pH and buffer - odd question

[PlumbLine]

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Came across a weird question and I can't remember how to work this. Help?

One liter of a 0.1M buffer (pK=8.3) is prepared and adjusted to a pH of 2.0. (yes, you read that correctly)

a)What are the concentrations of the conjugate base and weak acid at this pH?
b)What is the pH when 1.5mL of 3.0M HCl is added to 1.0L of the buffer?
c) What is the pH when 1.5mL of 3.0M NaOH is added to 1.0L of the buffer?

a) I calculate [HA] = 0.1M and [A-] = 5 x 10^-8M (so essentially no weak base available to buffer any acid)
b) I calculate pH = 1.83
c) ???

Thank you!

 

[PlumbLine]

Answer key says c) is pH = 7, which is based on using the HH equation. However, I don't think this takes into account the initial H+ concentration of 0.01M.

 

[Czarcasm]

Sorry, don't have the time to calculate this for you -- and to be honest, I'm not entirely sure this is right, but it's worth a try I guess:

a.) 0.1L of 0.1 M buffer = 0.001 moles each weak acid and conjugate base. At pH of 2, it's safe to assume all the conjugate base has been converted entirely to weak acid. Therefore, at pH 2, we have 0.002 moles weak acid. (The remaining protons of the strong acid that dissociates is free floating in solution and contribute to the significantly lower pH).

b.) 0.001 moles conjugate base - 0.0045 moles H = +0.001 moles weak acid (total weak acid: 0.002 moles) + 0.0035 moles remaining H+
c.) 0.001 moles weak acid - 0.0045 moles OH- = +0.001 moles weak base (total weak base: 0.002 moles) + 0.0035 moles remaining OH-

Convert these to concentrations. Note: Because 1L of solvent is considerably greater than the amount of strong/weak base that was added, you can assume total liters of solvent is 1L. But if you're looking for the exact answer, just realize its 1L + 0.0015 L = 1.0015 L. You'd divide moles / liters to find concentration and use for the calculation below.

For b and c, use the Ka (or Kb) expression to find out the H30+ (or OH-) concentration present at these concentrations of weak acid/base. Then add the remaining H+ (or OH-) from the value you obtained from that calculation. Then just calculate the pH of each in either case.

Maybe get a second opinion to be sure.

Hope this helps -- I'm sure there's probably something I'm overlooking and there's a more straight forward approach to this. These types of calculations were never my forte.

 

[PlumbLine]

Answer key says c) is pH = 7, which is based on using the HH equation. However, I don't think this takes into account the initial H+ concentration of 0.01M.

Finally got confirmation from my professor that the answer key is wrong. pH should calculate around 2.26