[Big-Daddy]

How is concentration of KCl defined in a solution which originally contained KCl, to which some moles of AgCl were added? Is it just defined as concentration of K⁺, or alternatively as concentration of all forms of Cl^- (i.e. [KCl]_total=[Cl^-]+Σ(v_i*c_i) where c_i is the concentration of every species containing Cl or which the Cl contributed to the formation of, and v_i is the coefficient of Cl in the molecular formula for that species). Or do you have to take into account the fact that some of this Cl^- comes from AgCl rather than KCl?

Or let's say I add NaCl to KCl solution. How is the concentration of KCl defined then?

I ask because I've got some weird problems focusing on this, e.g. "Calculate the concentration of a KCl solution at 298.15 K in which the solubility of AgCl is equal to its solubility in pure water at 50°C" (2 solubility products and the respective temperatures, 282.85 K and 298.15 K, were previously provided). Surely it will become simple when I understand what exactly is meant by "concentration of a KCl solution" now that AgCl has been added to the point of saturation of AgCl.

[magician4]

IMHO , the only "clean" definition of the concentration of a salt would be the one related to the (theoretical) c₀(salt) , i.e. what you would gain if the salt was in the solution stand - alone, and none of the ions would react any further.

... as with everything else you'd run into problems like the ones you're facing.

Now, for practical purposes, for example when you're dealing with mixed solutions, you'd have to come up with problem related "definitions" of your own.
example:
when dealing with the problem you posed, I would indicate even equal ions by the source they came from, like " Cl^-_(AgCl)" and "Cl^-_(KCl)" (as I would need those sources anyway).

For your problem, my solution then would look something like this:

general solubility product for AgCl : K_sp = [Ag⁺] * [Cl^-]

after that:
calculation of the solubility product at 50°C from "ΔG (T) = -RT lnK_sp(T) " and "ΔG(T) = ΔH - TΔS"

with this:
K_sp(50°C) = [Ag⁺]₅₀ * [Cl^-]₅₀ = [Ag⁺]²₅₀  [Ag⁺]₅₀ = [itex]\sqrt {K_{sp}(50°C)}[/itex]

moving on:
K_sp(25°C) = [Ag⁺]₅₀ * ( [Cl^-]₅₀ + [Cl^-]_(KCl) ) = [Ag⁺]₅₀ * ([Ag⁺]₅₀ + [Cl^-]_(KCl)) =  [itex]\sqrt {K_{sp}(50°C)}[/itex] * ([itex]\sqrt {K_{sp}(50°C)}[/itex] + [Cl^-]_(KCl))

hence:

[tex] [Cl^-]_{(KCl)} = \frac {K_{sp}(25 °C ) }{\sqrt {K_{sp}(50°C)}} \ - \ \sqrt {K_{sp}(50°C)} [/tex]

... and this chloride concentration would be directly related to the c₀ of the original KCl solution you were asked about

regards

Ingo

[Big-Daddy]

Thanks, but the marking scheme has a different idea. It says that Concentration of KCl = [Cl^-] + 2[AgCl₂]^-]. And by Solubility of AgCl, what is meant is [Ag⁺] + [AgCl₂]^-] (this one makes sense).

I don't understand how Concentration of KCl = [Cl^-] + 2[AgCl₂]^-], because Concentration of KCl = [K⁺], which must be the same as [Cl^-]_KCl. But if we can say [Cl^-]_KCl=[Cl^-] + 2[AgCl₂]^-] that suggests there are no other sources of Cl^- in the solution except KCl, which there are ... that's why the definition of "concentration of KCl" is so important to me.

[magician4]

Thanks, but the marking scheme has a different idea. It says that Concentration of KCl = [Cl^-] + 2[AgCl₂]^-]. And by Solubility of AgCl, what is meant is [Ag⁺] + [AgCl₂]^-] (this one makes sense).

I find this marking scheme a bit irritating, and for several reasons.

first, this looks more like a charge balance to me than the usual equations you would use for solubility

second, dealing with "[Ag⁺] + [AgCl₂]^-]" clearly indicates, that besides solubility product constants you'd have to consider complex formation constants, also  (i.e. the one related to [AgCl₂]^-] )
I didn't see any hint for that in your original question, nor do I see the respective constant anywhere. Besides, with solubility of AgCl being the limiting factor, the concentration of KCl can't be too high, and usually, in those situations this species "[AgCl₂]^-]" is being neglected

last not least - and here I agree with you - above formalism forces that the silver ions came from a different source than from silver chloride (i.e like you'd add silver nitrate, but after that consider the solubility of silverchloride anyway)

Maybe you could post the original problem description in original text? Might be that somebody finds a hint how to understand this...


regards

Ingo

[Big-Daddy]

I find this marking scheme a bit irritating, and for several reasons.

first, this looks more like a charge balance to me than the usual equations you would use for solubility

I think it's ok? Solubility of AgCl = [Ag⁺] + [[AgCl₂]^-] just says that the sum of Ag concentrations in the solution, which all came from AgCl, is the sum of the silver ion concentration plus its concentration in the complexed form. Concentration of KCl has got to equal to [K⁺] - even if there is more chloride than potassium ions, the limit on concentration of KCl is that of the potassium. but anyway clearly [K⁺] = [Cl^-] + 2[[AgCl₂]^-] - which seems unjustified to me, though it does give a nice answer after simplifying.

second, dealing with "[Ag⁺] + [AgCl₂]^-]" clearly indicates, that besides solubility product constants you'd have to consider complex formation constants, also  (i.e. the one related to [AgCl₂]^-] )
I didn't see any hint for that in your original question, nor do I see the respective constant anywhere. Besides, with solubility of AgCl being the limiting factor, the concentration of KCl can't be too high, and usually, in those situations this species "[AgCl₂]^-]" is being neglected

last not least - and here I agree with you - above formalism forces that the silver ions came from a different source than from silver chloride (i.e like you'd add silver nitrate, but after that consider the solubility of silverchloride anyway)

Maybe you could post the original problem description in original text? Might be that somebody finds a hint how to understand this...


regards

Ingo

My apologies, I forgot to note that we were given that complexation constant, as I didn't intend the discussion to end up focusing on this particular problem (I assumed concentration had a set and obvious way of being defined in the solution I mentioned in the OP - clearly this isn't true!).

Anyway the problem's full text is quite long, I will direct you to where you can find it instead of reproducing it: http://www.icho.hu/files/prep_problems_icho40.pdf Problem 13 part b) is the one.

[magician4]

first of all I have to apologize: I erroneously thought that silverchloride belonged to those salts with a positive enthalpy of hydratation, and hence would show decreased solubility with increases temperature (as as, for example , NaSO₄ above 30°C or NaCl or NaNO₃ do)
...and hence went into a completely pointless direction with my original proposal: the K_sp submitted by now clearly show that this isn't so

second: this isn't a simple solubility problem, to be approached by the usual equations, but something more complicated instead.
here, working with charge balance equations seems a good idea to me

[tex] [K^+] \ + \ [Ag^+] \ = \ [Cl^-] \ + \ [ [AgCl_2]^- ] [/tex]

(if you leave the consideration of water away, i.e. say that [H⁺] [itex]\approx [/itex] [OH^-] )

anyway, I didn't find any of your problematic expressions like  "KCl = [Cl^-] + 2[AgCl₂]^-]" in that text - where does that come from? (as I said, I think this is wrong, if the source of silver ions would be silverchloride. If it was, however, another soluble silver salt like silver nitrate, this would make sense...
... but then again, there is  not even the slightest hint / indication that we should think that way in the problem text)

[Big-Daddy]

The solutions include that line of text: http://www.icho.hu/Files/prep_problems_icho40_0521.pdf (solutions are after all the problems)

It comes from the idea that Cl- appears to be contributed to only by KCl and not by AgCl? That might be justifiable when working backwards but how is it obvious to someone reading that c0[KCl] >> c0[AgCl]?

[magician4]

1. to me, the "2" in question seems to be a typo (to avoid calling this an "error", as one of the Cl^- in [AgCl₂]^- has to be contributed by AgCl and hence doesn't count for KCl - as the author seems to have done anyway)
2. nevertheless, this typo/error seems to be irrelevant, because: if [KCl] [itex]\approx[/itex] [Cl^-] [itex]\approx[/itex] Cl^- + [[AgCl₂]^-] , then also [KCl] [itex]\approx[/itex] [Cl^-] [itex]\approx[/itex] Cl^- + [[AgCl₂]^-] [itex]\approx[/itex] Cl^- + 2 [[AgCl₂]^-] would be true.

even so: it is pointless here, and I can't see how this should be needed to solve this problem

2. I agree: that [[AgCl₂]^-]  should be low just because [Ag+] in equilibrium is low (due to the K_sp of AgCl) is not obvious (as we can learn from [Ag(NH₃)₂]⁺ in the presence of chloride, excess NH₃ ): you can't judge / guess the complex formation constant from the K_sp of AgCl


regards

Ingo

[Big-Daddy]

I see, so my general impression is that concentration is fuzzily defined in this case.

Could you help with my other question?

My book says:

"The cell arrangement Pt | H2 (g) | HCl (aq) | AgCl | Ag is a little special in the sense that both electrodes dip into the same electrolyte solution. The latter contains H⁺ ions which participate with the hydrogen gas, in establishing the potential at the platinum electrode, and also Cl^- ions which help produce the potential on the silver/silver chloride electrode. In other cases it is simply not possible to use a single solution.

"Suppose we wished to measure the standard electrode potential of the Fe²⁺/Fe³⁺ couple. A single solution cell, Pt | H2 (g) | H+ (aq), Fe2+ (aq), Fe3+ (aq) | Pt, is inappropriate since both platinum electrodes are exposed to the pair of iron ions. Thus at one electrode the appropriate equilibrium is set up (for the Fe²⁺/Fe³⁺ couple), but at the other both the Fe²⁺/Fe³⁺ couple and the H+/H2 couples will try and establish their potentials. It follows that if sensible measurements are to be made to find the standard electrode potential of the Fe²⁺/Fe³⁺ couple, the two 'half cells' must be separated using a salt bridge or diffusion barrier."

Can you explain more clearly what the problem is with having both electrodes exposed to the Fe²⁺ and Fe³⁺, and how this is different from the scenario described above that? Thanks for any help

[magician4]

Could you help with my other question?

sorry pal, for the moment I don't have a clear picture of what's up here (beginning with the question what setup is to be considered)

my proposal: put your question in a fresh thread  (so that everybody knows that there's a new question coming up, and hence can participate), maybe someone else immediately will know what setup is meant (and where the problem might be)


regards

Ingo