PH of saturated solution of CaCO3

[starlight5]

how do u calculate the pH of a solution of CaCO3(s) in 1.0 M NH4Cl?

 

[Borek]

NH₄Cl is in a large excess.

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[starlight5]

How is that related to finding the pH?

 

[Borek]

Concentration of NH₄⁺ can be assumed to be constant.

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[starlight5]

but wouldn't i need the concentration of Ca2+ or CO32- to find the [H3O+] to find pH? i don't understand how the solubility of CaCO3 is related to pH and how do we know NH4Cl is in excess?

 

[Borek]

pKso for calcium carbonate is around 8.4, that means saturated solution is about 10^-4M (a little bit more, as solution of NH₄⁺ will be slightly acidic and carbonates will be protonated). Still, even if solubility will go up tenfold, that still means concentration of carbonates (which work as a base and neutralize NH₄⁺) is about 1000 times bigger - so assumption that it has not changed is a safe one.

Yes, you need concentrations of Ca²⁺ and different forms of carbonates. Write equations of all equilirbia and mass balances, think what simplifying assumptions can be made.

In fact all equilibrium questions are to some extent identical - start with full set of equations, work your way down simplifying the set if some expressions can be neglected.

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[starlight5]

so to find the pH dependence of CaCO3 do we have to use the below equations

CaCO3 ---> Ca2+ + CO32-

H2CO3 + H2O ---> H3O+ + HCO3-

HCO3- + H2O ---> H3O+ + CO32-

H2O ---> H3O+ + OH-

and then do i have to manipulate the equilibrium constant expressions to obtain the solubility at a certain pH?

 

[Borek]

To be precise you should also use equilibrium of ammonia protonation.

But you are on the right track.

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[starlight5]

ammonia protonation? if i just wanted to find the solubility of CaCO3 at a given pH would i need to use those Ka1 and Ka2 and Ksp and the charge balance and mass balance equations ?

 

[Borek]

Yes, you need them all.

When calcium carbonate dissolves CO₃^2- (base) reacts with acids present (that means water and NH₄⁺) producing HCO₃^-. That means CO₃^2- is removed from the solution and according to the Le Chatelier's principle equilibrium of dissolution shifts to the right.

Most important reaction taking place will be

CO₃^2- + NH₄⁺ <-> HCO₃^- + NH₃

(strongest acid and strongest base present) but to calculate its equilibrium constant you need to combine several other reactions. then it may happen that some other reaction taking place in the solution has effects that can't be neglected, that'll become apparent once you start calculations.

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[Impossiblebt]

Sorry to bump such an old post but I'm having trouble with the same question...

The general K expression for the system would be: K = CaCO3(s) + NH4⁺ <-> NH3 + HCO3^- + Ca²⁺, right? After some manipulation I end up with K_rxn = Ksp CaCO3 * Ka NH4⁺ * (1/Ka HCO3^-).

For charge balance, [HO^-] + [HCO3^-] + [CO3^2-] = 1.0 = [H3O⁺] + [NH4⁺] + [Ca²⁺].

For material balance, carbonate-containing species: 1.0 = [CO3^2-] + [HCO3^-]. And for ammonium-containing species: 1.0 = [NH3] + [NH4⁺]

I have a feeling I have to use all of these things to come up with an answer because there are too many unknowns, but am unsure as to what my next step would be.

 

[Borek]

For material balance, carbonate-containing species: 1.0 = [CO3^2-] + [HCO3^-]

Why do you think it should equal 1?

Combining all reaction constants into one won't help much. Start writing all equations describing the system - once you have the same number of independent equations as number of independent variables, you can solve the system. However, this approach will yield (at best) high degree polynomial (probably something around 6^th degree), one that has to be solved numerically.

Best approach is to look for possible simplifications.

 

[Impossiblebt]

I suppose it shouldn't be equal to one... do we not know what it should be equal to?

I understand the kind of process I have to go through to get the answer by matching number of equations with unknowns but the only problem is I don't know my final destination. To solve for pH we have to get a handle on [H3O+], which, as far as I can tell is only accessible through the charge balance equation. The problem with that, however, is that it looks too easy. All that needs to be solved for then is [Ca2+] and [NH4+] which is only two unknowns but this appears to be much more of a monster of a problem than that.

As asked, the equations that describes the system are as follows:
CaCO3 ---> Ca2+ + CO32-

H2CO3 + H2O ---> H3O+ + HCO3-

HCO3- + H2O ---> H3O+ + CO32-

H2O ---> H3O+ + OH-

NH4+ + H2O ---> H3O+ + NH3

With the most significant, that is strongest base and strongest acid interacting, reaction being: CO32- + NH4+ <-> HCO3- + NH3 as you noted earlier.

Having all these reactions in front of me don't really help me, however, because I don't know what I'm looking for.

 

[Borek]

I suppose it shouldn't be equal to one... do we not know what it should be equal to?

Sure. Think where do the carbonates come from. What othe rions is produced in the same process?

As asked, the equations that describes the system are as follows:
CaCO3 ---> Ca2+ + CO32-

H2CO3 + H2O ---> H3O+ + HCO3-

HCO3- + H2O ---> H3O+ + CO32-

H2O ---> H3O+ + OH-

NH4+ + H2O ---> H3O+ + NH3

That's will give five equations (assuming we know all equilibrium constants). How many unknowns? What other equations do you have?

 

[Impossiblebt]

Sure. Think where do the carbonates come from. What othe rions is produced in the same process?

Would it be ok to state that [CO3^2-] + [HCO3^-] is equal to [H30⁺] - [NH3]? I derived that from looking at the reactions that occur in the system. I don't know if this conclusion helps me at all in finding the answer, but the statement does contain [H3O⁺ which is what I'm looking for.

That's will give five equations (assuming we know all equilibrium constants). How many unknowns? What other equations do you have?

Well we don't care about water, and the only quantity we know for sure is NH4⁺ being 1mol / 1M.
This may sound like a stupid question but with everything going on in the problem I'm losing track of the chemistry. Are any of the [H3O⁺] quantities in our reactions the same or are they all different? I don't know how many unknowns we have until I know the answer to that.

 

[Borek]

Would it be ok to state that [CO3^2-] + [HCO3^-] is equal to [H30⁺] - [NH3]?

Sum of their concentrations is equal to calcium concentration. That's just a mass balance.

Are any of the [H3O⁺] quantities in our reactions the same or are they all different? I don't know how many unknowns we have until I know the answer to that.

There is only one equilibrium concentration of H⁺, same about every other ion.

 

[Impossiblebt]

So then we have 7 unknowns and 5 equations. We can get the other two needed equations through material balance and charge balance.

[HO-] + [HCO3-] + [CO32-] = 1.0 = [H3O+] + [NH4+] + [Ca2+]

1.0 = [CO32-] + [HCO3-]

[Ca2+] = [CO3 2-] + [HCO3-]

Does all of that seem correct? My next step would then be to manipulate all the equations and then plug in unknowns to get all values in terms of one unknown.

Does it look like I'm on the right track?

 

[chemchem]

what do the H+ ions do to the CO3 in the CaCO3?
can someone please help!

 

[Borek]

what do the H+ ions do to the CO3 in the CaCO3?

Protonate them.

 

[chemchem]

could you please elaborate

 

[Borek]

https://www.physicsforums.com/showthread.php?t=634774

 

[chemchem]

thanks!