The pKa of a weak acid, HA is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be i. 7.01 ii. 9.22 iii. 9.58 iv. 4.79

To determine the pH of an aqueous solution of the salt BA, formed from the weak acid HA and the weak base BOH, we can use the relationship between the pKa of the acid, the pKb of the base, and the pH of the resulting solution. The key here is to recognize that the salt BA will hydrolyze in water, affecting the pH of the solution.

Understanding the Relationship

The pKa of the weak acid HA is given as 4.80, and the pKb of the weak base BOH is 4.78. To find the pH of the salt solution, we first need to calculate the pKw, which is the ion product of water at 25°C, typically around 14. This allows us to find the pKa of the conjugate base (A-) formed from the weak acid HA.

Calculating pKa of the Conjugate Base

Using the relationship:

• pKa + pKb = pKw

We can rearrange this to find the pKa of the conjugate base A-:

• pKa(A-) = pKw - pKb(BOH)
• pKa(A-) = 14 - 4.78 = 9.22

Finding the pH of the Salt Solution

Now that we have the pKa of the conjugate base A-, we can use it to find the pH of the salt solution BA. The pH can be calculated using the formula for the hydrolysis of the salt:

• pH = 0.5 * (pKa(A-) + pKw)

Substituting the values we have:

• pH = 0.5 * (9.22 + 14)
• pH = 0.5 * 23.22
• pH = 11.61

Final Consideration

However, we need to consider that we are looking for the pH of the salt solution, which is influenced by both the weak acid and weak base. A more accurate approach is to use the average of the pKa of the acid and the pKb of the base:

• pH = 0.5 * (pKa + pKb)
• pH = 0.5 * (4.80 + 4.78)
• pH = 0.5 * 9.58
• pH = 4.79

Thus, the pH of the aqueous solution of the salt BA is approximately 4.79. Therefore, the correct answer is iv. 4.79.