Question

How many stereoisomers are possible for glucose? A. 2 B. 8 C. 16 D. 32

Short answer

The correct answer is C: 16.

Step-by-step solution

- Determine the number of chiral centers in glucose

Glucose is an aldohexose with the chemical formula C6H12O6. To solve this, count the number of carbon atoms with four different groups attached to them, which are considered chiral centers. In glucose, there are 4 chiral centers (carbon atoms 2, 3, 4, and 5).

- Use the 2^n formula

The number of possible stereoisomers for a molecule is given by the formula 2^n, where n is the number of chiral centers. In glucose, n = 4.

- Calculate the number of stereoisomers

Apply the formula: 2^4 = 16. Therefore, the total number of stereoisomers possible for glucose is 16.

- Select the correct answer

Based on the calculation, the correct answer is option C: 16.

Key concepts

Chiral Centers in Glucose

Understanding chiral centers is essential for grasping stereoisomers in glucose. A chiral center, also known as a stereocenter, is a carbon atom that is attached to four different groups. This unique arrangement means that the molecule can exist in non-superimposable mirror images, known as enantiomers. In glucose, there are four chiral centers. These are located at carbon atoms 2, 3, 4, and 5. Each of these carbons is bonded to four distinct groups, making them chiral. Identifying these chiral centers in the glucose molecule is the first step in calculating its stereoisomers.

2^n Formula for Stereochemistry

The number of possible stereoisomers for any molecule with chiral centers can be determined using the formula \( 2^n \). In this formula, \( n \) represents the number of chiral centers. For instance, if a molecule has 3 chiral centers, the total number of stereoisomers would be \( 2^3 = 8 \). This formula is a quick and efficient way to calculate the number of possible stereoisomers without drawing each one. Applying this to glucose, which has 4 chiral centers, we use the formula \( 2^4 \). This calculation results in \( 16 \) possible stereoisomers. Therefore, glucose has 16 distinct stereoisomers due to its 4 chiral centers.

Calculating Stereoisomers

Calculating the number of stereoisomers is straightforward if you follow these steps:
1. Identify the number of chiral centers in the molecule.
2. Use the formula \( 2^n \), where \( n \) is the number of chiral centers.
Let's revisit glucose. First, we established that it has 4 chiral centers. Using the formula \( 2^n \), we substitute \( n \) with 4. This gives us \( 2^4 = 16 \).
This means the total number of stereoisomers for glucose is 16. This method is universally applicable to any molecule with chiral centers, allowing you to quickly determine the number of possible stereoisomers.