Phenolphthalein is a commonly used indicator that is colorless in the acidic form (pH < 8.3) and pink in the basic form (pH > 10.0). It is a weak acid with a pKa of 8.7. What is the ratio of the conjugate base concentration to the acid concentration, that is, [B-]/[HB] when the indicator switches to the acidic color? Hint given in feedback.
I don't have the benefit of the "feedback" session but I would use
8.3 = 8.7 + log(b)/(a)
solve for the ratio b/a.
i did it i found 0.4 but wrong
What was your feedback session?
To determine the ratio of the conjugate base concentration [B-] to the acid concentration [HB] when phenolphthalein switches to the acidic color, we can make use of the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation relates the pH and the pKa of a weak acid as follows:
pH = pKa + log([B-]/[HB])
Given that the pKa of phenolphthalein is 8.7 and the acidic form is colorless (pH < 8.3), we can assume that at equilibrium, almost all of the phenolphthalein is in the acid form and the concentration of [B-] is negligible.
Therefore, we can substitute pH = 8.3 and pKa = 8.7 into the Henderson-Hasselbalch equation to solve for the ratio [B-]/[HB]:
8.3 = 8.7 + log([B-]/[HB])
Subtracting 8.7 from both sides:
8.3 - 8.7 = log([B-]/[HB])
-0.4 = log([B-]/[HB])
Taking the antilog (or inverse logarithm) of both sides:
10^(-0.4) = [B-]/[HB]
0.398 = [B-]/[HB]
Therefore, the ratio of the conjugate base concentration [B-] to the acid concentration [HB] when phenolphthalein switches to the acidic color is 0.398, or approximately 0.4.
Please note that this ratio assumes that the concentration of the conjugate base is negligible compared to the concentration of the weak acid at the pH when the indicator switches to the acidic color.