Question

Using lines, solid wedges, and dashed wedges, draw the threedimensional shape of ethane, \(\mathrm{C}_{2} \mathrm{H}_{6}\). Indicate the numeric value of all bond angles.

Short answer

To draw the three-dimensional shape of ethane (\(\mathrm{C}_{2} \mathrm{H}_{6}\)), use lines for in-plane bonds, solid wedges for bonds coming out of the plane, and dashed wedges for bonds going into the plane. Start by drawing the carbon-carbon bond, then add three hydrogen atoms around each carbon represented by a combination of lines, solid wedges, and dashed wedges. All bond angles in ethane are approximately 109.5 degrees, so label the H-C-H and C-C-C bond angles accordingly.

Step-by-step solution

Draw the carbon-carbon bond

Draw a straight line representing the single bond between the two carbon atoms in ethane.

Draw hydrogen atoms around the first carbon

Draw three hydrogen atoms around the first carbon atom using lines, solid wedges, and dashed wedges. The solid wedge represents a bond coming out of the plane towards the observer, and the dashed wedge represents a bond going into the plane away from the observer. The line represents a bond that lies in the plane. - Draw a line from the first carbon to a hydrogen atom (H1) at an angle of approximately 109.5 degrees. - Draw a solid wedge from the first carbon to another hydrogen atom (H2) at an angle of approximately 109.5 degrees. - Draw a dashed wedge from the first carbon to the third hydrogen atom (H3) at an angle of approximately 109.5 degrees.

Draw hydrogen atoms around the second carbon

Now we need to draw the three hydrogen atoms around the second carbon atom in the same way we did for the first carbon. - Draw a line from the second carbon to a hydrogen atom (H4) at an angle of approximately 109.5 degrees. - Draw a solid wedge from the second carbon to another hydrogen atom (H5) at an angle of approximately 109.5 degrees. - Draw a dashed wedge from the second carbon to the third hydrogen atom (H6) at an angle of approximately 109.5 degrees.

Indicate the bond angles

Label each bond angle in the molecule with numeric values. In ethane, the bond angles are approximately 109.5 degrees. Use these values for each bond angle, focusing on the angles between the hydrogen-carbon-hydrogen (H-C-H) and the carbon-carbon bond angle (C-C-C): - Label the H-C-H bond angles around the first carbon atom (approximately 109.5 degrees). - Label the H-C-H bond angles around the second carbon atom (approximately 109.5 degrees). - Label the C-C-C bond angle between the two carbon atoms (approximately 109.5 degrees). Now you have successfully drawn the three-dimensional shape of ethane using lines, solid wedges, and dashed wedges, and indicated the numeric values for all bond angles.

Key concepts

Bond Angles

Bond angles are a crucial part of understanding molecular geometry, especially in three-dimensional shapes like ethane. In ethane, which has the chemical formula \(\mathrm{C}_{2}\mathrm{H}_{6}\), the carbon atoms are sp\(^3\) hybridized. This means they form a tetrahedral shape. A tetrahedral geometry always aims to minimize the repulsion between bonds, resulting in bond angles of approximately 109.5 degrees.

These angles are consistent across the hydrogen-carbon-hydrogen (H-C-H) and carbon-carbon-hydrogen (C-C-H) bonds in ethane. It's essential to keep these numerical values in mind, as they ensure that the geometric representation of the molecule aligns with its chemical reality. A clear understanding of bond angles allows for more accurate modeling and predictions of molecular interactions.

• H-C-H bond angles around each carbon are approximately 109.5 degrees.
• C-C-H bond angles maintain this same angle, being part of a continuous sp\(^3\) hybridization.

Ethane Structure

The ethane structure serves as an important example of a simple alkane in organic chemistry. Ethane consists of two carbon atoms singly bonded to each other, with each carbon atom also bonded to three hydrogen atoms to fulfill the carbon atom's valency of four. The carbon-carbon single bond permits free rotation, making the molecule relatively flexible.

This flexibility, however, does not change the canonical tetrahedral geometry around each carbon, dictated by the sp\(^3\) hybridized orbitals. Each tetrahedron in ethane is connected by sharing one edge, the C-C bond. Understanding ethane's 3D structure is essential for comprehending more complex hydrocarbons, as it provides the foundational geometric and steric principles seen in larger molecules.

• Two carbon atoms, each bonded to three hydrogen atoms.
• Tetrahedral geometry indicative of sp\(^3\) hybridization.
• Free rotation around the C-C bond.

Drawing Molecular Structures

Drawing molecular structures accurately reflects the spatial arrangement of atoms within a molecule. It's crucial for visualizing how molecules interact with each other. When illustrating molecules like ethane in 3D, it's vital to represent the bonds correctly. The carbon atoms are usually drawn in the center, with the hydrogen atoms arranged symmetrically around them.

To depict ethane's structure in three dimensions, start by drawing a line between the two carbon atoms, representing the C-C bond. Then, place the hydrogen atoms around each carbon. This can be done using solid lines for bonds in the plane, solid wedges for bonds pointing out of the plane, and dashed wedges for bonds going into the plane. This precise representation ensures clear communication of the molecule's geometry.

• Start with a line for the C-C bond.
• Use solid wedges for bonds out of the plane.
• Dashed wedges for bonds into the plane.
• Lines for bonds in the plane.

Wedge-Dash Notation

Wedge-dash notation is a technique used to convey the three-dimensional arrangement of atoms in molecules on a two-dimensional surface. This notation helps in differentiating bonds that are in the plane of the paper from those that extend towards or away from the viewer.

In ethane, to draw a tetrahedral geometry accurately, wedge-dash notation is used. Solid wedges indicate bonds coming out of the plane towards the observer, while dashed wedges represent bonds extending into the plane, away from the observer. Regular lines represent bonds that are flat on the plane. This system helps chemists communicate spatial aspects of molecules, vital for understanding reactivity and properties.

• Solid wedges: Bonds towards the observer.
• Dashed wedges: Bonds away from the observer.
• Lines: Bonds in the plane of the paper.