Equal volumes of 1 m solutions of citric acid, sodium citrate, sodium hydrogencitrate, and sodium dihydrogencitrate are combined and the ph is adjusted to 9.5 using 1 m naoh. what is/are the major species (other than h2o) in the solution?

Na⁺, A³⁻

Explanation:

For easy calculation, let's say you have mixed 1 L of each of these solutions to make 4 L total.

Citric acid (H₃A) has three acidic hydrogens.

The equilibria are

1. H₃A + H₂O ⇌ H₃O⁺ + H₂A⁻;   pKₐ =    3.08

2. H₂A⁻ + H₂O ⇌ H₃O⁺ + HA²⁻; pKₐ =    4.44

3. HA²⁻ + H₂O ⇌ H₃O⁺ + A³⁻;    pKₐ =   5.40

4. A³⁻ + H₂O ⇌ OH⁻ + HA²⁻ ;    pKb  =  8.60

5. 2H₂O ⇌ H₃O⁺ + OH⁻;           pKw  = 14.00

Now, we adjust to pH 9.

Let's look at the weakest acid (Equation3),

pH = pKa + log([A³⁻]/[HA²⁻])

9 = 5.40 + log([A³⁻]/[HA²⁻])

log([A³⁻]/[HA²⁻])= 3.6

[A³⁻]/[HA²⁻] = 10^3.6  = 4000

[A³⁻]= 4000[HA²⁻]

In other words, at pH 9, the weakest acid is completely neutralized. Then, the stronger acids are also completely neutralized.

It takes 3 mol of NaOH to neutralize the H₃A, 2 mol of NaOH for the NaH₂A, and 1 mol NaOH for the Na₂HA.

So, 6 mol of NaOH will neutralize the three acids, bring the pH to 9, and make a total volume of 10 L.

The final solution contains the species: H₃A, H₂A⁻, HA²⁻, A³⁻, Na⁺, H₃O⁺, and OH⁻.

Now we must assess their relative amounts.

Na⁺: 6 mol for neutralization + 6 mol in the original solution = 12 mol.  

[Na⁺] = 1.2 mol·L⁻¹

A³⁻: 1 mol from each of the four solutions = 4 mol A³⁻.

[A³⁻] = 0.4 mol·L⁻¹

The other species all have concentrations less than 10⁻⁴ mol·L⁻¹.

The major species are Na⁺ and A³⁻.