The pH of a 0.10-M solution of caffeine is 11.16. Determine Kb for caffeine from these data:
C8H10N4O2(aq)+H2O(l) ⇌ C8H10N4O2H+(aq)+OH−(aq)
To determine Kb, you need to use the pH of the solution and the concentration of the caffeine. In this case, the pH of the solution is given as 11.16, and the concentration of the caffeine is 0.10 M.
1. First, calculate the pOH of the solution using the pH:
pOH = 14 - pH
pOH = 14 - 11.16
pOH = 2.84
2. Once you have the pOH, you can determine the OH- concentration using the following equation:
OH- concentration = 10^(-pOH)
OH- concentration = 10^(-2.84)
3. Since caffeine is a weak base, it will react with water to form its conjugate acid (C8H10N4O2H+) and hydroxide ions (OH-). At equilibrium, the concentration of hydroxide ions will be equal to the concentration of the conjugate acid.
4. Determine the equilibrium concentration of the conjugate acid (C8H10N4O2H+) using the initial concentration of the caffeine (0.10 M):
[C8H10N4O2H+] = [caffeine]
[C8H10N4O2H+] = 0.10 M
5. Using the equilibrium concentration of the conjugate acid and the concentration of hydroxide ions, you can determine Kb using the following equation:
Kb = [C8H10N4O2H+][OH-] / [caffeine]
Kb = ([C8H10N4O2H+])^2 / [caffeine]
Substituting the values we have:
Kb = ([0.10 M])^2 / [caffeine]
Kb = (0.10 M)^2 / 0.10 M
Kb = 0.10 M
Therefore, Kb for caffeine is 0.10 M.