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### Course: Organic chemistry>Unit 14

Lesson 1: Infrared spectroscopy

# Signal characteristics - wavenumber

Learn how to use equations to predict the wavenumber for different types of chemical bonds. See how the frequency of bond vibration in molecules, likened to a spring oscillation, depends on the force constant and reduced mass. Learn how to calculate wave numbers for different bonds using these factors, as you develop your understanding of where signals appear in IR spectroscopy. Created by Jay.

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• At , it is mentioned that the k value for the single bond between C - O will be 5x10^5, which was the same k value for the bond C - H. Could anyone tell me where this number was taken from? I understand that a double bond would be double the constant but where does the original approximation come from?
• The approximation comes from modelling the bonds as a spring: https://www.khanacademy.org/science/organic-chemistry/spectroscopy-jay/infrared-spectroscopy-theory/v/bonds-as-springs

The amount of energy that a spring can hold varies depending on the type of spring. To account for this, springs are multiplied by a constant value.

The potential energy stored in a spring is given by the equation:

U=½kx^2

where U is equal to potential energy, x is displacement, and k is the spring constant.

k = "stiffness" of the spring.

Stiffness describes the rigidity of an object. A double bond is stiffer than a single bond, thus k increases with increasing bond order.

References
single bond between carbon and oxygen, k = 5 x 10^5 dyne/cm
double bond between carbon and oxygen, k =10 x 10^5 dyne/cm
triple bond between carbon and oxygen, k = 15 x 10^5 dyne/cm.
• at , why do we divide by avagadro's number to turn grams to amu? If we have grams written as k/grams (spring constant/reduced mass) then shouldn't we multiply by 1gram/6.022 X 10^23 amu to cancel out the grams and be left with only amu?
• I had the same question before, so I watched this and the last video several times. Then I noticed he did make a mistake, but it is not about dividing or multipling the Avogadro number. On the last video https://www.khanacademy.org/test-prep/mcat/physical-processes/infrared-and-ultraviolet-visible-spectroscopy/v/bonds-as-springs at , he said that the unit of the reduced mass is amu, not gram. However, he said it is gram in this video by mistake. Actually what he intended to do is to convert amu to gram, which requires dividing the Avogadro number. That makes sense because the unit of K is N/cm, N is g*cm/s^2, so the actual unit of K is g/s^2, and if we convert the unit of M from amu to gram, the only thing left inside the square root is 1/s^2. finally, the unit of 1/c is s/cm, so we could get the correct unit for the wave-number which is 1/cm.
• why do we use the reduced mass? Perhaps I missed it, but how is this derived? Thank you!
• How can we know the value of K the force constant?
• Where can we get more ks for various different bonds?
• The speed of light in this video was recorded as 3x10^10 instead of 3x10^8.
• I believe he was using units of cm/s. Therefore, since the speed of light is 3x10^8 m/s it would follow that the speed of light is 3x10^10 cm/s.
• where is the region for a double bond to an atom that's not carbon?
• The point of IR spectroscopy is to identify functional groups. So an alkene or the carbonyl of a carboxylic acid would be the two double bond groups frequently seen. Carbonyl's typically show up at 1700 1/cm.
• why use wavenumber instead of wavelength ?
• As we look for the electromagnetic radiation spectrum and compared different regions of it with respect to energy, frequency, and wavelength.
Then, the energy, frequency both are directly proportional to each other whereas energy, frequency both are inversely proportional to wavelength.
e.g. In the case of UV-Visible spectroscopy, at 200 nm (shorter wavelength) the energy and frequency of UV-Visible radiation are high as compared to 800 nm (Longer wavelength).
Now, wavenumber expressed as reciprocal to wavelength is expressed in centimeters. When wavelength converted to wavenumber, then, Wavenumber is directly proportional to energy and frequency (In case of wavelength, it is inversely proportional to energy and frequency).
So, to use direction correlation, between wavenumber, energy, and frequency, wavenumber to be used in IR
eg. In the case of the IR region, the range is 2.5 to 25 micron. At 2.5 micron (wavenumber 4000 cm-1) the energy and frequency of IR radiation are high as compared to 25 microns (wavenumber 400 cm-1).
(1 vote)
• so what is the value of k?