Question

1. Given 1 L of 0.05 M sodium bicine (conjugate base of the buffer), how much 0.1 N HCl must be added to make a bicine solution of pH 7.5? What is the molarity of bicine in the final buffer?   The pK_a is 8.26.

2. You take 2.38 g of HEPES in the acid form and bring the volume up to 100 mL with water. We will call this solution A. You then add 3 mL of 1 M NaOH to make solution B. Finally you add 7 more mL of 1 M NaOH to make solution C. What are the pH values of the 3 solutions? (The molecular weight of HEPES is 238. 3 g/mol and the pK_a is 7.55; HEPES is a weak acid commonly used for biological buffers.

Answer 1

Q1.

Assume sodium bicine --> NaA --> Na++ A-

A- + H+ <--> HA

then we need to add HCl to form HA, and A- so this become a buffer

recall that

A buffer is any type of substance that will resist pH change when H+ or OH- is added.

This is typically achieved with equilibrium equations. Both type of buffer will resist both type of additions.

When a weak acid and its conjugate base are added, they will form a buffer

The equations:

The Weak acid equilibrium:

HA(aq) <-> H+(aq) + A-(aq)

Weak acid = HA(aq)

Conjugate base = A-(aq)

Neutralization of H+ ions:

A-(aq) + H+(aq) <-> HA(aq); in this case, HA is formed, H+ is neutralized as well as A-, the conjugate

Neutralization of OH- ions:

HA(aq) + OH-(aq) <-> H2O(l) + A-(aq) ; in this case; A- is formed, OH- is neutralized as well as HA.

Now,

initially

pH = pKa + log(A-/HA) required

7.5 = 8.26 + log(A-/HA)

A-/HA = 10^(7.5-8.26) = 0.1737

A-/HA =0.1737

initially

mmol of NaA or (A-) = MV = 1*0.05 = 0.05 mol

mmol of HA = 0

after adding,

"x" mmol of HA = MV = 0.1 * Vacid

after addition:

mmol of NaA or (A-) = 0.05 - 0.1 * Vacid

mmol of HA = 0 +0.1 * Vacid

substitute

A-/HA =0.1737

(0.05 - 0.1 * Vacid ) / (0.1 * Vacid) = 0.1737

(0.05 - 0.1 * Vacid ) = 0.1737*0.1 * Vacid

0.01737*Vacid +0.1*Vacid = 0.05

Vacid = (0.05) / (0.1+0.01737)

Vacid = 0.4260 L = 426 mL of HCl required