Final answer:
The pH of lysine when it's 1/4 dissociated, with a pKa of 9, is approximately 8.48. This is calculated using the Henderson-Hasselbalch equation with the ratio of [A-]/[HA] being 1/3.
Step-by-step explanation:
When lysine is 1/4 dissociated, the ratio of [base] to [acid] is 1:3. Using the given pKa value of 9, we can use the Henderson-Hasselbalch equation to determine the pH. The ratio of [A-]/[HA] is 1/3 and by inserting these values into the Henderson-Hasselbalch equation pH = pKa + log([A-]/[HA]), we can calculate the pH.
Thus, the formula will look like this: pH = 9 + log(1/3). Solving for pH, we calculate that the pH is approximately 8.48. It's important to understand that the pKa value gives an estimate of the pH of the buffer system.
Therefore, understanding the dissociation of lysine and using the Henderson-Hasselbalch equation are keys to calculating the pH for a partially dissociated solution.
The pH of the lysine when it is 1/4 dissociated can be determined using the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is given by:
pH = pKa + log([A-]/[HA])
Here, [A-] is the concentration of the conjugate base (dissociated form) and [HA] is the concentration of the weak acid (undissociated form). Since lysine is a weak base, the concentration of the conjugate acid will be 1/4 of the total concentration of lysine. The pKa value provided is 9. Using the Henderson-Hasselbalch equation, we can calculate the pH of the lysine when it is 1/4 dissociated.
pH = 9 + log(1/4)
pH = 9 - log(4)
pH = 9 - 0.6021
pH ≈ 8.3979