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Why does Methane has a tetrahedral shape?
The Valence-shell electon pair repulsion theory applies which predicts that the shape of a molecule by placing the electron pairs on a central atom as far apart as possible to minimize the mutual repulsion of the electrons. In methane the bond to hydrogen is directed to the corners of a telrahedron with bond angles of 109.5*.

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telrahedron

The reason methane (CH4) has a tetrahedral shape is primarily determined by the Valence-Shell Electron Pair Repulsion (VSEPR) theory. This theory states that electron pairs around a central atom will arrange themselves as far apart as possible to minimize electron-electron repulsion.

To understand why methane has a tetrahedral shape, let's break it down step by step:

1. Start with the Lewis structure of methane:
- Carbon (C) is the central atom and has a total of four valence electrons.
- Each hydrogen (H) atom has one valence electron.
- So, in total, methane has eight valence electrons (4 from carbon and 1 from each hydrogen).

2. Distribute the electrons around the carbon atom:
- Place one electron pair (represented by a dash or a line) between carbon and each hydrogen atom, resulting in four bonding pairs of electrons.
- Carbon still has four remaining electrons that need to be accounted for.

3. Place the remaining electrons around the carbon atom:
- Since carbon needs eight electrons to complete its octet, we add four lone pairs of electrons around the carbon atom. These lone pairs do not form any bonds but contribute to the overall shape of the molecule.

4. Determine the arrangement of electron pairs:
- Each bonding pair and lone pair of electrons repels each other, and they try to get as far apart as possible.
- In the case of methane, the four electron pairs (four bonding pairs and no lone pairs) arrange themselves as far apart as possible.
- This arrangement results in a tetrahedral shape, where each hydrogen atom is positioned at one of the corners of the tetrahedron.

5. Measure the bond angles:
- The bond angles between the hydrogens in methane are all equal and measure approximately 109.5 degrees.
- This bond angle arises because the tetrahedral arrangement maximizes the distance between the electron pairs, minimizing their repulsion.

To summarize, the Valence-Shell Electron Pair Repulsion (VSEPR) theory explains that methane has a tetrahedral shape because it allows the bonding and lone pairs of electrons to be arranged as far apart as possible, minimizing electron-electron repulsion. The bond angles in methane are approximately 109.5 degrees due to this arrangement.