I need a chem pro's help with this question!

Question

the carbonate ion has a Kb (base dissociation constant) of 1.8X10^-4 mol dm-3. Find the volume of 0.10M of sodium hydrogen carbonate needed to be added to 25.0cm3 of 0.12M of Na2CO3 (sodium carbonate) to form a buffer solution of pH 9.50.

thx very much for ur help! i'll rmbr to give the best answer =)

Answer 1

find moles in  25.0cm3 of 0.12M of Na2CO3 :

0.025 litres @ 0.12 mol/litre = 0.0030 moles CO3)-2

Na HCO3 is your acid,  its Ka  is found by :

Kwater / Kb of CO3)-2 = 1e-14 / 1.8 e-4 = 5.6e-11

when the K = 5. 6e-11,  the pKa is 10.25

this is  easier setting up as the Henderson–Hasselbalch equation

http://en.wikipedia.org/wiki/Henderson_H...

pH = pKa + log [anion] / [acid]

9.50 = 10.25 & log [CO3)-2] / [HCO3)-1]

- 0.75 =  log [CO3)-2] / [HCO3)-1]

10^x of both sides:

0.178 = [CO3)-2] / [HCO3)-1]

this is the ratio of molarities that we need, it also is the ratio of moles that we need:

0.178 = [0.003 moles] / [HCO3)-1]

HCO3)-1 = 0.003 moles CO3)-2 / 0.178

HCO3)-1 = 0.1685 moles of NaHCO3 are needed to be added:

0.16854 moles of NaHCO3 @ 0.10 mol / litre = 0.016854 litres need to be added:

your answer is: 16.9 ml of NaHCO3 needs to be added, (aka 16.9 cm3)