Solubility question involving Q and K

[Meredith92]

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This is from a passage in BR (chapter 3 passage 10)
It may be a little hard to explain since some of it was in the passage but it should make more sense once you read the answer

63. When .1 gram of ZnCO3 is added to 100 mL of water at 25 degrees Celsius which of the following statements is true?
A It dissolves completely
B it dissolves almost completely with only a small portion not dissolving
C It dissolves slightly with most of the ZnCO3 remaining not dissolving
D none of the sample dissolves

Choice C is correct
This question boils down to whether Qsp or Ksp is larger. When Q>K there are too many products in which case the salt cannot completely dissociate. When Q<K there is room for more products in which case the salt dissociates. When Q=K it is exactly saturated. In this question it is far easier to decide whether the molarity of ZnCO3 in the event it fully dissociates exceeds the molar solubility as conveniently listed in Table 1 (=.000014). The molarity if ZnCO3 fully dissociates is calculated as follows:
.1g/125.4g/mol =.0008mol / .1L= .008 M
.008M> .000014 by a large amount. this means that very little of the ZnCO3 dissociates. on this question you must go even further. it will barely dissociate according to the numbers which implies C

I have a few questions regarding this answer description.

If Q>K, wouldnt that imply that there are more dissociate ions than at equilibrium? Wouldnt that mean it is very dissociated? I always get confused about this concept.
Then I get confused why they are figuring out the concentration and comparing it to the molar solubility. I thought molar solubility is how much dissociates, not how much you start with. I also dont understand how they were able to distinguish between choice C and D

If anyone can help clarify this that would be great! I think Im having some difficulty conceptually understanding molar solubility. Thank you

 

[TieuBachHo]

This is from a passage in BR (chapter 3 passage 10)
It may be a little hard to explain since some of it was in the passage but it should make more sense once you read the answer

63. When .1 gram of ZnCO3 is added to 100 mL of water at 25 degrees Celsius which of the following statements is true?
A It dissolves completely
B it dissolves almost completely with only a small portion not dissolving
C It dissolves slightly with most of the ZnCO3 remaining not dissolving
D none of the sample dissolves

Choice C is correct
This question boils down to whether Qsp or Ksp is larger. When Q>K there are too many products in which case the salt cannot completely dissociate. When Q<K there is room for more products in which case the salt dissociates. When Q=K it is exactly saturated. In this question it is far easier to decide whether the molarity of ZnCO3 in the event it fully dissociates exceeds the molar solubility as conveniently listed in Table 1 (=.000014). The molarity if ZnCO3 fully dissociates is calculated as follows:
.1g/125.4g/mol =.0008mol / .1L= .008 M
.008M> .000014 by a large amount. this means that very little of the ZnCO3 dissociates. on this question you must go even further. it will barely dissociate according to the numbers which implies C

I have a few questions regarding this answer description.

If Q>K, wouldnt that imply that there are more dissociate ions than at equilibrium? Wouldnt that mean it is very dissociated? I always get confused about this concept.
Then I get confused why they are figuring out the concentration and comparing it to the molar solubility. I thought molar solubility is how much dissociates, not how much you start with. I also dont understand how they were able to distinguish between choice C and D

If anyone can help clarify this that would be great! I think Im having some difficulty conceptually understanding molar solubility. Thank you

Reread the bolded words carefully. If the [ ZnCO3] is high, then [Zn]2+ and [CO3]2- is low. This means that Q is low (Q<<K). So C is correct.

For answer B, it means that Q almost equals to K.

 

[Laureatebarrel]

Basically it makes the assumption that if all of ZnCO3 is completely dissolved, it would have the molarity of .008M which is much larger than its Ksp .000014. A & B then is out. And as for D, if it has a Ksp, then there will always be some dissolution. Remember that Q is the temporary equilibrium point and the reaction always goes toward Ksp. So if Q is less than Ksp, the reaction will go forward and if Q is larger than Ksp, the reaction will go in the reverse.

 

[Meredith92]

Basically it makes the assumption that if all of ZnCO3 is completely dissolved, it would have the molarity of .008M which is much larger than its Ksp .000014. A & B then is out. And as for D, if it has a Ksp, then there will always be some dissolution. Remember that Q is the temporary equilibrium point and the reaction always goes toward Ksp. So if Q is less than Ksp, the reaction will go forward and if Q is larger than Ksp, the reaction will go in the reverse.

For some reason I'm still having trouble understanding how the initial molarity of ZnCo3 equals the molarity of the dissolved state. Since it dissolves into two molecules wouldn't the final molarity be two times greater? Also, aren't we comparing the molarity to the molar solubility not the ksp?

Thanks again for your help

 

[Meredith92]

I'm not sure if this is correct? Can we assume that Zn2+ and co3 2- are low based off of the molarity?
It says it's fully dissociated?? If someone could help with this that would be great!

 

[Shjanzey]

I'm not sure if this is correct? Can we assume that Zn2+ and co3 2- are low based off of the molarity?
It says it's fully dissociated?? If someone could help with this that would be great!

You have to think of it like this. The calculation made in the passage for the molarity of ZnCO3 makes the assumption that it ONLY applies to a solution where it is able to fully dissociate.

So in that hypothetical solution the Molarity will be .008M

However, we are told in the table that the Ksp of ZnCO3 is 0.000014, so we can say this is the amount that will actually dissociate. Let us compare our hypothetical with the real value.

0.008 > 0.000014. We see our Hypothetical is way bigger, and we know this is not possible. Since we know (from our real value) that at least some of the ZnCO3 will dissociate into the solution we can discount D, because that would mean our real value is effectively zero. Since our hypothetical value is 2 orders of magnitude greater than the real value, we can safely say that most of it will not dissolve into solution, so Choice C really is the only one that fits.

 

[Meredith92]

Thanks for your help! That really clarified it for me 🙂

Just a slight correction though- Ksp is not the same as molar solubility. The value .000014 is for the molar solubility not Ksp.