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

In summary, the conversation involves solving for the minimum quantity of ammonia needed to dissolve 0.1 mole of silver chloride in a 1L solution, given the values for Ksp and Kf. The student used an equation and made several assumptions to derive the solution, but the given answer was slightly different. They then discussed the maximum possible concentrations of [Cl-] and [Ag+] and calculated the required concentration of NH3 using the Kf value.
  • #1
zorro
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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?
 
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  • #2
Show your derivation.
 
  • #3
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.
 
  • #4
You want x to be around 0.1M. It is not small.
 
  • #5
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?
 
  • #6
What is [Cl-]?

What is maximum possible [Ag+]?

What is complex concentration?

Calculate ammonia concentration that fits.

--
 
  • #7
max [CL-] is 0.1
max [Ag+] is 10^-9

How to calculate ammonia concentratrion that fits?
 
  • #8
What is complex concentration?

Look at Kf.
 
  • #9
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.
 

What is the equation for calculating the solubility of AgCl using Ksp and Kf?

The equation is: [Ag+] = Ksp/[AgCl] - Kf[Ag(NH3)2+]

What is the value of Ksp for AgCl?

The value of Ksp for AgCl is 1.8 x 10^-10 at 25°C.

What is the value of Kf for Ag(NH3)2+?

The value of Kf for Ag(NH3)2+ is 1.7 x 10^7 at 25°C.

How do you calculate the minimum concentration of NH3 needed to fully dissolve 0.1 mol of AgCl in 1L of solution?

To calculate the minimum concentration of NH3, plug in the values for Ksp, Kf, and [AgCl] into the equation [Ag+] = Ksp/[AgCl] - Kf[Ag(NH3)2+]. Rearrange the equation to solve for [NH3] and then calculate the minimum concentration of NH3 required.

Why is it important to consider both Ksp and Kf when determining the solubility of AgCl?

Ksp represents the solubility product of AgCl, while Kf represents the formation constant for the complex ion Ag(NH3)2+. Both of these values affect the solubility of AgCl in a solution containing NH3. Ignoring one of these values would result in an inaccurate calculation of the solubility of AgCl.

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