Question: Adding Strong Acid to Buffer

[sam.]

A beaker with 135 mL of an acetic acid buffer with a pH of 5.00 is sitting on a benchtop. The total molarity of acid and conjugate base in this buffer is 0.1 M. A student adds 7.80 mL of a 0.400 M solution to the beaker. How much will the pH change? The pKa of acetic acid is 4.76.

What I did was find the total number of moles of acid + base = 0.0135. Then using the Henderson-Hasselbach equation, pH = pKa + log([base]/[acid]) I found the ratio of [base]/[acid] to be 1.74. Then using these two equations I found the moles of acid to be 4.93*10^-3 and base = 5.45*10^-3. Next I found the moles of HCl = 0.00312 mol and substracted that from the base and added it to the acid so: acid = 8.05*10^-3 and base = 5.45*10^-3. Now I put these values into pH = pKa + log([base]/[acid]) and got the pH to be 4.59...therefore the change would be -0.40...But I think this value is too high...I think it's supposed to be lower. Can anyone tell me where I went wrong? Any help is appreciated.

 

[lightarrow]

A beaker with 135 mL of an acetic acid buffer with a pH of 5.00 is sitting on a benchtop. The total molarity of acid and conjugate base in this buffer is 0.1 M. A student adds 7.80 mL of a 0.400 M solution to the beaker. How much will the pH change? The pKa of acetic acid is 4.76.

What I did was find the total number of moles of acid + base = 0.0135. Then using the Henderson-Hasselbach equation, pH = pKa + log([base]/[acid]) I found the ratio of [base]/[acid] to be 1.74. Then using these two equations I found the moles of acid to be 4.93*10^-3 and base = 5.45*10^-3.

No, it's 8.57*10^(-3) moles.

 

[ravenprp]

Your calculations seem to be correct, so I don't think you went wrong anywhere. The decrease in pH of 0.40 is reasonable considering that a strong acid (HCl) was added to the buffer. The addition of HCl would shift the equilibrium towards the formation of more acetic acid, leading to a decrease in pH. This change in pH is also supported by the fact that the pKa of acetic acid is 4.76, which means that it is a weak acid and its pH is sensitive to changes in concentration. So, overall, your calculations and result seem to be accurate.