The absorption spectrum of benzene dissolved in cyclohexane...

The absorption spectrum of benzene dissolved in cyclohexane contains bands at 183,204 and $256 \mathrm{nm} .$ (a) Which band corresponds to the lowest energy transition? (b) Which band corresponds to the lowest wavenumber? (c) For $\lambda=256 \mathrm{nm}$ $\log \varepsilon=2.30 .$ Determine the concentration of a solution (path length $=1.00 \mathrm{cm}$ ) which gives an absorbance of 0.25.

Key Concepts

Absorption Spectrum

An absorption spectrum shows how a substance absorbs light at different wavelengths, reflecting the electronic transitions within the molecule. It is used to determine energy levels and is critical for understanding the behavior of chemicals under light.

Energy-Wavelength Relationship

The energy of a photon is inversely proportional to its wavelength (E = hc/?), meaning that transitions associated with shorter wavelengths involve higher energy changes. This relationship is fundamental in comparing electronic transitions in a spectrum.

Wavenumber

Wavenumber, defined as the reciprocal of the wavelength (usually in cm?¹), provides an alternative measure of energy. It is particularly useful in spectroscopy for comparing transitions, as lower wavenumbers correspond to lower energy transitions.

Beer-Lambert Law

The Beer-Lambert Law relates the absorbance of a solution to the concentration of the absorbing species, the path length of the light through the sample, and the molar absorptivity. It is a key tool for quantitative analysis in spectrophotometry.

Transcript

00:01 Let's say that we have a solution of benzene dissolved in cyclohexane, and we put this through a uvvis spectrometer, and we get three signals.

00:11 We get 183 nanometers, 204 nanometers, and 256 nanometers signals.

00:20 So out of these three, which one has the lowest energy? well, remember, the larger the wavelength, the lower the energy and the lower the frequency.

00:29 So right off the bat, we can see.

00:32 256 nanometers is going to be our lowest energy.

00:38 And what if we wanted to know our lowest wave number? well, our wave number is related to wavelength as well.

00:46 So the larger the wavelength, the lower our wave number ends up being.

00:51 We can show this by quickly converting 256 nanometers, 256 nanometers into wave numbers.

01:03 We can do that by saying one nanometer is equal to negative 1 times 10 to the negative 7 centimeters.

01:13 So we're converting our value from nanometers to centimeters, and this will give us about 2 .6 times 10 to the negative 5 centimeters.

01:24 And the inverse of this number will be our wave numbers.

01:29 So 1 over 1 over 2 .6 times 10 to the negative 5 centimeters.

01:39 Will give us approximately 39 ,100 wave numbers.

01:52 So if we do the same thing for 183 centimeters, our lowest wavelength, we'll find out that this give us about 54 ,600 wave numbers.

02:15 So this gives us a much larger wave number than our other wavelength.

02:22 So 256 nanometers is going to give us our lowest wavelength.

02:27 I'm sorry, our lowest wave number.

02:32 Finally, let's say that we know the absorption value from this.

02:46 We got an absorption value of about 0 .25.

02:51 We also know that the log of the molar coefficient comes out to be about 2 .5.

03:03 3 and our path length l our path length is going to be equal to 1 centimeter...

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