**5. POLARIMETRY**

**VIDEO LINKS:**

https://www.youtube.com/watch?v=T78v_XBktyE

https://www.youtube.com/watch?v=OPVX1hd1Acg

**DATA**

Part I Exploring Path Length

Angle_{blank }(°) = 197.2

| Run 1 | Run 2 | Run 3 | Run 4 | Run 5 |

Sample height (cm) | 2.0 | 4.0 | 6.0 | 8.0 | 10.0 |

Angle_{sample} (°) | 198.0 | 199.2 | 200.5 | 201.4 | 202.8 |

Angle of rotation, α (°) = Angle_{sample} – Angle_{blank} | | | | | |

Part II Exploring Concentration

Angle_{blank }(°) = 37.9

| 10% sample | 20% sample | 30% sample |

Sample height (cm) | 10.1 | 10.0 | 10.1 |

Angle_{sample} (°) | 43.3 | 50.9 | 57.3 |

Angle of rotation, α (°) = Angle_{sample} – Angle_{blank} | | | |

Exact concentration (g/mL) | | | |

**DATA ANALYSIS**

(as given in the Vernier handout)

**5. POLARIMETRY**

**VIDEO LINKS:**

https://www.youtube.com/watch?v=T78v_XBktyE

https://www.youtube.com/watch?v=OPVX1hd1Acg

**DATA**

Part I Exploring Path Length

Angle_{blank }(°) = 197.2

| Run 1 | Run 2 | Run 3 | Run 4 | Run 5 |

Sample height (cm) | 2.0 | 4.0 | 6.0 | 8.0 | 10.0 |

Angle_{sample} (°) | 198.0 | 199.2 | 200.5 | 201.4 | 202.8 |

Angle of rotation, α (°) = Angle_{sample} – Angle_{blank} | | | | | |

Part II Exploring Concentration

Angle_{blank }(°) = 37.9

| 10% sample | 20% sample | 30% sample |

Sample height (cm) | 10.1 | 10.0 | 10.1 |

Angle_{sample} (°) | 43.3 | 50.9 | 57.3 |

Angle of rotation, α (°) = Angle_{sample} – Angle_{blank} | | | |

Exact concentration (g/mL) | | | |

**DATA ANALYSIS**

(as given in the Vernier handout)

Understanding Polarimetry

A polarimeter is a device that measures the rotation of linearly polarized light by an optically active sample. This is of interest to organic chemists because it enables differentiation between optically active stereoisomers, i.e., enantiomers. Enantiomers, chiral molecules, are molecules which lack an internal plane of symmetry and have a non-superimosable mirror image. One way to tell these molecules apart is to use polarimetry. Polarimetry is also helpful for biological applications because amino acids, nucleic acids, carbohydrates, and lipids are all optically active. Determination of the optical activity of a compound using polarimetry allows the user to determine various characteristics, including the identity, of the specific chemical compound being investigated.

As shown in Figure 1, incident non-polarized light is transmitted through a fixed polarizer that only allows a certain orientation of light into the sample. The sample then rotates the light at a unique angle. As the analyzer is turned, the rotated light is maximally transmitted at that unique angle, allowing the user to determine properties of the sample. A (+) enantiomer rotates the plane of linearly polarized light clockwise, *dextro*, as seen by the detector. A (–) enantiomer rotates the plane counter-clockwise, *levo*.

Figure 1 Schematic of the Polarimeter

A compound will consistently have the same specific rotation under identical experimental conditions. To determine the specific rotation of the sample, use Biot’s law:

*α = [α] ℓ c*

where *α *is the observed optical rotation in units of degrees, *[α]* is the specific rotation in units of degrees (the formal unit for specific rotation is degrees dm^{-1} mL g^{-1}, but scientific literature uses just degrees), *ℓ* is the length of the cell in units of dm, and *c* is the sample concentration in units of grams per milliliter.

This experiment allows you to explore the interplay between these parameters in order to better understand polarimetry and how to use a Polarimeter.

OBJECTIVES

In this experiment, you will

- Become familiar with the use of the Polarimeter.
- Experience how sample path length and concentration affect observed rotation.
- Calculate the specific rotation for a known sugar sample using Biot’s law.

MATERIALS

LabQuest or computer interface | sucrose |

LabQuest App or Logger *Pro* | 50 mL volumetric flasks |

Vernier Polarimeter | 50 mL graduated cylinder |

Polarimeter sample cell | 50 mL beaker |

PROCEDURE

Figure 2 Rotation of the analyzer

Part I Exploring Path Length

1. Obtain and wear goggles and gloves.

2. Accurately prepare 50 mL of a 10% aqueous sucrose solution.

3. Connect the two Vernier Polarimeter cables to their respective ports on your data-collection interface. Start the data-collection program and choose New from the File menu. **Note:** In Logger *Pro*, wait until a graph of Illumination (rel) on the y-axis and Angle (°) on the x-axis appears before continuing.

4. Calibrate the Polarimeter.

Pour distilled water in the Polarimeter cell to a height of 10 cm. It is important to read the height to the nearest 0.1 cm. Read to the bottom of the meniscus.

Place the cell in the Polarimeter.

Start data collection and slowly rotate the analyzer clockwise or counterclockwise, as shown in Figure 2, until data collection stops (15 s). Slowly rotating the analyzer produces smoother curves. **Note:** If you are using a LabPro interface, only rotate the analyzer while data collection is active. Allow a few seconds at both the beginning and ending of data collection without moving the analyzer.

Figure 3 Selection for fits

5. Record the first angle above 0° where the illumination is at a maximum for the blank. One way to locate this angle is to use a Gaussian fit:

- Highlight the peak of interest using Logger
*Pro* or LabQuest App, as shown in Figure 3. For best results, be consistent in the way you select your peaks. - Choose Curve Fit from the Analyze menu.

From the list of available General Equations, select Gaussian.

Select Try Fit in Logger *Pro*; in LabQuest App, the fit will run automatically.

The B coefficient presented represents the angle at maximum illumination.

Record this value as Angle_{blank} below.

6. Store the run. In Logger *Pro*, do this by choosing Store Latest Run from the Experiment menu. In LabQuest App, you can store a run by tapping the file cabinet icon.

7. You are now ready to add the optically active sample into the Polarimeter cell.

- Pour the sucrose solution in the Polarimeter cell to a height of 10 cm. Record this value to the nearest 0.1 cm in the table below.
- Place the sample cell in the Polarimeter.
- Start data collection and slowly rotate the analyzer clockwise or counterclockwise until data collection stops.

8. Record the first angle above 0° where the illumination is at a maximum for the optically active sample as Angle_{sample} below. Repeat Step 5 to determine this angle.

9. Repeat Steps 6–8 for 8 cm, 6 cm, 4 cm, and 2 cm. Make sure to measure both the actual height of the liquid and the angle of rotation of the plane of polarized light with each change in volume of sucrose solution. Record these values in the table provided.

Part II Exploring Concentration

10. Prepare 50 mL each of 10%, 20%, and 30% solutions of sucrose in water.

11. Calibrate the Polarimeter as you did in Step 4.

12. Record the first angle above 0° where the illumination is at a maximum. Determine this angle using the same method as before.

13. You are now ready to add the optically active sample into the Polarimeter cell.

- Pour the 30% sucrose sample in the Polarimeter cell to a height of 10 cm. Record this value to the nearest 0.1 cm in the table below.
- Place the sample cell in the Polarimeter.
- Start data collection and slowly rotate the analyzer clockwise or counterclockwise until data collection stops.

14. Record the first angle above 0° where the illumination is at a maximum.

15. Store the run.

16. Empty the Polarimeter cell and rinse with a small amount of your next sample.

17. Repeat Steps 13–16 for the remaining samples you prepared.

DATA tables

Part I Exploring Path Length

Angle_{blank }(°) =_{ __________}

| Run 1 | Run 2 | Run 3 | Run 4 | Run 5 |

Sample height (cm) | | | | | |

Angle_{sample} (°) | | | | | |

Angle of rotation, α (°) = Angle_{sample} – Angle_{blank} | | | | | |

Part II Exploring Concentration

Angle_{blank }(°) =_{ __________}

| 10% sample | 20% sample | 30% sample |

Sample height (cm) | | | |

Angle_{sample} (°) | | | |

Angle of rotation, α (°) = Angle_{sample} – Angle_{blank} | | | |

Calculated concentration (g/mL) | | | |

DATA ANALYSIS

Part I Exploring Path Length

1. Generate a graph of height of liquid (cm) on the x-axis *vs.* optical rotation in degrees on the y-axis.

Logger *Pro*

- From the Page menu, choose Add Page. Select New Data Set and Graph. Click OK. In the data table of the newly generated Page 2, you will see a new data set with a column named “X” and a column named “Y.”
- To rename the X column, double click on the column heading. Enter
**Sample Height** as the Column Name, **Height **as the Short Name, and **cm** as the Units. Click Done. - In the same manner, name the Y column. Enter
**Angle of Rotation** as the Column Name, **Angle** as the Short Name, and degrees (**°**) as the Units by choosing the symbol from the drop-down menu. - Enter your data in the appropriate columns. Make sure the graph is displaying Sample Height on the x-axis and Angle of Rotation on the y-axis.

LabQuest App

- Save your raw polarimetry data file on to LabQuest. Choose New from the File menu.
- Tap the Data Table tab. You should see a data set with a column named “X” and a column named “Y.”
- To rename the x column, tap the x-column heading. Enter
**Height** as the Column Name and **cm** as the Units. Select OK. - In the same manner, rename the y-column. Enter
**Angle** as the column name and **deg** as the units. Select OK. - Enter your data in the appropriate columns. Tap the Graph tab and confirm the graph is displaying Height on the x-axis and Angle on the y-axis.

2. Using the curve fit option in the Analysis menu, determine the relationship between liquid height and optical rotation.

3. Find the best-fit line through the data points. Determine the angle of rotation when the height of the sample is exactly 10.0 cm.

4. Calculate the specific rotation of sucrose using Biot’s law. Compare this value to the accepted literature value and calculate your percent difference.

Part II Exploring Concentration

5. Using the observed angle of rotation and Biot’s law, calculate the exact concentrations of each sample in g/mL. Record these values in the table above.

6. Generate a plot of the calculated concentration values in g/mL *vs.* optical rotation in degrees, as you did above.

7. Based on your data, what is the relationship between optical rotation and concentration?

Extension

1. Analyze your Polarimeter data using two different methodologies, as described below.

- Statistics: Highlight the peak of interest in Logger
*Pro* or LabQuest App. Choose Statistics from the Analyze menu. Record the angle value where the illumination is at a maximum. - Cosine Squared: Choose Curve Fit from the Analyze menu. From the list of available General Equations, select Cosine Squared. Select Try Fit in Logger
*Pro*; in LabQuest App, the fit will run automatically. In this fit, the x-value corresponding to the maximum y-value is obtained from the negative of the phase shift parameter, –C. This is a nonlinear fit which undergoes numerous iterations and has the possibility of not converging, which will result in an unreasonable answer. With all nonlinear fits, it is important to make sure the resulting value is reasonable based on the data presented in the graph.

2. Compare the three different results from the three different fits (Gaussian, Statistics, and Cosine Squared). Discuss which one you think is more accurate and why.