Calculate the pH for each of the following cases in the titration of 25.0 mL of 0.180 M pyridine, C5H5N(aq) with 0.180 M HBr(aq):

1)before addition of any HBr
2)after addition of 12.5 ml of HBr:
3)after addition of 16 ml of HBr:
4)after addition of 25 ml of HBr:
5)after addition of 32 ml of HBr:

number 1 and 2 are fuzzy

To calculate the pH for each case in the titration, we need to consider the reaction between pyridine (C5H5N) and HBr. Pyridine is a weak base, while HBr is a strong acid. In this titration, the pyridine will be neutralized by the HBr.

First, let's write the balanced chemical equation for the reaction:

C5H5N(aq) + HBr(aq) -> C5H5NH+(aq) + Br-(aq)

1) Before addition of any HBr:
Since no HBr has been added yet, the pyridine is still in its initial concentration. Therefore, the pH can be calculated using the pKa of pyridine, which is 5.25.

2) After addition of 12.5 ml of HBr:
To calculate the pH after adding 12.5 mL of HBr, we need to consider the moles of pyridine and HBr that react. From the balanced equation, we can see that for every 1 mole of pyridine, 1 mole of HBr is consumed. Therefore, since the initial concentration of pyridine is 0.180 M, we have (0.180 M x 0.0125 L) - (0.180 M x 0.0125 L) of pyridine left. We can then calculate the concentration of the pyridinium ion (C5H5NH+), and determine the pH using the Henderson-Hasselbalch equation.

3) After addition of 16 ml of HBr:
Using the same approach as in case 2, we can calculate the concentration of the pyridinium ion and determine the pH.

4) After addition of 25 ml of HBr:
At this point, 25 mL of HBr has been added, which corresponds to the total volume. Therefore, the concentration of pyridine is now zero, and only the pyridinium ion and Br- ion are present. We can calculate the concentration of the pyridinium ion using the moles of pyridine initially present and the volume of HBr added. From there, we can determine the pH.

5) After addition of 32 ml of HBr:
Similar to case 4, we use the same approach for calculating the concentration of the pyridinium ion and determining the pH.

Note: The Henderson-Hasselbalch equation for calculating pH is given by:

pH = pKa + log ([A-]/[HA])

where pKa is the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.

By following these steps and calculations, you should be able to determine the pH for each case in the titration.

This take a LOT of typing. Exactly what do you understand and not understand?