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Topic: Help with understanding tetrahedral bond angle proof vid  (Read 2108 times)

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Offline Bbrow

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Help with understanding tetrahedral bond angle proof vid
« on: June 26, 2016, 04:52:08 PM »
Hi,

Short version of question: in the video below at 2:25 - why is x √2 and not 1 when regarding the coordinates (√2,1,0) - I thought the hypotenuse of the triangle should be √2?

https://www.youtube.com/watch?v=2UTr46btzaY


Long version:
I've been struggling for sometime with understanding why bond angles in tetrahedral structured molecules are ideally 109.5 degrees.

I've looked at various proofs including a few involving drawing tetrahedrons in boxes but the closest I've come to understanding is the khan academy explanation below:

https://www.youtube.com/watch?v=2UTr46btzaY

I like the way the tetrahedron is lined up against the axis and get the use of Pythagoras and assuming equidistance between all points, however I don't understand how the coordinates of the first example point are obtained (2:25 mins in) - I see the right angled triangle as drawn and understand that √2 will be involved as the other two sides are length 1 and a^2+b^2=c^2

But.. why is x √2 and not 1 when regarding the coordinates (√2,1,0) - I can see y would be 1 and z would be 0

A maths question really but heavily linked to chemistry..

Thanks for looking


Offline Borek

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Re: Help with understanding tetrahedral bond angle proof vid
« Reply #1 on: June 26, 2016, 06:57:03 PM »
Doesn't matter how the point was chosen - what matters is that it meets the criteria mentioned (equal distances between each HH pair, and equal distance between each CH pair).

Can you check if the point you suggested (1,1,0) meets these criteria?

Finding these coordinates (√2,1,0) by calculations is more or less as difficult, as proving what the angle is just by the means of the simple geometry.
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Offline mjc123

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Re: Help with understanding tetrahedral bond angle proof vid
« Reply #2 on: June 27, 2016, 04:46:50 AM »
x is half the distance between two Hs along an edge of the tetrahedron, y is half the distance between the midpoints of opposite edges. I hope you can see from the attached diagrams that these distances are in the ratio 2:sqrt(2), or sqrt(2):1.

Offline Bbrow

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Re: Help with understanding tetrahedral bond angle proof vid
« Reply #3 on: July 07, 2016, 03:59:03 PM »
Thanks for this guys - slowly starting to make sense

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