Dissociation constant from absorbance

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Discussion Overview

The discussion revolves around calculating the dissociation constant (Ka) for picric acid based on absorbance measurements of its solutions in a sodium hydroxide environment. Participants explore the relationship between absorbance, concentration, and the dissociation equilibrium of the acid.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a homework problem involving absorbance measurements of sodium picrate and picric acid solutions, expressing uncertainty about how to proceed with the calculations.
  • Another participant suggests converting absorbance values to concentrations and questions how much undissociated weak acid can be present in the sodium hydroxide solution.
  • A participant clarifies that equilibrium concentrations are needed rather than total concentrations, raising questions about the relative concentrations of hydroxide and hydrogen ions in the solution.
  • One participant attempts to set up an equilibrium expression for the dissociation constant but is unsure how to incorporate absorbance values into their calculations.
  • Another participant critiques the understanding of the problem, emphasizing the need to determine the absorbance coefficient of the picrate anion in a high pH solution.
  • A participant calculates the molar absorptivity of picric acid from its absorbance and concentration, questioning whether this value can be used for the mixture with sodium picrate.
  • A later reply clarifies that the relevant absorptivity is that of the picrate anion and states that the contribution of sodium hydroxide to absorbance can be assumed negligible.
  • Finally, a participant calculates the concentration of the picric anion based on the absorbance and proposes a value for the dissociation constant, though this is not universally accepted.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the approach to calculating the dissociation constant, and there is no consensus on the correct method or final value. Participants express differing opinions on the significance of hydroxide concentration and the appropriate use of absorbance data.

Contextual Notes

Participants highlight the need for equilibrium concentrations and the potential complexities introduced by the presence of sodium hydroxide, indicating that assumptions about ion concentrations may affect the calculations.

hc772
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Homework Statement



A 0.120 M solution of sodium picrate ina 1 M sodium hydroxide solution was observed to have an absorbance of 0.335, due only to the absorption by the picrate anion. In the same spectrophotometer cell and at the same wavelength as in the previous measurement, a 0.300 M solution of picric acid was found to have an absorbance of 0.581. Calculate the dissociation constant for picric acid

Homework Equations



A=abc

Ka = [A]/[AB]

The Attempt at a Solution



I am not sure where to begin but this is what I thought so far:

0.335 = 0.120 a a=2.792
0.581 = .300 a a = 1.937

I am not sure how to use the absorption values in the dissociation constant equation.
 
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Convert them to concentrations.

Hint: how much undissociated weak acid can be present in the 1M NaOH solution?
 
I thought I was given the concentrations in the question?

will the [OH]- not matter because [H]+ >> [OH]-?
 
hc772 said:
I thought I was given the concentrations in the question?

You need equilibrium concentrations, you are given total concentrations.

will the [OH]- not matter because [H]+ >> [OH]-?

You have 1M NaOH and 0.12M weak acid and you think [H+] >> [OH-]? In terms of simple stoichiometry you have around 8 times more NaOH that is needed to completely neutralize the acid.
 
So to find the equilibrium concentrations I did:

NaA + NaOH ---> A + OH + 2Na
0.012 M 1.0 M 0 0 -
-x -x +x +x -
0.12 - x 1.0 -x x x -


Kc = [A][OH]/[NaH][NaOH] = (0.12 -x)(1.0 -x)/(x)(x)

=(0.12 -0.88x + x2)/x2

Where do I go from here? how do I incorporate the absorbances?
 
Looks like you have no idea what you are doing :frown:

First experiment is to find the absorbance coefficient of A-. You use very high pH solution to be sure that all acid is in the neutralized form.
 
Last edited:
the molar absorptivity of the picric acid would be

0.581 = a(0.300 M) a= (0.581/0.300) = 1.937 M

and for the mixture of sodium picrate and NaOH it would be

0.335 = a1(0.120 M) + a2(1 M)

This gives me two unknowns for one equation. can I use the molar absorptivity of the picric acid in the equation for the mixture?
 
It is not absorptivity of picric acid, but of the picrate anion. NaOH doesn't matter - you may assume its absorptivity coefficient is 0.
 
So if the absorbance of 0.335 is only due to the picric anion the concentration of the picric anion of the solution is as follows:

0.335 = (1.973)CA CA= 0.173 M

Ka = [A+]/[NaA][NaOH] = [0.173]/[.12][1] = 1.44 M
 

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