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?
If the R enantiomer is -33.6, then the S enantiomer must be + 33.6? right?
Yes! S enantiomer would be +33.6
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.