Animated Solution for Chemistry - Organic Chemistry: The dihedral angle in staggered form of Newman projection of 1, 1, 1-trichloro ethane is .........… degree. (Round off to the nearest integer)

Welcome to the fascinating world of stereochemistry! When we draw chemical structures on a flat piece of paper, it is easy to forget that molecules are dynamic, three-dimensional objects. They twist, turn, and vibrate. To truly understand how a molecule behaves, we need to visualize it in 3D.

One of the most powerful tools for this is the Newman projection. Imagine you are holding a molecule of $1,1,1\text{-trichloroethane}$ ($CC{l}_3-C{H}_3$). Instead of looking at it from the side, you rotate it so that you are looking straight down the carbon-carbon single bond. This perspective is the essence of a Newman projection. It allows us to see exactly how the atoms on the front carbon are positioned relative to the atoms on the back carbon.

Let's break down the construction of our Newman projection step by step. We start with the front carbon atom. Because it is closest to us, we represent it simply as a central dot. Attached to this front carbon are three bulky chlorine ($Cl$) atoms. Due to electron-pair repulsion (VSEPR theory), these three bonds spread out as far as possible in a plane. They form a perfect Y-shape, with the bonds exactly $120^{\circ }$ apart.

Now, what about the second carbon atom? It is hidden right behind the front one. To make it visible in our drawing, we represent this back carbon using a large circle drawn around the central dot. Attached to the edge of this circle are three small hydrogen ($H$) atoms. We draw their bonds starting from the edge of the circle, not the center, to clearly distinguish them from the front bonds.

Staggered vs. Eclipsed

Molecules are not static; they constantly rotate around their single bonds. Different rotational states are called conformations. However, not all conformations are created equal. The molecule prefers certain positions over others based on energy.

If the bonds on the front carbon perfectly align with the bonds on the back carbon, the atoms are as close to each other as possible. This is called the eclipsed conformation. Because the electron clouds of the bonds repel each other, this state has high energy and is highly unstable. This repulsion is known as torsional strain.

To escape this strain, the molecule rotates into the staggered conformation. In this state, the bonds of the back carbon perfectly bisect the angles between the bonds of the front carbon. The atoms are as far apart as possible, minimizing torsional strain and steric hindrance. This makes the staggered conformation the most stable, lowest-energy state for the molecule.

The question asks for the dihedral angle in this staggered conformation. The dihedral angle, denoted by the Greek letter $\varphi$, is the angle between a front bond and the nearest back bond when viewed down the carbon-carbon axis.

Let's do the math. Look at the full circle around the molecule; it represents a complete $360^{\circ }$. In the perfectly staggered conformation, the six bonds—three from the front carbon and three from the back carbon—are spaced evenly around this circle. They divide the $360^{\circ }$ space into six perfectly equal sectors.

Therefore, to find the angle between any adjacent front and back bond, we simply divide the total angle by the number of sectors:

And there we have it! The dihedral angle in the staggered form of $1,1,1\text{-trichloroethane}$ is exactly $60^{\circ }$. Visualizing these projections is a critical skill for mastering organic chemistry, so keep practicing!