Question

What is the solubility of MnS, in g/L, in a buffered solution that is 0.216 M HC2H3O2 and 0.331 M NaC2H3O2. (Hint what is the function of the buffer solution?) Ksp = 3.0 x 10–14 for MnS.

Please clearly show your work and explain steps

Answer 1

The effect of pH on solubility of salts is of significant importance, when dissociation of a compound into a solvent is under consideration. Changes in pH can affect the solubility of partially soluble ionic compounds, particularly when a common ion results due ionization of water ( ie H⁺ or, OH^- ). The ions formed due to ionization of water may result into increase or decrease of either H⁺ or OH^- as a result of common ion effect. Thus, affecting the solubility of a partially soluble salt.Hence, the use of buffer solution with a particular pH is is preferred.

Solubility of MnS :

Step 1 ,

Note that buffer solution prepared is a ( Sodium acetate - Acetic acid ) buffer solution ,where

[ CH3COONa ] =0.331 M & [ CH3COOH ] = 0.216 M

Ka for CH3COOH = 1.8 x 10^-5 , therefore pK_a  = - log K_a

........................................................................... = 4.74

Apply Handerson Hasselbalch's equation to calculate pH of the buffer solution -

pH = pK_a   + log [ salt ] / [Acid }

.... = 4.74 + log ( 0.331 / 0.216 )

.... = 4.93 ^#

Step 2 , -

Let the the solubility of MnS be represented by x moles / L'

then,..........as a result of ionic equilibria -

.................................MnS (aq) <------------> Mn²⁺ (aq) + S^2- (aq) ............

moles at equilibrium .....x..................................x................x.......

............Ksp = [Mn²⁺ ] [ S^2- ]

........3x10^-14  = (x ) (x )

..............x = 1.73 x 10^-7 moles / L

................or, ..= ( 1.73 x 10^-7 x 86.94* ).................* ( Molecular mass of MnS = 86.94 )

...................... = 1.50 x 10^-5 gms / L

^# It should be noted that ,

1) the acidic pH of buffer solution ( 4.93 ) would prevent separation of Mn (OH )₂

2 ) supress the ionization of H₂S in aqueous solution of partially soluble MnS ,

.....formed due to interaction of the ions of water with ions of the salt , if any.