Talk:Specific rotation

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The units for specific rotation are handled in a sloppy way -- not just in this article, but in the CRC Handbook as well. Because the definition specifies a path length of 10 cm, I assume one could correctly write that the rotation of a sucrose solution is:

  • = 66.47 deg (10 cm)-1 ml g-1
  • = 66.47 deg (10 cm)-1 cm3 g-1
  • = 6.647 deg cm2 g-1

However, the statement "The formal unit for specific rotation values is deg cm2 g-1 " implies that Sucrose has a specific rotation of +66.47 deg cm2 g-1 . I genuinely do not know which is correct. Spiel496 19:51, 27 February 2006 (UTC)

The definition is indeed in term of a 10 cm path. Note that the units for the 6.647 value are in terms of "(cm)-1" not "(10 cm)-1". You've changed the units by a factor of 10, so the value hasalso changes by a factor of 10. DMacks 01:07, 28 February 2006 (UTC)
Shouldn't the units should just follow from the equation?:
[\alpha]_\lambda^T = \frac{\alpha}{l * c}= \frac{66.47\mbox{ deg}}{(10\mbox{ cm}) * (1\mbox{ gm}/\mbox{ml})}= 66.47 \frac{ 0.1\mbox{ deg}\mbox{ cm}^2 }{ \mbox{gm} }
It looks to me like the "formal unit for specific rotation" is really "0.1 deg cm2 g-1". Spiel496 20:36, 6 March 2006 (UTC)
I agree that the "formal unit" description seems inconsistent with the math (which is consistent with the definition, i.e., 10 cm pathlength). Putting a scalar in the "units" seems weird, even though it might be technically correct. The key point that needs to be made in the text is that "degrees" is the common literature notation. Maybe the "formal unit" should use dm as the unit for the pathlength and not reduce (cm3 dm-1) into pure cm, so the scalar really does become part of the units? Would be good to get input from those who wrote the original here... DMacks 20:53, 6 March 2006 (UTC)

[edit] Units Nightmare

OK, I'm back once more to rant about units. First of all, my thanks go out to User:Orgchemprof for his/her contributions to the page, especially for adding the distinction between pure samples and solutions. But in my opinion, the article has become very confusing. Specifically, regarding the two forms of the equation

[\alpha]_\lambda^T = \frac{100 \alpha}{l \times c}, where c is in gm/100ml
vs.
[\alpha]_\lambda^T = \frac{\alpha}{l \times c}, where c is in gm/ml

What is a novice reader supposed to make of the following statement?:

"Mathematically, the two forms are the same, but chemically they are very different. "

I just don't follow it. If two formulas are mathematically the same, then they are the same. And the phrase "Because the units [of concentration] are not reported..." frankly points to a larger problem that no Wikipedia article is going to solve. Spiel496 23:23, 3 February 2007 (UTC)

I was initially confused about this as well. Orgchemprof is right about them being inequivalent chemically, though he doesn't give a reason why this would be significant. Since this is a phenomenon not entirely unlike that described with Beer's Law, it may be that the optical rotation values don't scale linearly with concentration when at high concentrations. In such an instance, the exact concentration used to generate the specific rotation would become important. --Uberhobo 17:20, 23 February 2007 (UTC)

Actually, upon asking around my department, the organic chemists use the "wrong" form of the equation, and my CRC handbook of chemistry and physics lists the g/mL version of the equation, as well. I'd be interested to see where Orgchemprof acquired his version. --Uberhobo 17:32, 23 February 2007 (UTC)

I did a Google book search, and found Orgchemprof's version of the equation in a couple of places. They were old books; maybe conventions have changed. If it is an issue with the rotation not scaling linearly with concentration, perhaps the equation should be dropped completely, as it implies linearity. The specific rotation could be defined solely with the statement at the top of the page: "the observed angle of optical rotation when plane-polarized light is passed through a sample with a path length of 1 decimeter and a sample concentration of 1 gram per 100 millilitre." Spiel496 18:11, 23 February 2007 (UTC)

The equation does imply linear scalability, and it holds for concentration ranges that would normally be used. Lots of linear relationships for solutions break down at high concentrations. But the equation is pretty essential here. I tried finding the IUPAC definition, since that would be as official as you get, but I couldn't find it on their website anywhere. The definition you propose above would be too small by 2 orders of magnitude. It does seem like a minor quibble, though. --Uberhobo 23:23, 23 February 2007 (UTC)

I didn't propose that definition -- it's from the lead paragraph of the article. I think it's consistent with the equations. Spiel496 06:26, 24 February 2007 (UTC)