Question

Hi. can some one please explain me the solution for this question. the correct answer is B. thanks.

6. What is the concentration of Zn(aq) ions in the solution made by adding water to zinc nitrate (0.10 mol) and ammonia (3.0 mol) so that the final volume of solution is 1.5 L? The Kb of Zn(NH).)" is 7.8 x 10° a) 4.9 x 10"M b) 9.5 x 10M c) 6.1 x 10M d) 2.8 x 10M e) 2.3 x 10M

Answer 1

ANSWER: b) 9.5 10 ^-12 M

Consider a complex formation reaction, Zn ²⁺ (aq) + 4 NH₃ (aq) [Zn( NH₃) ₄ ]²⁺ (aq)

Formation constant for above reaction is K f = [ [Zn( NH₃) ₄ ]²⁺ ] / [ Zn ²⁺] [ NH₃ ] ⁴ = 7.8 10 ⁸

Value of formation constant (7.8 10 ⁸) is very large, hence we can assume that all metal ion is converted into complex. Therefore, initially there is no metal ions present in the solution.

Now find out initial concentrations of metal ion , ligand and complex.

Initial moles of of Zn ²⁺ = 0.00 moles

Initial ,moles of [Zn( NH₃) ₄ ]²⁺ = 0.10 moles

Initial moles of NH₃ = 3.0 moles - 4 ( 0.10 moles) = 2.6 moles

Initial [Zn ²⁺ ] = No. of moles Zn ²⁺ / volume of solution in L = 0.00 M

Initial [NH₃ ] = 2.6 mol / 1.5 L =1.73 M

Initial [ [Zn( NH₃) ₄ ]²⁺ ] = 0.10 mol / 1.5 L = 0.0667 M

At equilibrium concentration of metal ion will be due to dissociation of complex ion. Let's use ICE table to find out equilibrium concentrations of metal ion, ligan and complex ion.

Concentration (M)	Zn 2+ (aq) + 4 NH3 (aq) [Zn( NH3) 4 ]2+ (aq)
Initial		1.73	0.0667
Change	+X	+ 4 X	- X
Equilibrium	X	1.73 + 4 X	0.0667 -X

Therefore, Kf = ( 0.0667 -X) / X ( 1.73 + 4 X) ⁴ = 7.8 10 ⁸

At equilibrium , value of X will be very small . Hence we can write 0.0667 - X 0.0667 and 1.73 + 4 X 1.73.

$\therefore$ 0.0667 / X ( 1.73 ) ⁴ =7.8 10 ⁸

X =  0.0667 / 7.8 10 ⁸ ( 1.73 ) ⁴

X = 9.5 10 ^-12 M = [Zn ²⁺ ] at equilibrium.