Methane Structure and Bond Angles

Overview

• Methane molecule features a central carbon atom surrounded by hydrogen atoms.
• The carbon atom in methane is sp3 hybridized.
• sp3 hybridization means atoms around carbon are in tetrahedral geometry.

Visualizing Tetrahedral Geometry

• Lewis Dot Structure:
  • Difficult to see tetrahedral geometry in 2D representation.
• 3D Representation:
  • Easier to visualize the tetrahedron.
  • Connecting hydrogen atoms reveals the four sides of the tetrahedron.

Bond Angles

• Bond angle in sp3 hybridized methane is 109.5 degrees.
• Bond angle is consistent around the molecule.

Proof of Bond Angle

• Proof provided by students Anthony Grebe and Andrew Foster.
• Method:
  • Place the tetrahedron on xyz axes.
  • Central carbon atom at the origin.
  • Choose four points representing hydrogen atoms with two conditions:
    • Each hydrogen point is equidistant from the other three.
    • Each hydrogen point is equidistant from the central carbon atom.
  • Orientation allows calculation of bond angle.

Calculating Bond Angle

• Point coordinates chosen:
  • Point 1: (sqrt(2), 1, 0)
  • Point 2: (-sqrt(2), 1, 0)
  • Point 3: (0, -1, sqrt(2))
  • Point 4: (0, -1, -sqrt(2))
• Finding bond angle (θ):
  • Calculate tan(θ) = opposite/adjacent.
  • For triangle, opposite = 1, adjacent = sqrt(2).
  • θ calculated using inverse tan: 35.26 degrees.
• Bond angle calculation:
  • Sum of angles in plane = 180 degrees.
  • Bond angle = 180 degrees - 2(35.26 degrees).
  • Resultant bond angle = 109.5 degrees.

Acknowledgment

• Special thanks given to students for their contribution to the proof.