Solve AgCl Solubility w/ Ksp & Kf: Find Min NH3 for 0.1 mol AgCl in 1L

Click For Summary

Discussion Overview

The discussion revolves around determining the minimum concentration of ammonia required to dissolve 0.1 moles of silver chloride (AgCl) in a 1L solution by forming the complex ion [Ag(NH3)2]+. Participants explore the solubility product constant (Ksp) and the formation constant (Kf) in their calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes using the equation s=c^2/(Ksp)(Kf) to derive the concentration of NH3 needed, suggesting that their calculations yield 1 mole of NH3.
  • Another participant requests the derivation of the initial equation used for the calculation.
  • A different participant suggests a more detailed equilibrium approach, defining variables for solubility and the amount of salt forming the complex, leading to a revised expression for solubility.
  • One participant challenges the assumption that the amount of salt forming the complex is negligible, indicating that it should be around 0.1M instead.
  • Another participant expresses concern that this assumption complicates the calculations and suggests adding an arbitrary amount of NH3 to simplify the process.
  • Participants discuss the maximum possible concentrations of chloride and silver ions, questioning how to calculate the ammonia concentration that would fit these values.
  • One participant calculates the ammonia concentration based on the complex concentration, arriving at a value of 1M, which differs from the previously mentioned 1.2M.

Areas of Agreement / Disagreement

There is no consensus on the correct method or final concentration of ammonia required, with multiple competing views and calculations presented throughout the discussion.

Contextual Notes

Participants express uncertainty regarding the assumptions made in their calculations, particularly about the concentrations of ions and the approximations used in deriving equations.

zorro
Messages
1,378
Reaction score
0

Homework Statement



What is the minimum quantity of ammonia which must be added to 1L of a solution in order to dissolve 0.1 mole silver chloride by forming [Ag(NH3)2]+.
Given Ksp- 10^-10 and Kf- 10^8


Homework Equations





The Attempt at a Solution



I used the equation (which I derived) s=c^2/(Ksp)(Kf) (assuming almost all amount of AgCl converts to complex and some other approximations)
where s is the solubility of AgCl and c is the concentration of NH3 (both in mol/litre)

I solved and got c as 1 mole.
But answer given is 1.2 mole.

Are my assumptions wrong, or there is some other thing?
 
Physics news on Phys.org
Show your derivation.
 
Let s be the solubility of AgCl in cM NH3. Let x mole/L be the amount of salt forming complex

At equilibrium.
Ag+ = s-x
ksp=(s-x)(s)
kf= x/(s-x)(c-2x)^2
Since kf is very high, x approaches s. Thus s-x would be very small. Let this value be y. Since x is small, 2x can be ignored w.r.t c.

i.e. c-2x = c
ksp=ys
kf=s^2/ksp(c)^2
i.e.
s=c x (ksp x kf)^1/2

Sorry, I wrote the earlier expression wrong.
 
You want x to be around 0.1M. It is not small.
 
Oops. Then that will make the calculations very lengthy.
Is there any method by which we solve this way and then add 0.2 mole by giving some reason?
 
What is [Cl-]?

What is maximum possible [Ag+]?

What is complex concentration?

Calculate ammonia concentration that fits.

--
 
max [CL-] is 0.1
max [Ag+] is 10^-9

How to calculate ammonia concentratrion that fits?
 
What is complex concentration?

Look at Kf.
 
Complex concentration will be practically 0.1.
From this
[NH3]^2 = 0.1/(10^-9)(10^8)
I got [NH3] as 1M
not 1.2.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
3K
Replies
7
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
2
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K