Tetrahedral bond angle proof
Mathematical proof of the bond angles in methane (a tetrahedral molecule). Created by Jay.
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- 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?(68 votes)
- 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(18 votes)
- People have had different questions about proving the distance between the points on the methane molecule. At3:08, 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.(24 votes)
- 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??(1 vote)
- how the x coordinate is root 2(8 votes)
- 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(21 votes)
- 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?(5 votes)
- 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.
- How did they determine the value "square root of 2", why not square root of 3"?(7 votes)
- 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(4 votes)
- How can you tell if a tetrahedral bond is non polar or polar? By their shape?(3 votes)
- 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.(8 votes)
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!(5 votes)
- at2:24how can I know that point?(4 votes)
- 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??(3 votes)
- It relates to the distance formula which the two students undoubtable performed prior to get these numbers.
Here's a youtube video about it in case you're interested further. https: //www.youtube.com/watch?v=OvKXN8T5oRc&t=141s
(note at the end set d=1 and multiply both side lengths by 2 to get rid of the fractions and you get the side lengths of 1 and sqrt(2) from the proof here).
Hope that helps.(1 vote)
- when will be the videos on hybridization including d orbitals will be uploaded??(2 votes)
On the left, we have the dot structure for methane. And we've seen in an earlier video that this carbon is sp3 hybridized, which means that the atoms around that central carbon atom are arranged in a tetrahedral geometry. It's very difficult to see tetrahedral geometry on a two-dimensional Lewis dot structure. So it's much easier to see it over here on the right with the three-dimensional representation of the methane molecule. So if I'm trying to see the four sides of the tetrahedron, I could find my first sides by connecting these hydrogen atoms like that. So there's the first side of my tetrahedron. And if I'm going to find the second side, I could connect these hydrogen atoms like that. And there's my second side. And to find my last two sides, if I connect this hydrogen atom to this one down here, I can now see the four sides of my tetrahedron. We're also concerned with the bond angle. So what is the bond angle? What is the angle between that top hydrogen, the essential carbon, and this hydrogen over here on the left? It turns out that bond angle is 109.5 degrees. And it's the same all the way around. So you could say that this angle is 109.5 degrees, or the angle back here. It's all the same. And so an sp3 bond angle is 109.5. And the proof for this was shown to me by two of my students. So Anthony Grebe and Andrew Foster came up with a very nice proof to show that the bond angle of an sp3 hybridized carbon is 109.5 degrees. And what they did was they said let's go ahead and take that tetrahedron, and let's go ahead and put it on the xyz axes. And let's put carbon at the center here. And we can choose any four points to represent the four hydrogen atoms of our tetrahedron, if we satisfy two conditions. Each point that we choose for our hydrogens is equidistant from the other three points, and also each point that we choose for our hydrogens is equidistant from the central carbon atom itself. And if you fulfill those two criteria, you guarantee that the points that you choose form a tetrahedron. And so, here we have the tetrahedron on our axes. And let's go ahead and look at the first point, so this point right here. And they chose this point to be at square root of 2, 1, and 0, meaning positive square root of 2 on the x-axis, positive 1 on the y-axis, and 0 on the z-axis. And then this point over here on the left, they were very clever and said this point is going to be in the same the plane. So this point on the left is in the same plane as the point we just talked about, the xy plane. And therefore, the coordinates for that point would be negative square root of 2, 1, and 0. We go to the hydrogen down here. So this point of our tetrahedron is located at 0, negative 1, and square root of 2. And then finally, this point going away from us right here would be at 0, negative 1, and negative square root of 2. So once again, you could choose any points that you want as long as you meet that criteria. And orienting the molecule in this way allows us to find this bond angle. So this is the bond angle that we are going for. And we don't know that bond angle yet, but we can figure out this angle right here. So I'm going to call this theta for this triangle that's formed. And I know that this x distance down here is positive square root of 2. And then we go up 1 on the y-axis and then 0 on the z-axis. So I can find out what theta is, because I know that tan of theta is equal to opposite over adjacent. So for this triangle I have here, the opposite side would be 1 and the adjacent side would be square root of 2. So to find theta, all I have to do is take inverse tan. So I take inverse tan of 1 over square root of 2 on my calculator, and I get 35.26 degrees. So I know that theta, this angle right in here, is 35.26 degrees. And therefore, this angle is also 35.26 degrees. So this is also going to be theta in here. And if I want to find my bond angle in here, I know that those three angles have to add up to equal 180 degrees since they're all in the same plane here. So to find my bond angle, all I have to do is take 180 degrees, and from that, we're going to subtract 2 times 35.26 degrees. And we, of course, come out with a bond angle of 109.5 degrees. So again, special thanks to my two students for showing me this proof.