91影视

A spontaneous change in the specific rotation of a solution of an optically active compound is known as mutarotation. This implies that the two samples are different but in solution they form an equilibrium mixture.

The diastereomers resulting from cyclisation are known as anomers. They differ only in the configuration around first carbon (C1) which is referred to as the anomeric carbon (hemiacetal carbon atom).

If the fraction of galactose present as the $伪$anomer is role="math" localid="1664865398062" $\left(\left[伪\right]=+150.7^0\right)$ is a, the fraction present as the 尾anomer is $\left(\left[伪\right]=+52.8^0\right)$, and the specific rotation of the mixture is +80.2, then we can write as:

role="math" localid="1664865861024" $a\left(+150.7^0\right)+b\left(+52.8^0\right)=+80.2^0$

The fraction present as the $伪$ anomer (a) plus the fraction present as 尾 anomer (b) should account for all the galactose.

a+b = 1 or we can write b = 1-a

Now,

$$\begin{gathered} a\left(+150.7^0\right)+b\left(+52.8^0\right)=+80.2^0 \\ 鈬�a\left(+150.7^0\right)+\left(1-a\right)\left(52.8^0\right)=80.2^0 \\ 鈬�a脳150.7^0+52.8^0-a脳52.8^0=80.2^0 \\ 鈬�a\left(150.7^0-52.8^0\right)=80.2^0-52.8^0 \\ 鈬�a脳97.9^0=27.4^0 \\ 鈬�a=\frac{27.4^0}{97.9^0} \\ 鈬�a=0.28 \end{gathered}$$

So,

$\begin{array}{rcl}b& =& 1-a\\ & =& 1-0.28\\ & =& 0.72\end{array}$

Hence, the amounts of two anomers present at equilibrium are $伪$ anomer = 28% and 尾 anomer = 72%.