The missing information in the question is the enantiomeric excess (ee) of the product. Since the product is slightly optically active, it means that both enantiomers are present in the mixture, but one enantiomer dominates over the other. The degree of this dominance is expressed by the enantiomeric excess, which is defined as:

ee = (major enantiomer - minor enantiomer) / (major enantiomer + minor enantiomer)

If the product has an ee of 100%, it means that only one enantiomer is present and the product is optically pure. If the product has an ee of 0%, it means that both enantiomers are present in equal amounts and the product is racemic.

Assuming that the chemist used (S)-epinephrine (the natural enantiomer) as the chiral additive, and that the reduction of butan-2-one is a stereospecific reaction (i.e. the stereochemistry of the product is determined by the stereochemistry of the starting material and the catalyst), we can calculate the expected specific rotation of the product using the following equation:

[α] = αobs / (l * c * ee)

where [α] is the specific rotation of the pure enantiomer (in degrees per cm per g), αobs is the observed specific rotation of the mixture, l is the path length of the polarimeter tube (in cm), c is the concentration of the sample (in g/mL), and ee is the enantiomeric excess (as a fraction between 0 and 1).

Assuming that the path length is 1 dm (10 cm) and the concentration is 1 g/mL, we can plug in the given values to get:

[α] = 0.45 / (10 * 1 * ee)

If we assume that the major enantiomer has a specific rotation of +1.0 (which is a typical value for a chiral ketone), and the minor enantiomer has a specific rotation of -1.0 (which is the opposite sign), we can calculate the enantiomeric excess from the observed specific rotation as follows:

αobs = [α] * (major enantiomer + minor enantiomer) / 2

Solving for ee, we get:

ee = (major enantiomer - minor enantiomer) / (major enantiomer + minor enantiomer) = (2 * [α] * αobs) / (αobs^2 - [α]^2)

Plugging in the given values, we get:

ee = (2 * 0.45 * 0.225) / (0.225^2 - 1^2) = -0.225

This result is negative, which means that the minor enantiomer dominates over the major enantiomer. However, the absolute value of the ee is greater than 1, which is not physically possible. This suggests that there is an error in the calculations or the assumptions made. One possible source of error is the assumption that the major and minor enantiomers have specific rotations of +1.0 and -1.0, respectively. In reality, the specific rotations of the enantiomers may be different, depending on the exact structure of the product and the wavelength of the polarimeter used. Another possible source of error is the assumption that