Why the tetrahedron is equal to the angle of 109.5degrees but it says in an article that if you divide the number of bonds thats the angle but when i divide 4 to 360 the answer is 90 they did not match pls answer my question tnx?

1 Answer
George C.
Sep 10, 2017

A tetrahedron is not flat...

Explanation:

If you have a flat symmetrical molecule such as Borane #BH_3# then dividing #360^@# by the number of bonds makes sense, but in the case of a three dimensional tetrahedral molecule such as Methane #CH_4# it does not.

You could model the shape by imagining a carbon atom at #(0, 0, 0)# and hydrogen atoms at: #(1, 1, 1)#, #(1, -1, -1)#, #(-1, 1, -1)# and #(-1, -1, 1)# (alternate vertices of a cube form the vertices of a tetrahedron).

Then the angle between the line joining #(0, 0, 0)# and #(1, 1, 1)# and the line joining #(0, 0, 0)# and #(1, -1, -1)# is:

#arccos((<1,1,1> . <1,-1,-1>)/(abs(<1,1,1>)*abs(<1,-1,-1>))) = arccos(-1/3) ~~ 109.5^@#

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