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