Soda Lab Report

Accuracy and Precision: Density of a Soda Can – September 29, 2008 The purpose of this experiment was to investigate the significance of precision and accuracy in scientific research. Throughout the course of this experiment, we explored how precision and accuracy related to working in a laboratory. Accuracy is a measure of how close an obtained value is to the true, or accepted, value. Precision is how consistent a set of measurements are, and how close they are to each other. Together, accuracy and precision tell if a set of measurements or results are reproducible and significant. This experiment also investigates which measuring device is more accurate and reliable to use. A 50 mL beaker and 10 mL were compared to see which instrument measured 10 mL of water more accurately. All of this is connected to the importance of accuracy and precision, regardless of the situation it is being used in. The first procedure of the experiment involved finding the relative density of soda cans in regards to water. Density measures how concentrated mass is in a particular space, or mass per unit volume. Density can be calculated by: Density = mass (g)/volume (mL) There were two cans of soda used – Pepsi and Diet Pepsi. Using the provided buckets of water, the cans were dropped, and any observations were recorded. The Pepsi can immediately sank straight to the bottom, while the Diet Pepsi remained floating on top of the water. The below data table ranks the two sodas in increasing relative density. Can of Soda Relative Density Diet Pepsi < water Pepsi > water

This occurrence of one can sinking, while another floats, can be explained by examining what each soda contains in its ingredients. Pepsi contains a sweetener known as high fructose corn syrup in large quantities, thus making up for its relatively high sugar content of 41 g. Diet Pepsi uses a non-nutritive sweetener known as aspartame. Because aspartame is much sweeter than high fructose corn syrup, it is used in smaller amounts. For example, high fructose corn syrup is a thick, dense substance constituting for nearly 10% of the soda. High fructose syrup is also a lot denser than water, so it will retain this attribute when added to Pepsi. Aspartame only makes up about 1% of the entire soda, making Pepsi denser than Diet Pepsi. Therefore, Pepsi’s higher density forces it to sink in water, while Diet Pepsi’s lower density allows it to float. Before calculating the density for these sodas, we had to find out which measuring device was capable of producing more accurate measurements. This device was determined by adding a specified volume into a pre-weighed container. Calculating the difference in mass, the mass of water can be found, which can then allow us to determine the delivered volume. By repeating this trial several times, the chance of error is minimized. Water was poured into both the beaker and graduated cylinder up to their marked 10 mL line. Then, that volume was poured

into a container, which had already been weighed by an electronic balance. The change in mass gave us the mass for the volume of water. Using a given density of water, 0.9998 g/mL, we found the measured volume of water, and determined its percentage of error to see how close it was to the 10 mL measured. The average volume of water determined from the 50 mL beaker was 6.393 mL, while the 10 mL graduated cylinder had an average volume of 9.667 mL. The average volume of water was determined by adding the volume of all three trials and dividing by the number of trials. Average Volume = Sum of all volumesNumber of Trials 50 mL beaker 10 mL graduated cylinder Average Volume = 6.51+6.30+6.373 Average Volume = 9.73+9.64+9.633 Average Volume = 19.183 Average Volume = 29.003 Average Volume ≈ 6.393 Average Volume ≈ 9.667 To determine the percentage of error, the following equation was used: percent error = |exp.value-true value|true value × 100% 50 mL beaker 10 mL graduated cylinder percent error = |exp.value-true value|true value ×100% percent error = |exp.value-true value|true value × 100% percent error = |6.393-10|10 × 100% error = |9.667-10|10 × 100%

percent

percent error = |-3.607|10 × 100% error = |-.333|10 × 100%

percent

percent error = 3.60710 × 100% error = .33310 × 100% percent error = .3607 × 100% error = .0333 × 100% percent error ≈ 36.07% percent error ≈ 3.33%

percent

percent

According to these results, the graduated cylinder was easily shown as the best measuring device, since it only had a 3.33% error, while the beaker had a 36.07% error. Having proved it more accurate, the graduated cylinder was used for the remainder of the experiment. The following data table on the next page gives exact measurements and results obtained from this part of the experiment.

1. mass of container 1. mass of container and water 1. mass of water 1. calculated volume of water 2. mass of container 2. mass of container and water 2. mass of water 2. calculated volume of water 3. mass of container 3. mass of container and water 3. mass of water 3. calculated volume of water Average volume of water Percent error Accuracy ranking

50 mL beaker 67.63

10 mL graduated cylinder 67.79

74.14 6.51

77.52 9.73

6.51 67.87

9.73 67.78

47.17 6.3

77.42 9.64

6.3 67.78

9.64 66.77

74.15 6.37

77.4 9.63

6.37 6.393 36.07% less accurate

9.63 9.667 3.33% more accurate

After determining that the graduated cylinder was the more accurate measuring device, the density of the sodas had to be determined. The procedure for finding the density of the soda was very similar to the previous procedure. Using a pipette, 10 mL of soda was poured into the graduated cylinder. The Pepsi was flat because the carbonation would cause errors in measurements. The mass of an empty container was calculated using an electronic balance. Then, the 10 mL of Pepsi was poured into the container, and the mass difference was the mass of the Pepsi for 10 mL of volume. Using the obtained mass and volume, the density was found for the Pepsi. This procedure was repeated several times to avoid any chance of error and ensure precision. The following data table shows the obtained results from this procedure. Measurements

1. mass of container 1. mass of container and Pepsi 1. mass of Pepsi 1. volume of Pepsi 1. density of Pepsi 2. mass of container 2. mass of container and Pepsi 2. mass of Pepsi 2. volume of Pepsi 2. density of Pepsi 3. mass of container 3. mass of container and Pepsi 3. mass of Pepsi 3. volume of Pepsi 3. density of Pepsi Average density of Pepsi

51.73 61.92 10.19 10 1.019 51.88 61.96 10.08 10 1.008 51.97 62.14 10.17 10 1.017 1.015

Since the average density of Pepsi was obtained as 1.015 g/mL or 1.02 g/mL, it will float in water, which only has a density of 0.9998 g/mL. While comparing these results with those of similar sodas, I noticed many differences. Several other measurements recorded the density of Pepsi as less than the density of water, which doesn’t make sense sine the Pepsi was observed sinking to the bottom. These other measurements include 0.996 g/mL, 0.998 g/mL, 0.994 g/mL, and 0.960 g/mL. These measurements contradict the fact that Pepsi has a greater density of water, since it sinks. Either these measurements contained errors, or there was something different about the can of Pepsi. The other 4 measurements supported my results, with measurements similar to mine, including 1.02 g/mL, 1.01 g/mL, 1.17 g/mL, and 1.05 g/mL. So, out of the 9 obtained measurements for Pepsi density, 5 out of the 9 measurements confirmed that Pepsi had a greater density in water, while the other 4 recorded that Pepsi was less dense than water. This confusion could have been caused by differences in the can or just slight errors in calculations, because Pepsi definitely sinks in water. For the most part, the Pepsi-sinks measurements which

supported my measurements were pretty precise. The measurements were very close together, with the exception of 1.17 g/mL. The Pepsi-floats measurements were also somewhat precise, but not accurate.