Hi Albert, your answer to the first problem is correct. I get pH = 4.74 + log(0.250 mol / 0.400 mol) = 4.74 �?0.204 = 5.54.
For the second problem, just plug into the dilution formula to get the molarity of the diluted solution of HCl:
VconcMconc = VdilMdil
(50.0 mL)(0.20 M) = (200 mL)Mdil
Mdil = 0.050 M
Since HCl is a strong acid, the H+ concentration is the same as the molarity, 0.050 M. Thus the pH is just –log(0.050 M) = 1.30. If you had a very dilute solution of HCl, then the concentration of H+ ion in the water itself would be significant (1.0 X 10�? M at 25°C) but it would be unusual to have to consider this.
Steve