Given the following information:


Ag^+(aq) + Cl^-(aq)<-->AgCl(s) Keq=1.8x10^-1

Ag^+(aq) + 2NH3(aq)<->Ag(NH3)2^+(aq) Keq=8.2x10^3

Explain why the AgCl(s) dissolved when NH3 was added to the test tube.

eqn 1. Ag^+(aq) + Cl^-(aq)<-->AgCl(s) Keq=1.8x10^-1

eqn 2. Ag^+(aq) + 2NH3(aq)<->Ag(NH3)2^+(aq) Keq=8.2x10^3

I think you made a typo in Keq (= Ksp) = 1.8 x 10^-10 and not -1.
Note the equation 2 has a large Keq which means the equilibrium is far to the right (more products and fewer reactants). Equation 1 is a small K so the reaction is far to the left (which is why AgCl is not very soluble and forms a ppt in water solvent. From Le Chatelier's Principle, equation 2 is far to the right which means (Ag^+) is decreased significantly. That makes Ag^+ small in equation 1 and the reaction shifts to the right (meaning the AgCl solid dissolves to increase the Ag^+ removed by equation 2. That continues until all of the AgCl solid is dissolved. Usually a relatively large excess of NH3 is used which shifts that equilibrium even farther to the right and that ends up dissolving all of the AgCl solid from equation 1.

To explain why AgCl(s) dissolved when NH3 was added to the test tube, we need to consider the equilibrium reactions involved and their equilibrium constants.

Based on the given equilibrium reactions and their equilibrium constants, we can compare the values to determine the relative extent of each reaction.

The equilibrium expression for the first reaction is:

Keq = [AgCl(s)] / [Ag^+(aq)][Cl^-(aq)]

The equilibrium expression for the second reaction is:

Keq = [Ag(NH3)2^+(aq)] / [Ag^+(aq)][(NH3)(aq)]^2

Now, let's analyze both reactions individually:

1. Ag^+(aq) + Cl^-(aq) <--> AgCl(s)
(Reaction 1)

The equilibrium constant Keq of Reaction 1 is 1.8x10^-1. A Keq value less than 1 indicates that the reaction favors the reactants. In this case, it suggests that the formation of AgCl(s) is not favored and only a small amount of AgCl(s) will dissolve in water.

2. Ag^+(aq) + 2NH3(aq) <-> Ag(NH3)2^+(aq)
(Reaction 2)

The equilibrium constant Keq of Reaction 2 is 8.2x10^3. A Keq value significantly greater than 1 indicates that the reaction favors the products. In this case, it suggests that the formation of Ag(NH3)2^+(aq) is highly favored, and a larger quantity of Ag(NH3)2^+(aq) can form in water.

Now, let's consider what happens when NH3 is added to the test tube:

When NH3 is added to water, it acts as a base and increases the concentration of NH3 in the solution. As a result, the increased concentration of NH3 leads to an increase in the concentration of Ag(NH3)2^+(aq) due to Reaction 2.

Increased concentration of Ag(NH3)2^+(aq) shifts the equilibrium of Reaction 1 to the right, favoring the dissolution of AgCl(s). This is because Ag(NH3)2^+(aq) can react with Cl^-(aq) to form AgCl(s) as shown in Reaction 1.

Therefore, when NH3 is added, the increased concentration of Ag(NH3)2^+(aq) drives the dissolution of AgCl(s) by shifting the equilibrium of Reaction 1 towards the right.