# Solubility Product

## 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

## 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?

Borek
Mentor

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.

Borek
Mentor
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?

Borek
Mentor
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?

Borek
Mentor
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.