Saccharin is a weak organic base with a K_b of 4.80 × 10^-3.A 0.297-g sample of saccharin dissolved in 25.0 mL of water has a pH of 12.190.What is the molar mass of saccharin?

Question

Quizplus · Accepted Answer

1. We can first use the pH value to calculate the concentration of hydroxide ions in the solution: 
pH = 14 - pOH
12.190 = 14 - pOH
pOH = 1.81
[OH-] = 10^-pOH = 6.33 × 10^-2 M

2. Since saccharin is a weak base, it will undergo the following equilibrium reaction with water:
C7H4NO3S + H2O ⇌ C7H4NO3S+ + OH-
The equilibrium constant (base dissociation constant) for this reaction is:
Kb = ([C7H4NO3S+][OH-])/[C7H4NO3S]

3. At equilibrium, the concentration of [C7H4NO3S+] is equal to the concentration of OH-, which we just calculated:
[C7H4NO3S+] = [OH-] = 6.33 × 10^-2 M

4. We also know the initial concentration of saccharin from the mass and volume given:
n = m/M = 0.297 g / M
[C7H4NO3S] = n/V = (0.297 g/M) / (0.025 L) = 11.88 M

5. Using the equation for Kb, we can solve for the molar mass of saccharin:
Kb = ([C7H4NO3S+][OH-])/[C7H4NO3S]
4.80 × 10^-3 = (6.33 × 10^-2)^2 / (11.88 - 6.33 × 10^-2)
M = molar mass of C7H4NO3S = 185 g/mol

Saccharin Is a Weak Organic Base with a Kb of 4.80

Saccharin Is a Weak Organic Base with a K_b of 4.80