[PiStOnS1287]

Hello,
I have a multiple part polyprotic acid question and am having a very difficult time getting started on calculating the concentrations that are asked for in this problem.  I figured out the pH for this problem which is 7.4 by using Henderson Hasslebach and using the pKa1 to get my answer.  I'm stumped though what to do from here in order to calculate the concentrations asked for in the problem.  I included hints given to me in the problem but am unsure how to utilize them.  Any help that could be offered would be greatly appreciated. 


The next 6 questions involve the calculation of concentrations of the molecular and ionic species in an aqueous solution that has an analytical composition of 0.260 M KH2PO4 + 0.410 M K2HPO4.
NOTE: The Ka's for the three acidic protons of phosphoric acid H3PO4 are: 7.11 x 10-3, 6.32 x 10-8, and 4.5 x 10-13. It may be helpful to write out the three dissociation reactions along with their Ka's and pKa's before starting these problems.

Here are the dissociation reaction I got:
    H3PO4(s)   + H2O(l)  is in equilibrium with H3O+(aq) + H2PO4−(aq)       

    H2PO4−(aq)+ H2O(l) is in equilibrium with H3O+(aq) + HPO42−(aq)       

    HPO42−(aq)+ H2O(l) is in equilibrium with H3O+(aq) +  PO43−(aq)

What is the pH of this solution?
pH = 7.4

What is the concentration of the molecular species H3PO4?
You need the correct answer to # 1 for this. Look at the 3 steps of dissociation of H3PO4. Some H2PO4- can combine with H+ to produce H3PO4 as governed by K1. So, set up the proper equilibrium expression based on K1, then use the pH as calculated from the HH equation to solve for [H3PO4].
   
What is the concentration of K+ in molarity?
Remember that potassium salts dissociate completely. Note how many mols of K+ are released when one mole of K2HPO4 dissociates
   
What is the concentration of OH-?
pOH=14 - pH
   
What is the concentration of PO43- in molarity?
Some HPO4-2 dissociates(or ionizes) to form PO4-3 as governed by K3. The pH is fixed by the main buffer as calculated in problem # 1. Set up the equil. expression for K3 and solve for [PO4-3].
   
What is [H2PO4-]?
Remember that [H2PO4-] refers to the equilibrium concentration of H2PO4-. [H3PO4] is negligble compared with [H2PO4-], so [H2PO4-] is approximately equal to the analytical concentration of H2PO4-.

[Borek]

Take a look at second equation here:

http://www.titrations.info/acid-base-titration-indicators

Remember that it is just rearranged dissociation constant, nothing realy fancy, no new special knowledge necessary. Try to understand how the frumla was rarranged - in a way it is similar to the approach that leads to Henderson-Hasselbalch equation.

Note: indicators are just a weak acids, you have to deal with weak acids in your question, and they are described by almost identically defined dissociation constant.

[PiStOnS1287]

Hi again,
I'm still having a hard time on how to setup the expressions for this problem in relation to each concentration.  The only one had luck finding was the OH- concentration which was 2.49e-7.  I did this by finding the pOH of the problem and then taking the antilog of this.  If you could please explain to me a little more I would greatly appreciate it.   

[Borek]

For example:

What is the concentration of the molecular species H3PO4?
You need the correct answer to # 1 for this. Look at the 3 steps of dissociation of H3PO4. Some H2PO4- can combine with H+ to produce H3PO4 as governed by K1. So, set up the proper equilibrium expression based on K1, then use the pH as calculated from the HH equation to solve for [H3PO4].

You know pH, you know Ka, have you tried to follow - literally - hint as given? What is the equation for Ka1 (write it down)? What concentrations that are present in this equation do you already know? This is really just plug and chug.

[PiStOnS1287]

Thank you Borek,
I did find the concentration of H3PO4 by using the expression  [H3PO4]=([H2PO4-][H30+])/Ka1 and i also found the conc. of H2PO4- to simply be equal to the concentration of KH2PO4.  I am still unsure though of the expressions that should be set up for P043- and the K+ concentrations.  Once again thanks for your help.

[Borek]

What about using Ka3 in exactly the same way?

K+ is the simplest one - it doesn't require any knowledge about acid/base equlibria, it is a high school question.

[AWK]

http://www.chem.usu.edu/~sbialkow/Classes/3600/alpha/alpha1.html

[PiStOnS1287]

Thank you for all your help, finally got them all figure out