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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 222 mL Pepsi ÷ 1.0032 g Pepsi 1 mL Pepsi 26 g sugar 222 mL Pepsi ÷ 1.0032 g Pepsi 1 mL Pepsi 26 g sugar 222 mL Pepsi × 1 mL Pepsi 1.0032 g Pepsi 26 g sugar 222 mL Pepsi × 1 mL Pepsi 1.0032 g Pepsi 26 g sugar 222 × 1 1.0032 g Pepsi 26 g sugar 222 × 1 1.0032 g Pepsi 26 g sugar 222×1.0032 g Pepsi 26 g sugar 222×1.0032 g Pepsi 26 g sugar 222.7 g Pepsi = 0.116 g sugar/g Pepsi Calculated percent sugar = (0.116 g sugar/g Pepsi)×100%= 11.6 % sugar

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. % error = |calculated value – experimental value| calculated value ×100% error = |11.6% – 8.0%| 11.6% ×100% = 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%.