# Chemistry - How is exact racemization possible?

## Solution 1:

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.

## Solution 2:

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.