Suppose you want to do a physiological experiment that calls for a pH 6.5 buffer

Question

Suppose you want to do a physiological experiment that calls for a pH 6.5 buffer. You find that the organism with which you are working is not sensitive to the weak acid H2X (Ka1= 2x10^2, Ka2= 5.0x10^-7) or its sodium salts. You have available a 1.0 M solution of this acid and a 1.0 M solution of NaOH. How much NaOH solution should be added to 1.0L of the acid to give a buffer with a pH of 6.5? (Ignore any volume change do to the addition of NaOH)

Please help this is an extra credit for a test i miserably failed and im getting a chance to redo it! I will give all points if shown the correct stephs. Im assuming this is close to a titration problem? not sure!

Explanation / Answer

This problem requires two ICE-like charts since it is a diprotic acid. (see page 718 in the textbook for an example) First set up an equation for the reaction.
H2X + OH- --> HX- + H2O (We are adding NaOH, so OH- is a reactant.)
Now you can set up the first table.
.........................H2X....OH-..HX...
Initial:................1.0 M...0.......0......---
Change:..............-x.......x.....+x....
Equilibrium:......1.0 - x...0......x......---
The OH- is completely used up in the reaction, so it is 0.
Write the formula for Ka:
Ka1 = [H+][HX-] / [H2X]
0.02 = (10^-6.5)(x) / (1 - x) ([H+] can be found from the given pH = 6.5)
x = 0.999984

And the second reaction: HX- + OH- --> X2- + H2O
.........................HX.........OH-...
Initial:............0.999984......0.......
Change:..............-x...........x.......
Equilibrium:.0.999984 - x...0....x.....---
And the second formula for Ka:
Ka2 = [H+][X2-] / [HX-]
(5*10^-7) = (10^-6.5)(x) / (0.999984 - x) ==> x = 1.632

Final answer: 1.6 L NaOH

I hope this helps!

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