what mass of (CH3)2 NH2 CI should the student dissolve in the (CH3)2NH solution

Question

A chemistry graduate student is given 500. mL of a 0.90M dimethylamine ((CH₃)₂ NH) solution. Dimethylamine is a weak base with K_b = - 5.4 × 10^-4 what mass of (CH₃)₂ NH₂ CI should the student dissolve in the (CH₃)₂NH solution to turn it into a buffer with pH = 11.32?

You may assume that the volume of the solution doesn't change when the (CH₃)₂ NH₂CI is dissolved in it. Be sure your answer has a unit symbol, and round it

to 2 significant digits.

Answer 1

pOH = pKb + log [salt] / [base]

pOH = 14 - pH = 14 - 11.32 = 2.68

pKb = -log Kb = -log 5.4x10^-4 = 3.27

pOH = 3.27 + log [x] / [0.90]

2.68 = 3.27 + log [x] / [0.90]

-0.59 = log [x] / [0.90]

0.257 = [x] / [0.90]

x = 0.231 M (CH₃)₂NH₂Cl

Molar mass (CH₃)₂NH₂Cl = 81.5 g / mol

500 ml = 0.500 L

0.500 L x 0.231 mol / L = 0.1155 mols (CH₃)₂NH₂Cl needed

0.1155 mols (CH₃)₂NH₂Cl x 81.5 g / mol = 9.4 g (CH₃)₂NH₂Cl need to be added

(be sure to check the math)