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Specific Rotation: Formula & Calculation

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  • 0:02 Chirality
  • 1:05 Specific Rotation Formula
  • 1:57 Sample Problem
  • 3:46 Lesson Summary
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Lesson Transcript
Instructor: Sarah Erhart

Sarah has taught college physical, organic, and general chemistry and high school biology. She has a master's degree in chemistry.

In this lesson, we'll talk about specific rotation. We'll go over the types of molecules that specific rotation is useful for and use the formula to complete a practice problem.

Chirality

Hold up your hands. It is easy to think that your right and left hands are identical, but in reality, they are mirror images of one another. No matter how much you rotate your hands, unless you disconnect one of them, you cannot superimpose them over each other. Two molecules can have the same relationship if they contain chiral centers. Chiral molecules, or mirror-image molecules, are known as enantiomers.

Like our hands, the mirror images found in chiral molecules are not superimposable but do perform similar functions. Although distinct, they share most physical and chemical properties, such as appearance or boiling and melting points. However, they can react somewhat differently, especially in relation to interactions in the human body.

The formula for specific rotation is important because it helps us distinguish between two enantiomers. This formula uses plane-polarized light to measure the rotation of light that occurs when it interacts with a molecule.

Specific Rotation Formula

We measure specific rotation with an instrument called a polarimeter. Once we obtain the measurement, we insert it into the specific rotation formula. This allows us to find the standardized specific rotation value, a characteristic property of a given compound. Specific rotation differs from observed rotation, which is not a typical feature of a given compound.

Let's take a look at the formula for specific rotation. In this formula:

  • alpha (a) represents the observed rotation measured with a polarimeter
  • l represents the length of the sample tube
  • C represents the concentration of a solution or density of a pure sample
  • T represents the temperature, typically 25 ºC
  • lambda represents the wave length of the light used, typically 589 nm

Sample Problem

Now let's look at an example using the formula for specific rotation.

Let's say we want to find the specific rotation of glucose. We place the glucose into a 0.2 dm polarimeter tube. Here we'll use the D-line of sodium, which is the typical wavelength to use with 589 nm. We'll perform the experiment at 25 degrees Celsius. The observed rotation is 16.2 degrees.

When we look up the density of glucose, we find that it is 1.54 g/cm cubed, which is equal to 1.54 g/mL.

So we need to plug all of this information into the formula:

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