Data Analysis Sugar Content in Beverages. Step 1 – The Calibration Curve Page 2 of the procedure presents a table of “Percent Sugar” vs. “Density at 20°C.”

Data Analysis

Sugar Content in Beverages

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?

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.

Step 1 – The Calibration CurveD

ensi

ty (g

/mL)

Percent Sugar

1% 5% 10% 15% 20%

1.000

1.020

1.040

1.060

1.080Use the entire length and width of the graph paper to make the graph.

Next, plot the data given in the data table.

Step 1 – The Calibration CurveD

ensi

ty (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.

Step 1 – The Calibration CurveD

ensi

ty (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.

Step 1 – The Calibration CurveD

ensi

ty (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.

Step 1 – The Calibration CurveD

ensi

ty (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.

Step 1 – The Calibration CurveD

ensi

ty (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.

Step 1 – The Calibration CurveD

ensi

ty (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.

Step 2 – Experimental Sugar ContentD

ensi

ty (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.

Step 2 – Experimental Sugar ContentD

ensi

ty (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.

Step 2 – Experimental Sugar ContentD

ensi

ty (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.

Step 2 – Experimental Sugar ContentD

ensi

ty (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.

Step 2 – Experimental Sugar ContentD

ensi

ty (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.

Step 2 – Experimental Sugar ContentD

ensi

ty (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%.

Step 2 – Experimental Sugar ContentD

ensi

ty (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.

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)

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)

Step 3 – Calculated Sugar Content26 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 sugar222 mL Pepsi ÷

1.0032 g Pepsi1 mL Pepsi

26 g sugar222 mL Pepsi ×

1 mL Pepsi1.0032 g Pepsi

26 g sugar222 mL Pepsi ×

1 mL Pepsi1.0032 g Pepsi

26 g sugar222 ×

11.0032 g Pepsi

26 g sugar222 ×

11.0032 g Pepsi

26 g sugar222×1.0032 g Pepsi

26 g sugar222×1.0032 g Pepsi

26 g sugar222.7 g Pepsi = 0.116 g sugar/g Pepsi

Calculated percent sugar = (0.116 g sugar/g Pepsi)×100% = 11.6 % sugar

Step 3 – Calculated Sugar Content

• The calculated percent sugar for Pepsi is 11.6%.

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.

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%

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%.