Question

The pH of a 0.10-M solution of caffeine is 11.70. Determine (K_b) for caffeine from these data:

a) (1.2 × 10⁻6)
b) (2.8 × 10⁻6)
c) (3.7 × 10⁻6)
d) (5.6 × 10⁻6)

Answer 1

The base dissociation constant (Kb) for caffeine can be calculated from the pH by converting the pH to pOH, then finding the OH- concentration, and finally using the formula for Kb. The approximate value of Kb is found to be 2.5 x 10^-6, which makes option b) (2.8 x 10^-6) the closest answer.

Step-by-step explanation:

To determine the base dissociation constant (Kb) of caffeine from the given pH, we first need to convert the pH to pOH, since Kb is related to the hydroxide ion (OH−) concentration. The pOH can be calculated using the formula:

pOH = 14 - pH

Substitute the given pH value:

pOH = 14 - 11.70 = 2.30

Now, calculate the concentration of hydroxide ions using the pOH value:

[OH−] = 10−pOH = 10−2.30

From here, we can use the formula for Kb:

Kb = ([OH−]^2) / ([Base] - [OH−])

Since caffeine is a weak base and given the high pH, we can assume that the initial concentration of the base is approximately equal to the concentration minus the concentration of hydroxide ions. So, Kb is approximately equal to:

Kb ≈ [OH−]^2 / [Base]

Calculate Kb:

[OH−] = 10−2.30 = 5.01 × 10−3 M

[Base] = 0.10 M

Kb ≈ (5.01 × 10−3 M)2 / 0.10 M

Kb ≈ 2.5 × 10−6

The option closest to this result is b) (2.8 × 10−6).