## Number 1.55

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Raquel Rodriguez
Posts: 68
Joined: Fri Sep 28, 2018 12:26 am

### Number 1.55

I am lost trying to answer this question can someone help me out?

Infrared spectroscopy is an important tool for studying vibrations of molecules. Just as an atom can absorb a photon of suitable energy to move an electron from one electronic state to another, a molecule can absorb a photon of electromagnetic radiation in the infrared region to move from one vibrational energy level to another. In infrared spectroscopy, it is common to express energy in terms of /c, with the units cm 1 (read
as reciprocal centimeters). (a) If an absorption occurs in the infrared spectrum at 3600 cm 1, what is the frequency of radiation that corresponds to that absorption? (b) What is the energy, in joules (J), of that absorption? (c) How much energy would be absorbed by 1.00 mol of molecules absorbing at 3600 cm 1?

Chem_Mod
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### Re: Number 1.55

You can take the inverse of 3600/cm which will give you wavelength in cm, then you can convert that to meters and use that value to solve for frequency and energy like we have been doing. Part c requires you to convert mol to molecules and multiply by the energy per photon.

jguiman4H
Posts: 31
Joined: Fri Sep 28, 2018 12:29 am

### Re: Number 1.55

For part a, the frequency = 3600cm-1 * c

So, frequency = 3600cm-1 * 2.998 x 88 m/s = 3600cm-1 * 2.998 x 108 cm/s
(Here, I converted everything to cm because it doesn't really matter, but you can convert to meters too.)
This gives you about 1.1 x 1014 s-1 when rounded and using correct sig figs.

For part b, you'd use E = h * frequency, using the value you just got in part a for frequency.

For part c, essentially you're multiplying the energy found in part b by Avogadro's number to calculate for one mol (because the energy you calculated for is for one molecule).