Kf and Kd Kaplan Question

[betterfuture]

Kf = 1.7 x 10^7

I have been literally sitting at my desk looking at how they solved this question for the past 1 hour. If anybody would be kind enough to explain how to solve this question. I don't understand Kd and Kf so much as I do other with the other equilibria constants. I would be very grateful for the help. I am honestly getting frustrated and demoralized because I do not understand this question. Thanks.

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[theonlytycrane]

I think you mean Kf = 1.7 * 10^-7

 

[betterfuture]

View attachment 202989

I think you mean Kf = 1.7 * 10^-7

Thank you for your generous help on working the problem out!!

Kaplan gave the Kf in the table in the passage. I believe Kf, the formation constant, is alway greater than 1 because complex ions are highly favorable so equilibrium favors products. So I don't think it would be 10^-7. But did you solve the problem using 10^-7 and got the right answer? Because if you did that is really odd.

 

[betterfuture]

Complex ion= [Ag(NH3)2]^+

 

[salemstein]

AgNO3 pretty much completely dissolves, leaving you with 0.01M Ag+ ions. Now, that Ag+ reacts with NH3 to form the complex Ag(NH3)2+. Ag+ + 2NH3- <=> Ag(NH3)2+. But you need 2 NH3 for every 1 Ag+. So your 0.01M Ag+ takes out 0.02M of NH3-, leaving you with 0.98M NH3- left. You also made 0.01M Ag(NH3)2+. Now set up the equation: Kf = [Ag(NH3)2+]/[Ag+][NH3-]^2. Plug in 0.98 for NH3, x for [Ag+], and 0.01 for Ag(NH3)2+.
1.7*10^7=(0.01)/(x)(0.98)^2
x = 0.01/(0.96)/(1.7x10^7)
Solve

 

[betterfuture]

AgNO3 pretty much completely dissolves, leaving you with 0.01M Ag+ ions. Now, that Ag+ reacts with NH3 to form the complex Ag(NH3)2+. Ag+ + 2NH3- <=> Ag(NH3)2+. But you need 2 NH3 for every 1 Ag+. So your 0.01M Ag+ takes out 0.02M of NH3-, leaving you with 0.98M NH3- left. You also made 0.01M Ag(NH3)2+. Now set up the equation: Kf = [Ag(NH3)2+]/[Ag+][NH3-]^2. Plug in 0.98 for NH3, x for [Ag+], and 0.01 for Ag(NH3)2+.
1.7*10^7=(0.01)/(x)(0.98)^2
x = 0.01/(0.96)/(1.7x10^7)
Solve

Thank you! So quick question. I always wondered when they mention 2 species being mixed together, how do you set up the reaction? They mention AgNO3 and NH3. So do I write

AgNO3 + NH3 --> [Ag(NH3)2]^+

OR

AgNO3-->Ag+ + NO3-
Ag+ + NH3 -->[Ag(NH3)2]^+

I always get confused

 

[salemstein]

Actually just Ag+ + 2NH3 -->[Ag(NH3)2]^+ is fine in this case. Always write the one that reacts last- one after which no new variables are introduced. I guess you can do AgNO3 + NH3 --> [Ag(NH3)2]^+ NO3 (if they give you the Kd for AgNO3), but why put extra work on yourself? These kinds of problems take the most time imo.

 

[betterfuture]

I think here we have to write out the net ionic equation to see what is left over. At least, that is what I have seen in some videos for complex ion equilibria questions. Any guess?

 

[theonlytycrane]

noob question: How do you know to form Ag(NH3)2 instead of just Ag(NH3)

 

[betterfuture]

@theonlytycrane

 

[theonlytycrane]

Shouldn't Ag(NH3)2 have a charge of +2?

 

[betterfuture]

I don't think so. The complex ion takes the charge of the Ag, which is +1. Since the ammonia is neutral, it contributes no charge to the ionic molecule.

 

[aldol16]

Shouldn't Ag(NH3)2 have a charge of +2?

Always remember charge conservation. Ag(I) has charge of +1 and ammonia is considered a dative neutral ligand that donates two electrons and therefore neither oxidizes the metal center nor adds charge.

 

[theonlytycrane]

I guess I was thinking that each N atom would have a charge of +1 in forming a coordinate covalent bond with the metal.

 

[aldol16]

Doesn't each NH3 form a coordinate covalent bond with the metal?

Yes. Each ammonia acts as an L-type ligand (you don't have to know the terminology here) and acts as Lewis base, donating two electrons to the metal center. It's important to note that for purposes of oxidation state and electron-counting, all electrons in M-L bonds "belong" to the ligand.