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### Course: Organic chemistry>Unit 1

Lesson 2: Hybridization

# Tetrahedral bond angle proof

Mathematical proof of the bond angles in methane (a tetrahedral molecule). Created by Jay.

## Want to join the conversation?

• Weren't those distances of root 2 and 1 chosen specifically so that the bond angle would work out as planned? If so this isn't so much a proof as much as students being clever and working backwards. Or is there somewhere else that the x and y distances come from?
• The distances, or rather positions, of the first two points are chosen with care as to make the calculations simpler. Any other two points could have been chosen, but you would still come to the same end result. Look at it this way: Choosing the first two points merely determines the size and position of the tetrahedron. As long as you follow the first criteria mentioned in the video (All points should have an equal distance to each other) you will end up with a tetrahedron. This is true for all geometric shapes; the angles in a cube are always 90 degrees, no matter its position or size
• People have had different questions about proving the distance between the points on the methane molecule. At , the coordinates can be seen. The formula for a distance between two points in three dimensional space is: distance = √((x2-x1)^2+(y2-y1)^2+(z2-z1)^2). For the top two points this would equal, √((√2--√2)^2+(1-1)^2+(0-0)^2 = √(2√2)^2)=2√2. For the distance between the top right point and the bottom close point it would equal √((√2-0)^2+(1--1)^2+(0-√2)^2)=√(2+4+2)=√(8)=2√2. You can complete it with all of the other points as well, but the distance between each point is 2√2, and the distance between any point and the origin is √3, which you can also calculate using this formula.
• Why the method of multiple bond is not applicable on BF3 molecule according to idea of multiple bond it should be sp3 but really it is sp2 why??
• how the x coordinate is root 2
• They chose these coordinates arbitrarily to meet the conditions stated earlier in the video. Personally, I do not like this proof (although it works).
If you put a tetrahedral carbon atom in the centre of a cube, the bonds will point towards the opposite corners of the cube. You can use this fact to calculate the bond angles in a much easier way. See the calculation at http://mathcentral.uregina.ca/QQ/database/QQ.09.00/nishi1.html
• When I do this with different numbers such as root 3 and 1.5 instead of root 2 and 1 I get a different answer, I think all my atoms are equidistant from each other and the origin but my angle is 99 degrees
Where am I going wrong?
• Your trigonometry is wrong. The video is using a tetrahedron inscribed in a cube of side 2. This gives you the numbers root 2 and 1. If instead you use a cube of side 3, the numbers become 1.5root2 and 1.5 (not 3 and 1.5).
Here is a link to another proof that may be easier to understand.
http://mathcentral.uregina.ca/QQ/database/QQ.09.00/nishi1.html
• How did they determine the value "square root of 2", why not square root of 3"?
• It's part of the trigonometry involved.
The carbon atom is inscribed inside a cube of side 2, with the bonds pointing to diagonally opposite corners of the cube and the C atom in the centre.
The diagonal of a side of the cube is √(2² +2²) = √(2×2²) = 2√2.
If we define our xyz plane as the H-C-H plane with the C atom at the centre, each H is half of the diagonal (√2) apart on the face of the cube, and the C atom is 1 unit below them.
The coordinates become C = (0,0,0), H(left) = (-√2,1,0), and H(right) = √2,1,0).
See, for example, http://mathcentral.uregina.ca/QQ/database/QQ.09.00/nishi1.html
• How can you tell if a tetrahedral bond is non polar or polar? By their shape?
• Their shape would tell you some information, but it's by analyzing what's connected. For example, CFH3 (a carbon bonded to 3 hydrogens and 1 fluorine) is clearly polar. This is because the Fluorine is very electronegative, pulling some electron density from the carbon, which thus pulls some electron density from the hydrogens. However, in CF4 (a carbon bonded to 4 fluorines), each fluorine is pulling equally strong, so there is no net polarity, and it is thus nonpolar.

In short, structure doesn't tell you as much: you want to look at the relative electronegativities of the substituents.
• What is the VSEPR Theory?
• http://en.wikipedia.org/wiki/VSEPR_theory

Basically, it's the part of chemistry where you can be given a chemical formula and tell somebody what hybridization it is and what shape it would be and what angles it has. You should brush up on VSEPR Theory before trying out Organic Chemistry: VSEPR Theory is a MUST!
• at how can I know that point?
• Got a question, why did they choose the coordinates using the number 1, 0 and √2? I mean, 0 and 1 are intuitive, but √2??
• It relates to the distance formula which the two students undoubtable performed prior to get these numbers.