Question

A weak acid (HA) has a pKa = 2.77. Assuming the volumes are additive, calculate the volume (in mL) of 0.500 M HA, O.500 M NaA, and water required to make 250.00 mL of a buffer with a total concentration of 0.400 M and (a) pH= 2.77; (b) pH= 2.25; (c) pH= 3.00.

Calculate the buffer strengths of the thee buffers in the problem.

Please show work on buffer strength calculation.

Answer 1

(a) 100 mL HA + 100 mL NaA + 50 mL H2O --> 2.77 pH
250 mL of 0.4 M has 100 millimoles of HA+NaA. (0.100 moles / 0.250 L = 0.400 M)
pH = pKa + log(A-/HA)
100 mL x 0.50 M = 50 mmol (0.050 moles)
log(0.050/0.050) = log(1) = 0

(b)
2.25 = 2.77 - 0.52
log(A-/HA) = -0.52
10^-0.52 = 0.30
A-/Ha = 0.30 = mL A / mL HA
mL A + mL HA = 100
mL HA = 100 - mL A-
0.30 = mL A- / (100 - mL A-)
30 - 0.30 (mL A-) = mL A-
30 = 1.30 mL A-
mL A- = 23 mL
mL HA = 77 mL

(c)
3.00 = 2.77 +0.23
log(A-/HA) = 0.23
10^0.23 = 1.70
A-/Ha = 1.70 = mL A / mL HA
mL A + mL HA = 100
mL HA = 100 - mL A-
1.70 = mL A- / (100 - mL A-)
170 - 1.70 (mL A-) = mL A-
170 = 2.70 mL A-
mL A- = 63 mL
mL HA = 37 mL

Buffer strength?
Buffer (a) has the greatest buffering capacity. 50 mM of H+ or OH- could be added before the buffering capacity is exhausted. I'm not certain what you mean by buffer strength.