Calculating pH of buffer after adding HCl

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To calculate the pH of a Tris buffer after adding 1 ml of 0.05 M HCl to 4 ml of 0.01 M Tris at pH 9.0, the initial concentrations of the base ([A-]) and acid ([HA]) forms of the buffer are determined. The calculations show that after the addition of HCl, the concentration of the base form becomes negative, indicating that all base has been converted to the acid form. This suggests that excess HCl remains, which must be accounted for in the pH calculation. The Henderson-Hasselbalch equation is not applicable in this scenario due to the negative concentration, necessitating a different approach to determine the pH based solely on the remaining HCl. The discussion emphasizes the importance of recognizing when the buffer capacity is exceeded and how to handle excess strong acids in pH calculations.
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Homework Statement


If the Tris buffer was exactly pH=9.0, calculate expected pH value after addition of 1 ml of 0.05 HCl.

Buffer: 4 ml of 0.01M Tris, pH 9.0
HCl: 1 ml of 0.05M HCl

Homework Equations


H-H: pH=pKa+log[A-]/[HA]

The Attempt at a Solution


9.0=8.21+log[A-]/[HA]
[A-]/[HA]=6.17

[A-]+[HA]=0.01M so, [A-]=6.17[HA], and 6.17[HA]+[HA]=0.01
7.17[HA]=0.01, so [HA]=.0013M
0.01-.0013=.0087M=[A-]

HCl: 1ml x 0.05M= 0.05mmols HCl

[A-]=.0087M x 4 ml= .0348mmol A-
[HA]=.0013M x 4 ml= .0052 mmol HA

Here's the part I'm unsure of:
If I plug these values into the Henderson-Hasselbalch, I'm going to get a negative value for the base part of the equation. I'm aware that this means that all of the base has been converted to the acid form, and that there is actually HCl left over that contributes to the pH. I'm just not sure how to calculate the pH from here, since the H-H equation can't be used.
 
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Assuming your calculations were right - just from the excess HCl.
 

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