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Data Analysis

This document outlines a step-by-step procedure for analyzing sugar content in beverages using a calibration curve. It presents a table correlating the percent sugar to density at 20°C based on previous experiments. The experiment includes plotting data on graph paper, creating a calibration curve, and deriving the sugar content from beverage density measurements such as Pepsi. Additionally, it features calculated sugar content from nutritional labels and discusses percent error analysis to compare measured and calculated values.

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Data Analysis

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  1. Data Analysis Sugar Content in Beverages

  2. Step 1 – The Calibration Curve • Page 2 of the procedure presents a table of “Percent Sugar” vs. “Density at 20°C.” • This is data obtained from previous experiments. • Question: What kind of experiment would you design to produce a similar table?

  3. Step 1 – The Calibration Curve • The data from this table will give us the experimental value of the sugar content of the beverages tested. • We use graph paper to make a plot of the data.

  4. Step 1 – The Calibration Curve Use the entire length and width of the graph paper to make the graph. 1.080 Next, plot the data given in the data table. 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  5. Step 1 – The Calibration Curve 1% sugar has a density of 1.002 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  6. Step 1 – The Calibration Curve 5% sugar has a density of 1.018 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  7. Step 1 – The Calibration Curve 10% sugar has a density of 1.038 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  8. Step 1 – The Calibration Curve 15% sugar has a density of 1.059 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  9. Step 1 – The Calibration Curve 20% sugar has a density of 1.081 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  10. Step 1 – The Calibration Curve Next, we draw the “best fit” straight line through the data points. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  11. Step 2 – Experimental Sugar Content In Step 2 of the Data Analysis, we get an experimental estimate of the percent sugar of the beverages using the graph. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  12. Step 2 – Experimental Sugar Content We use our experimental density data to get our estimate. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  13. Step 2 – Experimental Sugar Content For example, suppose we determined the density of Pepsi to be 1.0032 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  14. Step 2 – Experimental Sugar Content We draw a line from the “Density” axis, at a value of 1.0032 g/mL, over to our calibration curve. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  15. Step 2 – Experimental Sugar Content Then we draw a line down from the calibration curve to the “Percent Sugar” axis. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  16. Step 2 – Experimental Sugar Content Then, we read off the value of the percent sugar in Pepsi as about 8.0%. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  17. Step 2 – Experimental Sugar Content We do the same thing for each beverage density value. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  18. Step 3 – Calculated Sugar Content • Step 3 of the Data Analysis uses the nutritional labels of the beverages to give us a calculated value of the sugar content of the beverages. • Pepsi has 26 g of sugar in 222 mL of beverage. • This is (26 g sugar/222 mL Pepsi) • Pepsi has a measured density of 1.0032 g/mL. • This is (1.0032 g Pepsi/1 mL Pepsi)

  19. Step 3 – Calculated Sugar Content • We calculate the sugar content of the beverage by • taking the nutritional data (26 g sugar/222 mL Pepsi) and • dividing it by the measured density (1.0032 g Pepsi/1 mL Pepsi)

  20. Step 3 – Calculated Sugar Content 26 g sugar/222 mL Pepsi = 1.0032 g Pepsi/1 mL Pepsi 26 g sugar 26 g sugar 1.0032 g Pepsi 1.0032 g Pepsi ÷ ÷ 222 mL Pepsi 222 mL Pepsi 1 mL Pepsi 1 mL Pepsi 26 g sugar 26 g sugar 26 g sugar 26 g sugar 1 mL Pepsi 1 × × 222.7 g Pepsi 222 mL Pepsi 222×1.0032 g Pepsi 222 1.0032 g Pepsi 1.0032 g Pepsi 26 g sugar 1 mL Pepsi × 222 mL Pepsi 1.0032 g Pepsi 26 g sugar 1 × = 0.116 g sugar/g Pepsi 222 1.0032 g Pepsi 26 g sugar Calculated percent sugar = (0.116 g sugar/g Pepsi)×100% = 11.6 % sugar 222×1.0032 g Pepsi

  21. Step 3 – Calculated Sugar Content • The calculated percent sugar for Pepsi is 11.6%.

  22. Step 4 – Percent Error • The calculated percent sugar for Pepsi is 11.6%. • This is different from the measured percent sugar we determined using the calibration curve. • We measured 8.0% sugar.

  23. Step 4 – Percent Error • The percent error is an indication of the magnitude of the error. |calculated value – experimental value| |11.6% – 8.0%| % error = % error = ×100% ×100% calculated value 11.6% = 31%

  24. Review of Data • The measured percent sugar from the calibration curve is 8.0%. • The calculated percent sugar from the nutritional data is 11.6%. • The percent error is 31%.

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