[Rutherford]

The absorbance of solutions of the weak acid HX were obtained. Associate the expected form of the resulting working curve with those shown in figure, under the following conditions:
a) Pure aqueous solutions of HX were used. Only the undissociated species HX absorb.
b) Pure aqueous solutions of HX were used. Only the anionic species X- absorb.
c) All solutions of HX contain an excess of a strong base. Only the undissociated HX species absorb.
d) All solutions of HX contain an excess of a strong acid. Only the undissociated HX species absorb.
e) Pure aqueous solutions of HX were used. Both HX and X- absorb. Measurements were obtained at a wavelength where the molar absorptivities of X- and HX are equal and different than zero.

The diagrams are attached. The formula is A=ε·c·l, the bigger c is, the bigger A gets.
For a), after HX gets dissolved, it ionizes, so the concentration of HX reduces, thus the absorbance should reduce and I thought that it is B, but it is actually A, why?
For b) is the opposite.
c) HX gets neutralized so it is D.
d) HX is only present and its concentration is constant. Why is it C?
e) It's C again. Why is it C i.e. why does the absorbance increase?

I got also a question where it is asked if absorbance is linearly related to the wavelength. I answered no, but it is yes. How so when it is a curve in the function?

I posted it once in high school subforum, but no response, so I thought that it is more appropriate here.

[Borek]

For a), after HX gets dissolved, it ionizes, so the concentration of HX reduces, thus the absorbance should reduce and I thought that it is B, but it is actually A, why?

How does the dissociation fraction depend on the concentration? Does it increase with the concentration, or goes down? How is that reflected by the HX concentration in more concentrated solutions?

[Rutherford]

K=c·α², where α is the dissociation degree and K is the acidity constant. From here, α=sqrt(K/c). When the concentration gets bigger the degree of dissociation get lower, but isn't this against Le Chatelier principle?

[Corribus]

d) HX is only present and its concentration is constant. Why is it C?

Because your assumption about its concentration being constant is wrong.  If you put n molar HX in a strongly acidic solution, what will be the concentration of HX and X- as a function of n?  Don't worry about absorption for a moment.  Just plot out the concentrations of everything first, then worry about absorption.

e) It's C again. Why is it C i.e. why does the absorbance increase?

As before, worry about concentrations first, then absorbance.  If you put n molar HX in a neutral solution, what will be the concentration of HX and X- as a function of n?  Plot them out.  Then worry about plotting absorbances. 

I got also a question where it is asked if absorbance is linearly related to the wavelength. I answered no, but it is yes. How so when it is a curve in the function?

Don't understand the original question. 

[Borek]

K=c·α²

This is only an approximation, working for small α.

When the concentration gets bigger the degree of dissociation get lower, but isn't this against Le Chatelier principle?

Why? Quite the opposite. Substances get 100% dissociated when they are infinitely diluted, and that's exactly what we should expect from the LeChatelier's principle.

[Rutherford]

Why? Quite the opposite. Substances get 100% dissociated when they are infinitely diluted, and that's exactly what we should expect from the LeChatelier's principle.

HA H⁺+A^-
If I increase the concentration of HA, shouldn't the equilibrium shift to right, therefore α should increase?

Because your assumption about its concentration being constant is wrong.  If you put n molar HX in a strongly acidic solution, what will be the concentration of HX and X- as a function of n?  Don't worry about absorption for a moment.  Just plot out the concentrations of everything first, then worry about absorption.

I don't understand. The strong acid should prevent the dissociation of HX.
I understood aboue e).
The question was: Is absorbance linearly related to the wavelength?

[Corribus]

I don't understand. The strong acid should prevent the dissociation of HX.
I understood aboue e).
The question was: Is absorbance linearly related to the wavelength?

If strong acid, equilibrium shifts pretty much completely to the left, correct?  Meaning that the concentration of [HX] in solution is always the concentration of [HX] you begin with.  So the concentrationof HX in solution after equilibrium, [HX]_e, is the concentration you put into solution to begin with [HX]₀.  So if [HX]₀ = n, then [HX]_e = n in a strongly acidified solution.

Absorbance, A is given by A = ε [HX]_e L, and ε and L don't change as a function of n.  Therefore A = ε n L and since ε and L are constant, A is linear with respect to n, or [HX]₀.

(I guess use of n was superfluous.  But easier to write out. )

Now do the same thing for the more complicated problem where both [HX] and [X] are absorbing using the same method.

EDIT:

Re: your other question.  I don't understand it.  The plot is absorption vs concentration, not vs. wavelength.  Absorption changes as a function of wavelength because the extinction coefficient changes as a function of wavelength, and the dependence is far from linear.  There are peaks associated with molecular absorption.

EDIT2:

Fixed a small typo.  Also, just keep in mind that in general, A(λ) = ε_HX,λ [HX]_e L + ε_X-,λ [X^-]_e L, where in the case I've described ε_X-,λ = 0 measured at λ.

[Borek]

Why? Quite the opposite. Substances get 100% dissociated when they are infinitely diluted, and that's exactly what we should expect from the LeChatelier's principle.

HA H⁺+A^-
If I increase the concentration of HA, shouldn't the equilibrium shift to right, therefore α should increase?

It shifts to the right, and concentrations of H⁺ and A^- increase, but increase of α doesn't follow, as equilibrium concentration of HA goes up even faster.

Think about it: what you are suggesting is that when the concentration goes up, the dissociation fraction goes up, so the pure acid is 100% dissociated, while infinitely diluted acid is not dissociated at all. Do you see it is nonsensical?

[Rutherford]

Got c) d) and e).

Corribus, I don't see the relation between wavelength and absorbance. In your formula, wavelength is only in the index. The question is from another problem.

Borek, point taken. From the formula α=N_dis/N₀, when the starting number of molecules increases faster than the number of dissociated molecules, α gets lower.

So for a), α decreases with the increase of concentration, and as c goes towards ∞, α goes towards zero, so absorbance increases rapidly with concentration increase. For b) is the same, but now I watch the c_X- (it increases slower at bigger c_HX concentrations).

[Corribus]

The absorption spectrum plots out the number of photons absorbed as a function of wavelength.  Absorption occurs (most often) at a resonance condition, when a photon of energy is incident upon an electron in a molecule and the energy difference between the state in which an electron currently lies and some higher lying electronic state is the same (well, nearly the same) as the energy of the incident photon.  Most molecules are in their ground electronic state at room temperature.  Therefore peaks in the electronic (UV/Vis) absorption spectrum occur at energies that are identical to the gaps between molecular electronic states.*  It is common to express the photon energy in terms of the wavelength of the photon (although this is not a linear relationship) - so absorption spectra plot absorption vs. wavelength typically, even though this isn't a strict energy axis.  Anyway, because electronic energy levels are unique to each molecule, the location of peaks in an electronic absorption spectrum is unique to the molecule.  Therefore there's no simple, generic relationship between wavelength and absorption - it completely depends on the sample being measured.  And it certainly is never linear.  So if the answer is "yes" to that question about whether wavelength and absorption are linearly related, either they are wrong or the question is worded poorly.

What is typically linear is the relationship between absorption and concentration, at least up to a certain concentration.  This is because Beer's law suggests that absorption is equal to the product of the molar extinction coefficient, the concentration and the length of the measurement cell.  The cell dimensions are obviously not dependent on concentration and while the extinction coefficient can be dependent on concentration, in most cases the effect is small enough that you don't have to worry about it.  [The extinction coefficient is related to the probability of the molecule absorbing a photon at a given wavelength; it incorporates the resonance condition described above, as well as other selection rule parameters which include molecular symmetry, vibrational level overlap, the strength of the dipole moment change during the electronic transition, and so-forth.]  Therefore Beer's law is accurate for most molecules and predicts a linear relationship between absorption and concentration.  It fails in cases where the extinction coefficient is not concentration independent (usually in molecules that can efficiently aggregate or have molecular states that undergo strong intermolecular interactions with each other at high concentration - which changes the energies of the absorbing electronic states) OR at very high concentrations, where certain environmental and instrumental deviations (changes to solvent index of refraction or limitations in instrument sensitivity)  begin to occur.

Well there you go - everything you ever wanted to know about absorption spectroscopy condensed into two paragraphs.

* Note: Actually between vibronic states, because electronic and vibrational transitions are coupled.  But concept is the same for purpose of this discussion.

[Rutherford]

Thanks for explaining that. The correct answer is not 'yes', as they stated.

Thanks to Borek, too.