Ksp question

[iceman132]

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A sparingl soluble metal hydroxide M(OH)2 has a molar solubility of S mol/L at 25 degrees C. It's Ksp value is...

4S^3

I know that Ksp = concentations of products raised by their coefficients divided by the concentrations of the reactions raised to their coefficients.

M(OH)2 --> M^2+ + 2 OH-

ksp= [M^2+] [OH]^2


ksp= (S)(2S)^2
ksp=4S^3

Question:
1. Why is it not ksp= [M^2+] [2OH]^2

I understand there are 2 OH ions..... But why does the ksp value change from the [OH]^2 to (2S)^2

2. Why are the reactants^coefficients not in the answer

 

[MShopes]

A sparingl soluble metal hydroxide M(OH)2 has a molar solubility of S mol/L at 25 degrees C. It's Ksp value is...

4S^3

I know that Ksp = concentations of products raised by their coefficients divided by the concentrations of the reactions raised to their coefficients.

M(OH)2 --> 2 M^3+ + 2 OH-

ksp= [M^2+] [OH]^2


ksp= (S)(2S)^2
ksp=4S^3

Question: Why is it not ksp= [M^2+] [2OH]^2

I understand there are 2 OH ions..... But why does the ksp value change from the [OH]^2 to (2S)^2

Simply because the 2 in M(OH)2 refers only to OH not to M...if they wanted the 2 to refer to both M and OH they would write 2 MOH....that's all

Since there is 2 OH, then the value would be (2X)^2 or [2 OH]^2...And since there is only one M, it would be just plain X...so X*(2X)^2=4X^3

I'm not sure if I understood your question correctly and not sure Why you said the KSP value change from OH^2 to 2S^2 because that's the same thing just OH is replaced with an S and number 2 is added since there are two OH.

In short, it can't be M^2 because there is only one M..and anything to the power of 2 must have a 2 in front of it as well just to keep in mind.

EDIT: I finally got what you wanted to ask for. There are two parts that are confusing to you I can tell. First you think the 2 is applied to both the M and OH. That's wrong; it only applies to OH since it is after the OH. M has a value of just one M. Second, When you have 2 OH, you must write 2 OH and then raise them to the power of 2 since they are 2 OH so it would be [2OH]^2. You can't just say [OH]^2. Now you shouldn't raise the M to any power since it is just M or for your convenience, you can put [1M]^1 just to apply the rule and it is apparently equal to just M. So now Ksp=[M]*[2OH]^2=S*(2S)^2=4S^3.

For your second question: Ksp is equalibrium constant and you should know that in equilibrium problems, we don't include solids and pure liquids...only gas and aqueous solutions are in included because solids and pure liquids have equilibrium constant of 1 and so they don't affect anything. M(OH)2 is solid and you should know that from the state next to the compound and because this is a solubility problem so that means the reactant must be solid because it is being dissolved in a liquid and we are trying to find it's solubility so it is always solid.

 

[iceman132]

Simply because the 2 in M(OH)2 refers only to OH not to M...if they wanted the 2 to refer to both M and OH they would write 2 MOH....that's all

Since there is 2 OH, then the value would be (2X)^2 or [2 OH]^2...And since there is only one M, it would be just plain X...so X*(2X)^2=4X^3

I'm not sure if I understood your question correctly and not sure Why you said the KSP value change from OH^2 to 2S^2 because that's the same thing just OH is replaced with an S and number 2 is added since there are two OH.

In short, it can't be M^2 because there is only one M..and anything to the power of 2 must have a 2 in front of it as well just to keep in mind.

EDIT: I finally got what you wanted to ask for. There are two parts that are confusing to you I can tell. First you think the 2 is applied to both the M and OH. That's wrong; it only applies to OH since it is after the OH. M has a value of just one M. Second, When you have 2 OH, you must write 2 OH and then raise them to the power of 2 since they are 2 OH so it would be [2OH]^2. You can't just say [OH]^2. Now you shouldn't raise the M to any power since it is just M or for your convenience, you can put [1M]^1 just to apply the rule and it is apparently equal to just M. So now Ksp=[M]*[2OH]^2=S*(2S)^2=4S^3.

For your second question: Ksp is equalibrium constant and you should know that in equilibrium problems, we don't include solids and pure liquids...only gas and aqueous solutions are in included because solids and pure liquids have equilibrium constant of 1 and so they don't affect anything. M(OH)2 is solid and you should know that from the state next to the compound and because this is a solubility problem so that means the reactant must be solid because it is being dissolved in a liquid and we are trying to find it's solubility so it is always solid.

Thank you, you definitely answered my second question.

Second, When you have 2 OH, you must write 2 OH and then raise them to the power of 2 since they are 2 OH so it would be [2OH]^2

This is the area I am having trouble with..... They say you CAN NOT have it be [2OH]^2.

Somehow when you do this problem it goes from

ksp= [M^2+] [OH]^2

to

ksp= (S)(2S)^2
ksp=4S^3

I don't understand why the ksp is not [2OH]^2

 

[MShopes]

Thank you, you definitely answered my second question.





This is the area I am having trouble with..... They say you CAN NOT have it be [2OH]^2.

Somehow when you do this problem it goes from

ksp= [M^2+] [OH]^2

to

ksp= (S)(2S)^2
ksp=4S^3

I don't understand why the ksp is not [2OH]^2

If they say it can't have it to be [2OH]^2 then how did you finally obtain 4S^3, it comes from [2OH]^2 which is [2S]^2 or 4S^2 and the M is equal to just one S and so S*4S^2=4S^3. I'm pretty sure that's the right away to write it up.

Plus who says it can't be this way? Tell me their full explanation because I'm pretty sure my answer is right.

P.S: ksp= [M^2+] [OH]^2 is that your solution or their solution..I just don't want to get confused..please separate your solution from their solution.

 

[iceman132]

If they say it can't have it to be [2OH]^2 then how did you finally obtain 4S^3, it comes from [2OH]^2 which is [2S]^2 or 4S^2 and the M is equal to just one S and so S*4S^2=4S^3. I'm pretty sure that's the right away to write it up.

Plus who says it can't be this way? Tell me their full explanation because I'm pretty sure my answer is right.

P.S: ksp= [M^2+] [OH]^2 is that your solution or their solution..I just don't want to get confused..please separate your solution from their solution.

(BTW it is problem 22 on AAMC 8 🙂. Thank you for your help again )

Their answer says the ksp for

M(OH)2 = [M2+][OH]^2.


With a solubility of S mol/L when S moles of M(OH)2 dissolve we get S mols of M2+ ions and 2S moles of OH- ions.
Why do we get 2S moles of OH- ions? Because every dissolved molecule of M(OH)2 has two OH ions.

Ksp= (S) (2S)^2
Ksp= 4S^3

-------------------------

I am just wondering why you can not have [2OH]^2 for the Ksp

 

[MShopes]

(BTW it is problem 22 on AAMC 8 🙂. Thank you for your help again )

Their answer says the ksp for

M(OH)2 = [M2+][OH]^2.


With a solubility of S mol/L when S moles of M(OH)2 dissolve we get S mols of M2+ ions and 2S moles of OH- ions.
Why do we get 2S moles of OH- ions? Because every dissolved molecule of M(OH)2 has two OH ions.

Ksp= (S) (2S)^2
Ksp= 4S^3

-------------------------

I am just wondering why you can not have [2OH]^2 for the Ksp

Isn't this part in bold similar to M*(2OH)^2...maybe they should write [2OH]^2 but they just assumed you knew there is 2. I know that our professor initially write it like 2OH only without the exponent and he expects us to continue and write the exponent. So I don't know.

But since it is 4S^3 AND especially since it is S*(2S)^2, then it has to be like what I said...just common sense it can't be any other way.

 

[geeyouknit]

(BTW it is problem 22 on AAMC 8 🙂. Thank you for your help again )

Their answer says the ksp for

M(OH)2 = [M2+][OH]^2.


With a solubility of S mol/L when S moles of M(OH)2 dissolve we get S mols of M2+ ions and 2S moles of OH- ions.
Why do we get 2S moles of OH- ions? Because every dissolved molecule of M(OH)2 has two OH ions.

Ksp= (S) (2S)^2
Ksp= 4S^3

-------------------------

I am just wondering why you can not have [2OH]^2 for the Ksp

I think the < M(OH)2 = [M2+][OH]^2 > (Eqn A) and the < Ksp= (S) (2S)^2 > (Eqn B) are two slightly different things here.

Eqn A is for the general Solubility product. It's just the numerical concentrations. Meaning at equilibrium, if you had 2 M of the metal, and 4 M of OH, the Ksp would be 2*16=32.

But Eqn B is for the quantitative analysis. If you had no idea of specific numbers, you would say, that you had S mol/L of M, so you had to have 2S mol/L of OH. If you had 4 mol/L of OH-, you wouldn't write, Ksp = [2]*[2*4]^2, because the 4 is already assumed to be 2* whatever the metal is.

Hope that's right and makes sense. Feel free to call me out. Disclaimer: numbers are bsed.

Edit: Just want to point out, for explanation of Eqn A, that's not how you go about those kinds of problems generally. You usually start with a known Ksp and then say that Some ksp = [M]*[OH]^2. So then you say, that for every S mol of M that dissolves, you have 2 S mol of OH, so then it becomes
Some ksp = *[2S]^2.

 

[Majik]

For every 1M M(OH)2 that dissociates, it produces: 1M M2+ and 2M OH-.

For this particular reason, the Ksp reaction is this:
Ksp = [M2+][OH-]^2

The reason you put [OH-] instead of [2OH-] is because the [brackets] represents the total concentration of the product you're considering (in this case, the [OH-] represents amount of hydroxide Ions upon dissociating). In fact, it would be wrong to put [2OH-] in the Ksp expression.

Now, to find the Molar Solubility, this is where we use symbolism: Again, looking at the dissociation expression - For every 1M M(OH)2 that dissociates, we get 1M M2+ and 2M OH-. Regardless of the amount M(OH)2 dissociates, this relationship will always be true. So instead: We can simply say that for every "X" amount of salt that dissociates, we get "X" amount of M2+ and "2X" amount of OH-. The reason we use this symbolism is to solve for the unknown (x; "molar solubility), using the Ksp expression.

Therefore, using the Ksp expression, we can substitute the concentrations with these variables:

Ksp = [M2+][OH-]^2
Ksp = (X)(2X)^2

Now simplify:

Ksp=4X^3

Then you could solve for "X" (molar solubility) using the provided Ksp value. Molar solubility is the max amount of salt that can dissociate. Once fully dissociated, the salt is said to be saturated. After we find molar solubility, we can find the actual concentration of both M2+ and OH- for the saturated solution.

Let's say we find "X" to be 5M (a little unreasonable, but let's use it). This would mean the concentration of M2+ is: 5M and the concentratoin of OH- is 10M, since 5M of the salt (the molar solubility) dissolves in the solution. At this point, the salt is considered to be saturated.

Hope this helps.

 

[MShopes]

For every 1M M(OH)2 that dissociates, it produces: 1M M2+ and 2M OH-.

For this particular reason, the Ksp reaction is this:
Ksp = [M2+][OH-]^2

The reason you put [OH-] instead of [2OH-] is because the [brackets] represents the total concentration of the product you're considering (in this case, the [OH-] represents amount of hydroxide Ions upon dissociating). In fact, it would be wrong to put [2OH-] in the Ksp expression.

Now, to find the Molar Solubility, this is where we use symbolism: Again, looking at the dissociation expression - For every 1M M(OH)2 that dissociates, we get 1M M2+ and 2M OH-. Regardless of the amount M(OH)2 dissociates, this relationship will always be true. So instead: We can simply say that for every "X" amount of salt that dissociates, we get "X" amount of M2+ and "2X" amount of OH-. The reason we use this symbolism is to solve for the unknown (x; "molar solubility), using the Ksp expression.

Therefore, using the Ksp expression, we can substitute the concentrations with these variables:

Ksp = [M2+][OH-]^2
Ksp = (X)(2X)^2

Now simplify:

Ksp=4X^3

Then you could solve for "X" (molar solubility) using the provided Ksp value. Molar solubility is the max amount of salt that can dissociate. Once fully dissociated, the salt is said to be saturated. After we find molar solubility, we can find the actual concentration of both M2+ and OH- for the saturated solution.

Let's say we find "X" to be 5M (a little unreasonable, but let's use it). This would mean the concentration of M2+ is: 5M and the concentratoin of OH- is 10M, since 5M of the salt (the molar solubility) dissolves in the solution. At this point, the salt is considered to be saturated.

Hope this helps.

You are right about the bracket part which is what I forgot about. But at the end, it's still 4x^3 which is what matters. I wouldn't care about brackets or anything as long as I understand the concept and can get the final answer.