Question

Saccharin is a weak organic base with a Kb 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?
A) 0.616 g/mol
B) 19.3 g/mol
C) 184 g/mol
D) 181 g/mol
E) 119 g/mol

Answer 1

So, you need to use the equilibrium expression for the reaction of the base. Ultimately you wanna find the concentration, and using the volume, find the moles of base. Then use the mass to find the molar mass.

Answer 2

Ok I was thinking along the same lines but when I tried it I got an answer that wasn't one of the answer options.

Answer 3

So one of the first things I did was I took the pH and converted it to pOH since when saccharin reacts with water, one of the products would be OH-.

Answer 4

you're right about that. hold on i'm gonna try it out

Answer 5

Ok

Answer 6

sorry my comp died.

\(\sf K_b=\dfrac{[OH^-][Saccharin^+]}{[Saccharin]}\rightarrow K_b=\dfrac{x^2}{[Saccharin]-x}\)

\(\sf (4.8*10^-3)=\dfrac{0.01548^2}{[Saccharin]-0.01548}\)

\(\sf [Saccharin]=0.065403~M\)

\(\sf n_{sacc}=0.065403~M*0.025~L=0.001635075~moles\)

\(\sf Molar ~mass=\dfrac{0.297~g}{0.001635075~moles}=181.64~g/mol\)

Answer 7

That's ok!

Answer 8

And I see what I did wrong! I didn't subtract by 0.01548

Answer 9

Thank you!

Answer 10

no problem! yup, make sure you write out the ICE table before plugging stuff into the equation.