What is the dipole moment of BF3

The dipole moment μ describes the asymmetry of the charge distribution in the molecule as a measurable quantity.

μ is defined as "charge x distance". Is measurable μ (more precisely the amount of μ) from the evaluation of physical measurements (dielectric constant and refractive index). For qualitative considerations it is only important that μ is a quantity with magnitude and direction is.
μ is usually still in the unit D (1 D = 3.34 x 10-30 C m). D = "Debye" after the Dutch physicist Peter Debye.

Graphically we symbolize μ with a arrow the from the positive to the negative charge shows. The length of the arrow corresponds to the Amount of μ.

 

In Molecules the entire asymmetry of the charge distribution can be expressed as "geometric sum" the Asymmetry in the individual bonds are formed. (Total dipole moment = sum of bond dipole moments). For the "geometric sum", the arrows are added, taking into account the amount and the direction. In physics, this construction is known as the "force parallelogram". Mathematically, this construction is called a "vector addition". You can quickly understand this with examples.

Example 1: CO2 - linear molecule

O is more electronegative than C.
There are two bond dipole moments.
These have the same amount (twice the same situation C = O),
but opposite direction.

 

Because of the opposite direction, the two individual moments cancel each other out, overall that has linear symmetric molecule CO2no dipole moment (μ = 0).

 

If two people of equal strength pull on a rope in exactly the opposite direction, the forces cancel each other out - and nothing happens.

 

Example 2: H2O - angled molecule

O is more electronegative than H.
Two binding dipole moments with the same amount
but different directions.

 

The two individual moments are added:
The arrows are drawn side by side at the end point,
then a parallelogram is drawn,
the diagonal of this parallelogram is the "geometric sum".

 

The angled molecule H2O Has a dipole moment (μ > 0).

 

Example 3: BF3 - trigonal plane molecule (central atom + 3 equal partners in one plane)

F is more electronegative than B.
Three binding dipole moments of equal magnitude
but different directions.

 

The three individual moments are added:
The arrows are drawn side by side at the end point.
With an exact (!) Sketch you can see that the sum of
arrow 1 and arrow 2 as long as arrow 3 is.
arrow 3 and the sum 1+2 point in exactly the opposite direction.
As in the example 1 these two moments cancel each other out.

 

The trigonal plane molecule BF3Has no dipole moment (μ = 0).

 

Example 4: NH4+ - Tetrahedral structure (central atom + 4 equal partners in tetrahedral environment)

N is more electronegative than H.
Four binding dipole moments with the same amount
but different directions.
{Here as a plane projection drawn.}

 

The addition of the four individual moments yields the sum 0.
For a three-dimensional figure, the drawing is a little more complicated.
The tetrahedral built up ion NH4+ Has no dipole moment (μ = 0).

 

 

Please provide a sketch of the "geometric sum" in a tetrahedron!

Mathematical solution for "just trigonal":

Mathematical solution for "tetrahedral":

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