Q: If the equilibrium constant for $$Ag^+ + 2NH_3 \rightleftharpoons [Ag(NH_3$)_2]^+ is$$ $$K_{12} = 1.7 \times 10^7$, and the equilibrium concentrations are $$[Ag($$NH_3)_2$$]^+ = 4.0 \times $$10^{-3}$$ \ M$$ and $$[$$NH_3$$] = 0.492 \ M$$, what is the equilibrium concentration of $$[Ag^+]$$?

$$9.6 \times 10$$^{-10}$$ \ M$$

Q: If $$[Ag^+] at $$equilibrium is found to be $$9.6 \times 10$$^{-10}$$ \ M in a $$solution with $$[NH_3$] = 0.492 \ M$$ and $$[Ag(NH_3$)_2]^+ = 4.0 \times 10$$^{-3}$$ \ M$$, which calculation correctly verifies the value of $$K_{12}$$?

$$K_{12} = \dfrac{4.0 \times 10$$^{-3}$$}{(9.6 \times 10$$^{-10}$$)(0.492)^2$$}$

Question 1

Which of the following best describes a complex ion?

Accepted Answer

A polyatomic cation or anion composed of a central metal ion bonded to other groups (molecules or ions).

Question 2

What is the coordination number of the complex ion $$[Cu(NH_3$)_4]^{2+}$$?

Accepted Answer

$$4$$

Question 3

Which of the following is a ligand in the complex ion $$[Ag(NH_3$)_2]^+$$?

Accepted Answer

$$NH_3$$

Question 4

Given the following stepwise formation constants: $$K_1 = 2.1$$ 	imes $$10^3$$ and $$K_2 = 8.2$$ 	imes $$10^3$$ for the formation of $$[Ag(NH_3$)_2]^+$$, what is the overall formation constant $$K_{12}$$?

Accepted Answer

$$1.7 	imes 10^7$

Question 5

A solution is prepared with $$[Ag^+] = 4.0 	imes 10$$^{-3}$$ \ M$$ and $$[NH_3$] = 0.500 \ M. $$Assuming the reaction goes nearly to completion, what is the approximate equilibrium concentration of $$[Ag(NH_3$)_2]^+$$?

Accepted Answer

$$4.0 	imes 10$$^{-3}$$ \ M$$

Question 6

In the context of complex ion equilibria, why is it often valid to assume that the reaction goes nearly to completion when $$K is $$very large?

Accepted Answer

Because the equilibrium lies far to the right, resulting in almost all reactants being converted to products.

Question 7

If the equilibrium constant for $$Ag^+ + 2NH_3 ightleftharpoons [Ag(NH_3$)_2]^+ is$$ $$K_{12} = 1.7 	imes 10^7$, and the equilibrium concentrations are $$[Ag($$NH_3)_2$$]^+ = 4.0 	imes $$10^{-3}$$ \ M$$ and $$[$$NH_3$$] = 0.492 \ M$$, what is the equilibrium concentration of $$[Ag^+]$$?

Accepted Answer

$$9.6 	imes 10$$^{-10}$$ \ M$$

Question 8

Which of the following best explains why $$[Ag^+] is $$extremely small at equilibrium in the presence of excess $$NH_3$$?

Accepted Answer

Because $$Ag^+ is $$almost completely converted to $$[Ag(NH_3$)_2]^+$$ due to the large formation constant.

Question 9

A chemist wants to selectively precipitate $$AgCl$$ from a solution containing $$Ag^+$$ and $$NH_3. $$Which of the following would decrease the $$[Ag^+]$$ available for precipitation the most?

Accepted Answer

Adding excess $$NH_3 to $$form $$[Ag(NH_3$)_2]^+.$$

Question 10

Which of the following is the correct expression for the overall formation constant $$K_{12}$$ for the reaction $$Ag^+ + 2NH_3 \rightleftharpoons [Ag(NH_3$)_2]^+$$?

Accepted Answer

$$K_{12} = \dfrac{[Ag(NH_3$)_2^+]}{[Ag^+][NH_3$]^2}$$

Question 11

If $$[Ag^+] at $$equilibrium is found to be $$9.6 	imes 10$$^{-10}$$ \ M in a $$solution with $$[NH_3$] = 0.492 \ M$$ and $$[Ag(NH_3$)_2]^+ = 4.0 	imes 10$$^{-3}$$ \ M$$, which calculation correctly verifies the value of $$K_{12}$$?

Accepted Answer

$$K_{12} = \dfrac{4.0 	imes 10$$^{-3}$$}{(9.6 	imes 10$$^{-10}$$)(0.492)^2$$}$

Question 12

Which of the following statements about coordination number is correct?

Accepted Answer

It is the number of ligands attached to the central metal ion in a complex ion.

Question 13

A solution contains $$[Ag^+] = 1.0 	imes 10$$^{-3}$$ \ M$$ and $$[NH_3$] = 0.100 \ M. If$$ $$K_{12} = 1.7 	imes 10^7$, what will be the approximate equilibrium concentration of $$[Ag($$NH_3)_2$$]^+$$, assuming $$[$$NH_3$$]$$ does not change significantly?

Accepted Answer

$$1.0 	imes 10$$^{-3}$$ \ M$$

Question 14

Which of the following best describes the effect of adding $$NH_3 to a $$solution containing $$Ag^+$$ ions?

Accepted Answer

It decreases $$[Ag^+] by $$forming the complex ion $$[Ag(NH_3$)_2]^+.$$

Question 15

Which of the following is a real-world application of complex ion equilibria?

Accepted Answer

Using $$NH_3 to $$dissolve silver halide films in photographic development.

Question 16

A student mixes $$AgNO_3$$ and $$NH_3 in $$water. Which of the following best explains why the solution remains clear instead of forming a precipitate?

Accepted Answer

The $$Ag^+$$ ions form a soluble complex with $$NH_3$$, preventing precipitation.

Question 17

Which of the following is NOT a plausible coordination number for a complex ion?

Accepted Answer

$$3$$

Question 18

If $$K_1$$ and $$K_2$$ are both very large for a two-step complex ion formation, which calculation shortcut can be used to determine the equilibrium concentration of the free metal ion?

Accepted Answer

Use the overall formation constant $$K_{12} = K_1$ 	imes K_2$ and solve in one step.

Complex Ion Equilibria: Formation and Calculation of Equilibrium Concentrations

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