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General : A few Questions
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 Message 1 of 4 in Discussion 
From: MSN NicknameN_2006  (Original Message)Sent: 3/19/2008 4:04 AM
Hey Steve, I have a few questions that I have no idea how to solve!!
 
First:
As a technician in a large pharmaceutical research firm, you need to produce 250 mL of 1 M potassium phosphate solution of pH = 7.31. The {\rm p}K_{\rm a} of \rm H_2PO_4^{~-} is 7.21. You have 2 \rm L of 1 \rm M~KH_2PO_4 solution and 1.5 \rm L of 1 \rm M~K_2HPO_4 solution, as well as a carboy of pure distilled \rm H_2O. How much 1 \rm M~KH_2PO_4 will you need to make this solution?
I have tried this over and over.. and I keep getting the wrong answer!!!
 
Another quesiton:
A certain weak acid, \rm HA, with a K_a of 5.61 \times 10^{-6}, is titrated with \rm NaOH.A solution is made by mixing 9.00 millimoles of \rm HA and 3.00 millimoles of base. What is the resulting pH?
Some how I got 0.48 as the pH.. which I didn't think was right, and it turns out it isn't
 
I took the Ka and converted to pKa which is 5.25.  But everytime I take the concnetrations and do the ICE chart it never comes up with the right answer.
 


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Reply
 Message 2 of 4 in Discussion 
From: MSN Nickname·Steve·Sent: 3/19/2008 4:59 AM
First Question

This is going to be one of those two equations, two unknowns type problem.  First, plug into the Henderson-Hasselbalch equation to calculate the ratio [K2HPO4] / [KH2PO4] :

7.31  =  7.21  +  log { [K2HPO4] / [KH2PO4] }

[K2HPO4]    =  1.2589
[KH2PO4

Since both are in the same solution with one total volume, we can simply use moles of substances in the last term of the Henderson-Hasselbalch equation.  So,

moles of K2HPO4    =   1.2589
moles of KH2PO4

Or, rearranging,

moles of K2HPO4   =   1.2589  X  moles of KH2PO4

Molarity is volume  X  molarity.  Letting "VK2" be the volume of K2HPO4 and "VK" be the volume of KH2PO4, and "MK2" and "MK" are the corresponding molarities, we have

VK2 MK2   =   1.2589 VK MK

But, the molarities of the two solutions are the same, 1 M, so MK2  =  MK.  Therefore,

VK2   =   1.2589 VK         Equation 1

Another note:  Since each solution is 1 M, and the desired buffer solution is also supposed to be 1 M in total phosphate concentration, we do not have to make any dilutions.  That is, no matter what amount of each solution we mix together, the total phosphate concentration will still be 1 M after mixing.
 
OK, for the second equation, we know that the total volume is 250 mL.  So....

VK  +  VK2   =   250        Equation 2

From Equation 2,
 
VK2   =   250  �?nbsp; VK

Substituting into Equation 1, we have

250  �?nbsp; VK   =   1.2589 VK

Solve for VK.  VK2 will be 250 �?VK, and there will be your two volumes! 

I'll look at the second question in the next post.
 

Steve

Reply
 Message 3 of 4 in Discussion 
From: MSN Nickname·Steve·Sent: 3/19/2008 5:23 AM
Second Question

First thing to do is calculate the amounts of substances after the reaction with NaOH :

                   HA (aq)    +    NaOH (aq)     ––�?gt;     NaA (aq)    +    H2O (l)

Initially:       9.00 mmol       3.00 mmol                    0                 (solvent)
                   excess            limiting

After Rxn:    6.00 mmol           0                          3.00 mmol       (solvent)
 

So, the resulting solution contains 6.00 mmol of HA and 3.00 mmol of NaA.  This is a weak acid HA plus its conjugate base A�?/SUP> (Na+ is a spectator ion here), which is a classic buffer solution.

Buffer solution  =  we can use Henderson-Hasselbalch to calculate the pH.

pH   =   pKa   +   log { [A�?/SUP>] / [HA] }

In the log term on the right side, we can use moles of A�?/SUP> and HA instead of molarities.  Each molarity would be the moles divided by the total volume, but the numerator and denominator would be divided by the same total volume.  Therefore, volume cancels and [A�?/SUP>] / [HA]  =  moles of A�?/SUP> / moles of HA.  Or we can use millimoles; the ratio will still have the same value.  Convenient, but we have to be careful, because we usually want to use molar concentrations when working pH problems.  But because this is a ratio of molarities in the same solution, the volume cancels and we can just use moles of substances in this case. 

So, plugging in, we have

pH   =   –log (5.61 X 10�?)   +   log (3.00 mmol / 6.00 mmol)

from which you can get the pH.
 

Steve

Reply
 Message 4 of 4 in Discussion 
From: MSN NicknameN_2006Sent: 4/9/2008 3:07 PM
thank you steve.. again very helpful

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