Optical Activity: Videos & Practice Problems

Optical activity is a property of chiral molecules that allows them to rotate plane-polarized light, measured using a polarimeter. The observed rotation depends on specific rotation, concentration, and tube length, represented by the equation: $\alpha =\mathrm{[\alpha ]}\times c\times l$. Clockwise rotation is dextrorotatory (positive), while counterclockwise is levorotatory (negative). These designations do not correlate with the chirality of the molecule, emphasizing the distinction between optical activity and molecular configuration.

Specific rotation vs. observed rotation.

So optical activity is a special feature of chiral molecules. Alright? And what it basically means is that chiral molecules, when light is passed through them, they're able to rotate plane polarized light. Okay? And the machine that measures this is called, let me just write this down here, a polarimeter. What I'm going to do here is I'm going to show you how light travels through a polarimeter and show you guys where the numbers come into play. Alright? So first of all, we have some light bulb. Okay? That light bulb is a source of multi-directional light. What do I mean by that? It doesn't just shoot light in one direction. It scatters light throughout a space. Then we have a polarizer. A polarizer is just a type of lens, just like your polarized glasses, how it filters light and makes sure that it's only going in one direction. So, the light is going to pass through the polarizer and it's going to turn into what's called plane polarized light. It's only going on one plane. Alright? So then it passes through the actual functional part of the polarimeter, and that is this tube right here. This tube is going to carry a chiral concentration. It's going to carry a chiral mixture. And the interesting thing about chiral molecules is that as light passes through them, it rotates the light so that it basically changes its angle after it has passed the chiral molecule. This is something that scientists discovered a long time ago and it's still used today. Alright? Now what's going to affect the rotation? What kind of equations come into play to determine the angle of the rotation?

Well, what's going to affect it is a few things. First of all, every molecule has what's called a specific rotation. The specific rotation is just a random number that has to do with the amount of rotation that you would get if you had 100% of that enantiomer or 100% of that molecule present. What's the maximum rotation that you could get? Okay? Just so you know, the specific rotation is truly a random number. It doesn't have to do with the chirality necessarily, and it doesn't have to do with the size of the molecule. There's no way to predict it. You will always be given the specific rotation, or you'll be given the other variables to solve for the specific rotation, but you're not supposed to know it. That's all I'm saying. Okay? Just so you know, the specific rotation could be a positive rotation or a negative rotation. We're going to talk about that in a second as well. Then the next thing is the concentration of my reagent. So, the more my specific rotation and the higher the concentration in the tube, obviously, the more it's going to turn. The last thing is the length of the tube. Okay? And that just makes sense. The longer the tube is, the more time that light has to rotate as it's passing through. So, all these things are going to come together to equal my observed rotation. The observed rotation is just going to be the product of these three things combined. It's going to be the specific rotation times the concentration times the length of the tube. Does that make sense? And that's going to affect what I observe at the end. If I make my tube twice as long, I'm going to get twice the amount of rotation. Cool? Awesome. Well, it turns out that sometimes we're not always going to solve for observed rotation. A lot of times, we're going to be solving for specific rotation. So instead, in the problem, they're going to give us the observed, the concentration, and the length, and then we're going to have to solve for specific, in which case we would just flip the formula, use a little bit of algebra, and it looks like this:

<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mfrac>
    <mi>observed&t;rotation</mi>
    <mrow>
      <mi>concentration</mi>
      <mo>×</mo>
      <mi>length</mi>
    </mrow>
  </mfrac>
</math>

Easy stuff, right? We're just solving by basically taking out a variable.

Now, let's talk about the actual rotations. A clockwise rotation is called dextrorotary and it's symbolized using a positive symbol. And that's what I was talking about; how you can have a positive rotation or a negative. A counterclockwise rotation is known as levorotary and has a negative symbol. These are just words that were given to these rotations a long time ago. Just remember that if you see dextrorotary, that's positive; levorotary, that's negative. Now, these positive and negative names have nothing to do with the chirality of the molecule. So what that means is that a lot of people get confused and they think that positive means that you have an R chiral center or negative means you have an S chiral center because they see the clockwise and they think it's the same thing. They're completely different. A clockwise rotation of light has nothing to do with a clockwise chiral center. The clockwise thing just has to do with how we name the chiral center. It doesn't have to actually do with what the chiral center looks like. So what I'm trying to say is that in an R enantiomer, for some molecules, that could be a positive; for other molecules, that could be a negative. The only thing that it tells you is that it is chiral, but it doesn't tell you what type of chirality you have. Does that make sense? I just have to really emphasize that point.

Here’s what students ask on this topic:

What is optical activity in organic chemistry?

Optical activity is a property of chiral molecules that allows them to rotate plane-polarized light. This rotation occurs because chiral molecules have non-superimposable mirror images, which interact with light differently. The degree of rotation is measured using a device called a polarimeter. The observed rotation depends on the specific rotation of the molecule, the concentration of the chiral substance, and the length of the tube through which the light passes. The relationship is given by the equation: $\alpha =\left[\alpha \right]\times c\times l$.

How does a polarimeter work?

A polarimeter measures the angle of rotation caused by passing plane-polarized light through a chiral substance. The device consists of a light source, a polarizer, a sample tube, and an analyzer. The light source emits multi-directional light, which is then filtered by the polarizer to produce plane-polarized light. This light passes through the sample tube containing the chiral substance, which rotates the light. The analyzer measures the angle of rotation, which is used to calculate the specific rotation of the substance using the formula: $\alpha =\left[\alpha \right]\times c\times l$.

What factors affect the observed rotation in a polarimeter?

The observed rotation in a polarimeter is influenced by three main factors: specific rotation, concentration, and tube length. Specific rotation is an intrinsic property of the chiral molecule and is a constant value. Concentration refers to the amount of chiral substance in the solution, and tube length is the distance the light travels through the sample. The relationship between these factors is given by the equation: $\alpha =\left[\alpha \right]\times c\times l$. Increasing either the concentration or the tube length will result in a greater observed rotation.

What is the difference between dextrorotatory and levorotatory substances?

Dextrorotatory substances rotate plane-polarized light clockwise and are denoted by a positive sign (+). Levorotatory substances rotate plane-polarized light counterclockwise and are denoted by a negative sign (−). These terms describe the direction of light rotation but do not correlate with the chirality (R or S configuration) of the molecule. For example, an R enantiomer can be either dextrorotatory or levorotatory, depending on the specific molecule. The direction of rotation is an empirical property and must be determined experimentally.

How do you calculate specific rotation from observed rotation?

To calculate specific rotation from observed rotation, you use the formula: $\left[\alpha \right]=\frac{\alpha }{c\times l}$, where $\alpha$ is the observed rotation, $c$ is the concentration of the solution, and $l$ is the length of the tube. Rearranging the formula allows you to solve for the specific rotation: $\left[\alpha \right]=\frac{\alpha }{c\times l}$. This calculation is essential for determining the intrinsic optical activity of a chiral substance.