Question

36)

1.

An aqueous solution contains 0.219 M carbonic acid and 0.166 M nitric acid.

Calculate the carbonate ion concentration in this solution.
[CO₃^2-] = ____mol/L.

2.

An aqueous solution contains 0.110 M carbonic acid and 0.146 M perchloric acid.

Calculate the carbonate ion concentration in this solution.
[CO₃^2-] = _____mol/L.

Answer 1

1. Sol :-

ICE table of H₂CO₃ :

.........................H₂CO₃ (aq) ------------------------------> HCO₃^-(aq)..............+..................H⁺ (aq)

Initial (I).............0.219 M ..............................................0.0 M..........................................0.0 M

Change (C) .........- y ......................................................+ y ............................................+ y

Equilibrium (E).....(0.219-y) M............................................y M............................................y M

Expression of K_a1 is :

K_a1 = [H⁺].[HCO₃^-] / [H₂CO₃]

4.2 x 10^-7 = y²/(0.219-y)

If y<<0.219, then neglect y as compare to 0.219.

4.2 x 10^-7 x 0.219  = y²

y = 0.00030 M = [HCO₃^-]

ICE table of HCO₃^-:

.........................HCO₃^- (aq) ------------------------------> CO₃^2-(aq)..............+..................H⁺ (aq)

Initial (I).............0.00030 M ..............................................0.0 M..........................................0.0 M

Change (C) .........- y ......................................................+ y ............................................+ y

Equilibrium (E).....(0.00030-y) M............................................y M............................................y M

Expression of K_a2 is :

K_a1 = [H⁺].[CO₃^2-] / [HCO₃^-]

4.7 x 10^-11 = y²/(0.00030-y)

If y<<0.219, then neglect y as compare to 0.00030 .

4.7 x 10^-11 x 0.00030 = y²

y² = 1.41 x 10^-14

y = 1.19 x 10^-7 M = [CO₃^2-]

Now, ICF table when HNO₃ reacts with CO₃^2-

............................CO₃^2- (aq)................+................HNO₃ (aq) -----------------> HCO₃^- (aq)...........+............NO₃^- (aq)

Initial (I) ..............1.19 x 10^-7 M .............................0.166 M .............................. 0.00030 M ...............................

Change (C)..........-1.19 x 10^-7 M...........................- 1.19 x 10^-7 M......................+1.19 x 10^-7 M ..........................

Final (F)...................0.0 M......................................0.166 M (approx.).................0.00030 M(approx.).................

So,

[HCO₃^-] = 0.00030 M

and we already calculated the concentration of CO₃^2- in 0.00030 M HCO₃^- = 1.19 x 10^-7 M

Hence, Concentration of CO₃^2- = [CO₃^2-] = 1.19 x 10^-7 M