On addition of 1 c.c. of dilute hydrochloric acid (1% concentration) to 80 c.c. of a buffer solution of pH = 4, the pH of the solution becomes

ANS:C - 4

To solve this problem, we need to calculate the change in pH of the buffer solution upon addition of the dilute hydrochloric acid (HCl). The buffer solution resists changes in pH upon addition of small amounts of acid or base due to the presence of a weak acid and its conjugate base, or a weak base and its conjugate acid. Given:

• Initial pH of the buffer solution = 4
• Addition of 1 cc of dilute hydrochloric acid (1% concentration)

The pH change in a buffer solution upon addition of acid can be calculated using the Henderson-Hasselbalch equation: pH=pKa+log⁡([A−][HA])pH=pKa+log([HA][A−]​) Where:

• pH = the pH of the buffer solution
• pKa = the negative logarithm of the acid dissociation constant (𝐾𝑎Ka​) of the weak acid in the buffer solution
• [A^-] = the concentration of the conjugate base
• [HA] = the concentration of the weak acid

Since the pH is 4, we assume that the weak acid in the buffer solution is dissociated 10 times less than the conjugate base. Therefore, we can assume that [A−]=80[A−]=80 and [HA]=8[HA]=8. Let's calculate the pKa using the Henderson-Hasselbalch equation: 4=pKa+log⁡(808)4=pKa+log(880​) 4=pKa+log⁡(10)4=pKa+log(10) 4=pKa+14=pKa+1 pKa=4−1=3pKa=4−1=3 Now, we can use the Henderson-Hasselbalch equation to calculate the new pH after adding 1 cc of dilute hydrochloric acid: pH=3+log⁡(808+1)pH=3+log(8+180​) pH=3+log⁡(809)pH=3+log(980​) pH=3+log⁡(809)pH=3+log(980​) pH=3+log⁡(809)pH=3+log(980​) pH=3+log⁡(8.888)pH=3+log(8.888) pH≈3+0.95pH≈3+0.95 pH≈3.95pH≈3.95 Therefore, the pH of the solution becomes approximately 3.95 after adding 1 cc of dilute hydrochloric acid. So, the closest option is 4.