With reference to different projection formulas used in stereochemistry (Fischer, Newman and Sawhorse projections), which one of the following statements is not correct?

Introduction / Context:
This question belongs to the domain of organic stereochemistry and asks about different ways of representing three dimensional structures on a two dimensional plane. Fischer, Newman and Sawhorse projections are widely used projection formulas to visualise conformations and configurations, especially for molecules like alkanes, substituted ethanes and carbohydrates. The task here is to find the statement that is not correct among the given options by recalling how each type of projection relates to molecular conformation and stability.

Given Data / Assumptions:
Fischer projections are commonly used for carbohydrates and amino acids to represent stereochemistry in a planar form.
Newman projections show the view along a particular carbon carbon bond and can depict eclipsed, staggered or skew conformations.
Sawhorse projections also show a carbon carbon bond but from an oblique angle, making the relative orientation of substituents clearer.
More stable conformations usually correspond to staggered arrangements, while eclipsed conformations are generally less stable due to torsional strain.

Concept / Approach:
The key idea is to understand what each projection represents. Fischer projections are essentially a convention to show stereochemical relationships and usually correspond to an eclipsed representation when converted to a simple carbon chain. They are convenient but do not necessarily depict the most stable conformation. Newman projections explicitly show the relationship between front and back substituents along a sigma bond and can be drawn in different conformational forms, such as staggered or eclipsed. Sawhorse projections offer a slightly tilted view of the same bond, allowing us to visualise torsional angles and interpret relative positions. The incorrect statement must contradict these standard ideas, particularly concerning whether a Fischer projection represents a most stable conformation.

Step-by-Step Solution:
Step 1: Evaluate the statement that a Fischer projection represents the molecule in an eclipsed conformation. When simple carbon chains are shown in Fischer projection, the substituents on adjacent carbons are implied to be eclipsed, so this statement is essentially correct. Step 2: Consider the statement that a Newman projection can be represented in eclipsed, staggered and skew conformations. This is true because Newman projections are specifically used to analyse conformations and can show all possible torsional arrangements. Step 3: Examine the statement that a Fischer projection of the molecule is its most stable conformation. Since the Fischer representation corresponds more closely to an eclipsed arrangement, and eclipsed conformations are not the most stable due to torsional strain, this statement is not correct. Step 4: Finally, check the statement about Sawhorse projections. In a Sawhorse projection, the carbon carbon bond is drawn diagonally and the substituent bonds are drawn at approximately 120 degrees to reflect the tetrahedral angle, so this statement is acceptable. Step 5: Based on this analysis, the only incorrect statement is that the Fischer projection corresponds to the most stable conformation of the molecule.

Verification / Alternative check:
If you take ethane as a simple example, its most stable conformation is the staggered form, which is best shown by a Newman projection. However, drawing ethane in a Fischer style projection would imply that the hydrogen atoms on adjacent carbons are aligned one behind the other, that is an eclipsed arrangement, which is higher in energy. Textbooks often highlight that Fischer projections are a stereochemical shorthand rather than true conformational pictures. This confirms that interpreting the Fischer projection as the most stable conformation is conceptually incorrect, reinforcing our choice of the wrong statement.

Why Other Options Are Wrong:
Option A is not the incorrect statement because Fischer projections do indeed treat adjacent substituents as if they were in an eclipsed arrangement when converted to simple conformational drawings.
Option B is correct because Newman projections are specifically designed to show different conformations and can be drawn for eclipsed, staggered or intermediate skew conformations as the dihedral angle changes.
Option D is also correct because Sawhorse projections usually depict the carbon carbon bond at an angle and the substituent bonds roughly at the tetrahedral angle of about 109.5 degrees, which is commonly idealised as 120 degrees in the drawing for clarity.

Common Pitfalls:
Students often confuse stereochemical representation with conformational stability. A projection that is easy to draw, such as a Fischer formula, is not automatically the lowest energy conformation. Another typical mistake is to assume that all projection formulas show the same conformation, which is not true because Newman and Sawhorse projections are primarily used for conformational analysis, whereas Fischer projections emphasise configuration at stereocentres. Carefully separating these concepts helps avoid misinterpretation in questions about projections and conformations.

Final Answer:
The statement that is not correct is the claim that Fischer projection of the molecule is its most stable conformation.