# How to calculate dipole moment of #"NH"_3#?

##### 1 Answer

There's no easy way to do it without having a nice molecule whose dipole moment is already known.

*We always have to either do it computationally (ab initio) or after already having experimental data available for a classroom exercise...*

And in this exercise, we need to calculate the dipole moment along one bond first. Then we can get its

This is because

As a result, we can say that the dipole moment along each

In that case, each **bond dipole moment** is based on:

#vecmu = i cdot qvecr# where

#q# is the charge of an electron and#vecr# is the separation distance between two charges. Here, we ascribe ionic character to the value of#i# , where#0 < i < 1# .

First, we'll need that its bond length is

Using data from CCCBDB,

Next, we'll need the **percent ionic character** of an *unless we already knew* the dipole moment....

But this website shows a value of

In that case, the dipole moment **along** the

#vecmu("N"-"H") = i cdot qvecr#

#= overbrace(0.270 cdot 1.602 xx 10^(-19) cancel"C")^(i cdot q) xx overbrace(1.0124 xx 10^(-10) cancel"m")^(r) xx "1 D"/(3.336 xx 10^(-30) cancel("C"cdot"m"))#

#~~# #"1.313 Debyes"# , or#"D"#

*But this is not the net dipole moment. The net dipole moment is what we want, and is the vertical arrow shown below.*

Now what we want to do is get the **angle relative to the vertical**, so that we can get the **component** of the dipole moment we just found for the bond, since only the vector components in the same direction add.

This angle is based on a right triangle formed by an

So, this angle is found to be:

#costheta = 0.3816/1.0124#

#=> theta = 67.86^@#

Since the vertical is the **net dipole moment** is found from the addition of the

One of these vectors (the

#vecmu_z("N"-"H") = "1.313 D" xx cos(67.86^@) = "0.4948 D"#

The addition of three of these

#color(blue)(vecmu_"net"("NH"_3)) = vecmu_z("N"-"H") + vecmu_z("N"-"H") + vecmu_z("N"-"H")#

#=# #color(blue)("1.484 D")#

for the net dipole moment. The actual value from a casual google search is around

Another reference is from CCCBDB, which says it is