# Organic chemistry:

an attempt at synthesizing a certain optically active compound resulted in a mixture of its enantiomers. The mixture had an observed specific rotation of 11.0 degrees. If it is known that the specific rotation of the R enantiomer is -33.6 degrees, determine the percent of each enantiomer in the mixture.

So i have the equation set up:

11= x(-33.6) +(1-x)(spec. rot of S)

but how do i solve for x when the specific rotation of S is unknown?

13 years ago

11 years ago

## Yes! S enantiomer would be +33.6

1 year ago

## To solve for x in the equation, you need to find the specific rotation of the S enantiomer.

Since the observed specific rotation of the mixture is 11.0 degrees and the specific rotation of the R enantiomer is -33.6 degrees, you can set up the equation:

11 = x(-33.6) + (1-x)(spec. rot of S)

Let's rearrange the equation to solve for the specific rotation of the S enantiomer:

11 = x(-33.6) + (1-x)(spec. rot of S)

11 = -33.6x + spec. rot of S - x(spec. rot of S)

Now, substitute the value of spec. rot of S with 'y' to simplify the equation:

11 = -33.6x + y - xy

To solve for y, let's isolate it by moving the other terms to one side of the equation:

-33.6x - xy + y = 11

y - xy = 33.6x - 11

y(1 - x) = 33.6x - 11

y = (33.6x - 11) / (1 - x)

Now, substitute this value back into the original equation:

11 = x(-33.6) + (1-x)(y)

11 = -33.6x + (1-x)((33.6x - 11) / (1 - x))

Simplifying the equation further:

11 = -33.6x + (33.6x - 11)

11 = -11

Since this equation leads to an invalid statement, it indicates that there is no specific rotation value for the S enantiomer that satisfies the given values. This means that the specific rotation of the S enantiomer is unknown or not provided.

Thus, in this case, you cannot determine the percent of each enantiomer in the mixture without knowing the specific rotation of the S enantiomer.