Question

Caffeine (C8H10N4O2) is a weak base with a pKb of 10.4. Calculate the pH of a solution containing a caffeine concentration of 455 mg/L.

Answer 1

Caffeine (C8H10N4O2) is a weak base with a pKb of 10.4. Calculate the pH of a solution containing a caffeine concentration of 455 mg/L

this is a base so:

B + H2O <-> HB´+ + OH-

Calcualte concentration of caffein

455 mg/L

MW of Caffeine = 194.19 g/mol

455 mg of caffeine --> 0.455 g

mol of Caffeine = 0.455/194.19 = 0.002343 mol of Caffeine per L

now...

Kb = [BH+][OH-]/[B]

Kb = 10^-pLKb = 10^-10.4= 3.981*10^-11

now, in equilibirum

[BH+]= [OH-] = x

[B] = 0.002343 -x

3.981*10^-11 = x*x/(0.002343 -x)

x^2 + (3.981*10^-11)x+ 9.327*10^-14 = 0

x = 3.0538*10^-7

so:

[OH-] = x= 3.0538*10^-7

pOH = -log(3.0538*10^-7) = 6.51

pH =14-pOH = 14-6.51

pH = 7.49