Representing three-dimensional molecules on a flat surface requires specialized drawing conventions. Chemists use these systems to convey a molecule’s true spatial arrangement, or stereochemistry. Molecules with specific geometries also possess fixed, distinct locations for atoms, known as positional geometry. The question of whether a wedge or a dash corresponds to an axial or equatorial position arises from relating these two separate concepts: a drawing convention and a fixed geometric location. Understanding their individual meanings is the first step in clarifying their relationship.
The Purpose of Wedge and Dash Notation
The wedge and dash notation is a fundamental tool for depicting a molecule’s three-dimensional structure relative to the observer. This system shows the stereochemistry and orientation of a bond in space. A solid wedge represents a bond projecting out of the drawing plane, extending toward the viewer. Conversely, a dashed line represents a bond receding into the plane, pointing away from the viewer. Bonds lying within the plane are typically shown using a simple, straight line.
This notation depends entirely on the perspective chosen by the drawer. If the molecule is rotated, the same bond might change from a wedge to a dash or a straight line to represent the new orientation correctly. Therefore, the wedge and dash system describes the bond’s orientation relative to the drawing plane, not a fixed location within the molecule itself. This notation is primarily used to distinguish between stereoisomers.
Defining Axial and Equatorial Positions
Axial and equatorial positions are fixed, inherent geometric locations within certain polyatomic structures, independent of how the molecule is drawn. These positions are defined by the molecular geometry. A clear example is the trigonal bipyramidal \(\text{AX}_5\) geometry, such as phosphorus pentafluoride (\(\text{PF}_5\)).
In this geometry, the central atom is surrounded by five atoms separated into two distinct sets of positions. Three atoms occupy the equatorial positions, lying in a triangular plane around the center atom. The remaining two atoms occupy the axial positions, located directly above and below this equatorial plane, forming a linear axis perpendicular to the plane.
The concept also applies to cyclic molecules, such as the chair conformation of cyclohexane. Here, the six bonds attached to the ring carbons are separated into axial and equatorial sets. The six axial bonds are oriented roughly parallel to the ring’s central axis. The six equatorial bonds project outward, nearly parallel to the ring’s average plane. These positions are fixed features defined by the molecule’s internal geometry.
Connecting Notation and Position
Wedge/dash notation and axial/equatorial position are two independent concepts describing different properties of a bond. A wedge or a dash is a visual convention for two-dimensional representation. Axial or equatorial is a fixed, three-dimensional location within a specific molecular geometry. Consequently, a bond in an axial position can be represented by a wedge, a dash, or a straight line, depending solely on the molecule’s orientation when drawn.
Consider a trigonal bipyramidal molecule like \(\text{PCl}_5\), where the two axial chlorine atoms are fixed \(180^{\circ}\) apart. If the molecule is drawn with the axial bonds oriented vertically, they would most likely be shown as straight lines because they lie in the plane of the page. However, if the entire molecule were rotated \(45^{\circ}\) around a horizontal axis, those same two axial bonds would now be projecting out of and into the page, requiring them to be drawn with a wedge and a dash, respectively. The geometric position of the bond remains axial, but its drawing notation changes with the viewing angle.
The notation system describes the stereochemistry relative to the observer, indicating if the atom is in front of or behind the paper plane. The positional term describes the geometry relative to the molecule’s structure itself, indicating a fixed location based on bond angles and symmetry. There is no rule that an axial bond must be a straight line or that an equatorial bond must be a wedge; the notation simply follows the perspective of the drawing.
Case Study: Cyclohexane Conformers
The common confusion often stems from the standard way the cyclohexane chair conformation is drawn. In this conventional representation, the six axial bonds are drawn nearly vertical, which often leads to them being represented by simple straight lines.
The six equatorial bonds are drawn projecting outward from the ring at a slight angle. To accurately convey their three-dimensional tilt relative to the observer, these bonds are frequently represented using wedges or dashes. For example, an equatorial bond projecting slightly up and toward the viewer might be drawn with a wedge.
This is merely a drawing convention that aids visualization, not a fundamental definition. The wedge or dash shows the up/down spatial orientation of the substituent, which is independent of its axial or equatorial label. After a ring flip, a substituent that was axial and “up” becomes equatorial and still “up,” but the drawing notation may change to maintain the correct three-dimensional perspective.