(+) - Sucrose has a specific rotation of +66.5, while D - (+) - glucose and D - (-) - fructose have specific rotations of +52.5 and -92.4 respectively. After complete hydrolysis of (+) - sucrose by dilute acid, what will be the specific rotation of the hydrolysis product, called invert sugar [a \[1:1\] mixture of D-(+) - glucose and D - (-) – fructose] ?
A.-39.9
B.-72.4
C.-19.9
D.-34.9

Hint: To solve this question, we need to first understand the reaction that is taking place. Then we need to assess the optical rotation values of the individual products formed in order to find the optical rotation of the entire product as a mixture.

Complete Step-by-Step Answer:
Before we move forward with the solution of the given question, let us first understand some important basic concepts.
In the given question, we are performing the complete hydrolysis of sucrose by using a dilute acid. This hydrolysis reaction results in the formation of equal amounts of D – glucose and D – fructose or invertase of D – glucose D – fructose. Also, the specific rotations of the products as well as the reactant is given as:
(+) - Sucrose specific rotation = +66.5
D - (+) – glucose specific rotation = +52.5
D - (-) - fructose specific rotation = - 92.4
This entire data can be represented in the form of a chemical reaction as:
 \[
  {C_{12}}{H_{22}}{O_{11}}\,\, + \,\,{H_2}O\xrightarrow{{\text{dil. acid}}}\,\,\,\,{C_6}{H_{12}}{O_6}\,\,\,\,\,\,\,\, + \,\,\,\,\,\,{C_6}{H_{12}}{O_6} \\
  \text{sucrose}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{D - Glucose}\,\,\,\,\,\,\,\,\,\text{D - Fructose} \\
 \]
Since the specific rotation of D – glucose is less than that of D – fructose, the product formed by the hydrolysis of sucrose will be laevorotatory. This is the reason why the product of hydrolysis of a Dextro compound like sucrose is known as an inversion product.
The specific rotation of the product can be calculated as:

S. R. of product \[ = \dfrac{{\{ \left[ {D - \left( - \right) -\text{ fructose specific rotation}} \right] + \left[ {D - \left( + \right)-\text{glucose specific rotation}} \right]\} }}{2}\]
S. R. of product \[ = \dfrac{{\left( { - 92.4 + 52.5} \right)}}{2}\]
S. R. of product = -19.9

Hence, Option A is the correct option

Note: Optical activity occurs due to molecules dissolved in a fluid or due to the fluid itself only if the molecules are one of two (or more) stereoisomers; this is known as an enantiomer.