[MrTeo]

Another answer to check  
Here's the exercise:

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Of a diprotic acid H₂A both K₁ and K₂ are known (the equilibrium constants for the first and the second dissociation). A salt soluble in water, MHA, of a monovalent metal M dissociates completely according to the following equation:

MHA→M⁺+HA^-

Take a diluted solution of this salt:
a) Demonstrate that K₁K₂>K_w it's necessary (pay attention to these words) for pH<7 (the solution is acidic).
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b)Is this condition sufficient too?
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- • -

These equations describe the hydrolysis and the dissociation of HA^-:



a)







I suppose it's ok, but obviously if you find any mistake tell me ^^

b)

Here's the main problem: I'd say that yes, this condition is sufficient too... but my question is: to demonstrate this fact should I rewrite the whole thing starting from K₁K₂>K_w? Or do I have to find another way to reach the acidity condition? (but in fact up to now I haven't been able to find one)

[Borek]

Compare equation 12.9 here:

http://www.chembuddy.com/?left=pH-calculation&right=pH-amphiprotic-salt

[MrTeo]

Right... so starting from my expression and using equation 12.8 I get:



And this is what I've looked for a long time, a different way to get to the original statement, thus demonstrating that this condition is sufficient too 

Now, just a few more things to ask:

Is my work right (I mean the original demonstration) and the approximations justifiable?
Would be right to consider the "reverse" demonstration a justification for the second question (starting from K₁K₂>K_w and getting to the acidity condition using the same steps)?

[MrTeo]

Any ideas about this problem? Just need to check if my assumptions are correct...

[AWK]

Considering the acid-base equilibria we are interested in a concentration of oxonium ions (H₃O⁺) or pH of solution, and we prefer using equations, not inequalities.

[Borek]

List your assumptions, it will be easier.

AWK: as I understand the situation, inequality is a part of original formulation of the problem.

[MrTeo]

AWK: as I understand the situation, inequality is a part of original formulation of the problem.

Yes, the text asks for the condition necessary to obtain an acidic solution so we need pH<7 or [H₃O⁺]>1e-7

List your assumptions, it will be easier.

a)

Is my demonstration right and the approximations justifiable? (I think so, as they're the same used when we analyze hydrolysis or weak acid dissociation phenomena)

b)Is this condition sufficient too?
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Would be right to consider the "reverse" demonstration a justification for the second question (starting from K₁K₂>Kw and getting to the acidity condition using the same steps)? (Here I'm a bit more uncertain... I found another way to get back to the original condition using Borek's equation so I know that the condition is sufficient too, but I don't know if this fact could be demonstrated simply considering in a reverse order the whole first part of the problem)

I listed the questions that need to be checked with the original part of the problem (or of my solution) they're linked with... Hope it's all clear now 

[MrTeo]

Any answers? Sorry to be so boring but I'd like to hear your opinions about this problem... no hurry obviously, but I just don't want it to be forgotten