). v) Stopper the flask and invert several times to mix thoroughly. Observations of solid sugar (color, state, texture, etc.) Table 1: Raw Data Concentration of Known Solution Prepared by Mass of sugar Solution Observations of solution (color, state, clarity, viscosity, etc.) 2. Measure the mass and volume of each table sugar (sucrose) solution by the following method: i) Weigh a clean, dry 50 ml graduated cylinder. ii) Take the graduated cylinder back to your bench and add about 20 ml of your sugar solution. Record the precise volume with proper significant figures. Remember, it doesn t matter exactly how much solution you add, but it is very important that you measure the volume precisely (estimate between the lines). iii) Weigh the graduated cylinder with the sugar solution in it.

8 General Chemistry Lab 4: Density Determinations 8 Table 2: Mass and Volume Raw Data Mass of empty graduated cylinder Mass of graduated cylinder plus sugar solution Calculated mass of solution Volume of solution Solution Data Analysis 5: Calculate the density of your sugar solution. Show all work. Data Analysis 6: Fill in the results table below. %w/v g solute x 100% ml solution Table 3: Density and Percent Sugar Results Density Percent sugar (w/v) Solution 3. Share data on class spreadsheet by entering calculated densities and percent sugar for your solution. Your instructor will prepare a graph and lead you in a class discussion. i) What quantity and units are on the x-axis? ii) What quantity and units are on the y-axis? iii) Write the equation for the best fit line. Use numerical values for the slope (m) and the y-intercept (b). Instead of writing x and y in your equation, write the corresponding physical quantities (hint: what are the labels on the axes?). iv) This calibration curve relates density of a solution to its percent sugar in the solution. What two methods can be used to determine the percent of sugar in an unknown solution from the calibration curve? v) Do the points of the calibration curve fall near the line, or is there much scatter? How reliable do you think this calibration curve will be for determining the percent sugar of an unknown solution?

9 General Chemistry Lab 4: Density Determinations 9 B. Density of Soda (mass and volume data) 1. Obtain sample of soda. 2. Measure the mass and volume of the sample as in step 2 on p. 7. Soda brand / type Mass of sugar from nutritional label on soda can Volume of soda from nutritional label on soda can Observation of soda (Include color, state, clarity, viscosity, etc.): Mass Volume Clean all equipment and glassware. Return materials to the community area. Wipe down the lab bench. Return the key to the front desk. Do not remove your safety goggles until ALL GROUPS have finished cleaning up. Obtain instructor initials before leaving the lab. Instructor Initials Data Analysis 7: Calculate the density of your soda. Show all work. Data Analysis 8: Using the calibration curve, determine the percent sugar in your soda by two methods: a. Print the graph. Mark the density of the soda on the y-axis. Use a ruler to draw a line horizontally from that point to the calibration line. Then use a ruler to draw a vertical line from that point to the x-axis. Record the value at that point with correct significant figures. Attach the graph to this handout. Concentration from visual analysis of graph b. Use the equation for the line to calculate the percent sugar in your soda. Show all work below. Concentration from best fit line equation

10 General Chemistry Lab 4: Density Determinations 10 Data Analysis 9: Calculate the % (w/v) of the soda from the manufacturer information on the nutritional label. Be sure to take into account the serving size. How does your experimentally determined value compare? (hint: what calculation can you do to for a more quantitative comparison?) Data Analysis 9: Results Table result % error Density of unknown metal by method 1 Density of unknown metal by method 2 Identity of unknown metal Concentration of sugar in soda Questions 1. Consider the data analysis portion of the scientific method. One important component is assessing the reliability of your results. Comment on the reliability of your results for each experiment. In your discussion, you may find it useful to cite the percent error, the precision of the original measurements, uncertainty in the experimental method, potential sources of loss of substance, graphical anomalies, class data vs. individual data, etc. A. Density of a solid: geometric parameters for volume vs. liquid displacement: B. Percent sugar in soda:

11 General Chemistry Lab 4: Density Determinations Blood plasma volume for adults is about 3.1 L. Its density is g/cm 3. How many pounds of blood plasma are there in your body? 3. Diamonds, density = 3.51 g/cm 3, are commonly measured in carats; 1 carat =200 mg. What is the volume of a 2.0 carat diamond? 4. Explain how any one aspect of this lab relates to your daily life. (Hint: See learning goals, techniques used in the lab, and chemistry concepts explored for ideas.)

12 General Chemistry Lab 4: Density Determinations 12 Conclusion Answer the two Experimental Questions using grammatically correct English sentences. Be sure to give the unknown number for your metal and the type of soda in your answers. Explain your answers using evidence from your experimental data. In other words, refer to specific data, note where to find the data, and then explain how your data supports your conclusion. Note: you do not need to describe each step of your calculations. How can density be used to identify an unknown metal? Evidence: What is the percent sugar in soda? (Be sure to answer this question based on your experimental results.) Evidence: Turn in this handout with the labeled calibration curve stapled to the back at the beginning of the next lab period.