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A racemate consists of 50 % $d$ and 50 % $l$ forms of an optically active compound. But how can someone ensure exact 50% quantity comparing molecule by molecule? There will always be some difference in number of molecules in both forms of optically active compounds. Is this sufficient for the mixture to rotate the plane polarised light in clockwise or anticlockwise direction?

According to wikipedia "Racemization can be achieved by simply mixing equal quantities of two pure enantiomers."

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Racemization isn't "exact," but rather very very close to equality. It is just simple probability.

Think of flipping a coin, p=probability for heads, and q=probability of tails. Now for a fair flip p=q=0.5. From binomial theory the standard deviation is $\sqrt{n\cdot p \cdot q}$ where n is the number of flips. Now let's assume 2 standard deviations difference, which is roughly at the 95% confidence interval.

If you flip 10 pennies then a two standard deviation difference is $2\times \sqrt{0.5^2\times 10} \approx 3$ in the number of heads.

Now flip $6.022\times10^{23}$ dimes then a two standard deviation difference is $2\times \sqrt{0.5^2\times 6.022\times10^{23}} \approx 7.8\times10^{11} $ in the number of heads.

But now think of the % difference.

  • $3$ heads in 10 tries for the pennies is $30\%$.

  • $7.8\times10^{11}$ more heads when flipping $6.022\times10^{23}$ dimes is only a difference of $1.3\times 10^{-10}\%$ which is an insignificantly small difference.

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  • $\begingroup$ Nice way to interpret! I believe this explains the racemization occurring during a reaction. What are your thoughts about manually mixing equal quantities of two pure enantiomers (as stated in last line of question)? $\endgroup$ – Apurvium Apr 26 at 10:45
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    $\begingroup$ @Apurvium - mixing enantiomers would be much less precise. It would easy to create a solution that was measurably optically inactive, But about 4 digit equality would be a very precise manual mixture. So 0.01% difference would be very very good work. $\endgroup$ – MaxW Apr 26 at 16:39
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It's just theory vs. real life. When mixing components, you always have limitations with the purity of chemicals and the accuracy of the balance available.

When you look at chemical reactions which yield chiral compounds, starting from achirals and there is no bias towards d or l, then you will end up with a true racemate.

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It is pretty much possible in asimptotic way - if you enable l and d form to change into each other. For example, there are enzymes called "something-racemase".

Even if you start with pure L or D form, you will get a mixture approaching equal concentrations of L and D.

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Stereoselectivity is a very important factor in organic synthesis. Most of the natural chemistry in the world, at least the world that involves biology and chemistry, is chiral, favoring one enantiomer over another. Speaking from the perspective of pharmaceuticals, chirality is critical to biological activity with respect to therapeutic benefit or toxicity. It is often desirable to produce one enantiomer in large excess to increase the yield of the desired "useful" product and reduce expense, waste, or extra steps required to isolate or purify the product, especially when multiple steps are required in synthesis and even small losses accumulate with each step.

In the case of many reactions, the ratio of stereoisomers produced can be random, leading to a near 50:50 split. In other cases, factors such as the intrinsic chirality or sterics of one or more reactants may influence the enantiomeric ratio. In some cases, one enantiomer is preferred almost exclusively because a reactant cannot approach the reaction site because of steric hindrance or factors including molecular conformations, such as hydrogen bonding, solvent, or temperature.

Books have been written about this topic, as well as numerous individual publications and review articles. A few references that might be helpful are listed below.

https://en.wikipedia.org/wiki/Stereoselectivity

https://www.researchgate.net/publication/316322015_Principles_of_Asymmetric_Synthesis

https://www.researchgate.net/publication/262607017_Editorial_Thematic_Issue_Enantioselective_Synthesis_in_Organic_and_Medicinal_Chemistry

http://www.carborad.com/Volume%20I/Chapter%2011/Stereoselectivity.pdf

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