EK solubility question

[kwokkit]

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If Ag2SO4 and BaSO4 had the same Ksp value, I would think that Ag2SO4 would be LESS soluble than BaSO4, but EK says the opposite.
Ksp = 4x^3 (for Ag2SO4)
vs
Ksp = x^2
Yes?

 

[dundunham]

hm.... I was reading in my kaplan book about rules of solubility and there's one particular rule that says "All salts of the sulfate ion (SO4 2-) are water soluble, with the exceptions of Ca2+, Sr2+, Ba2+, and Pb2+.

So i'm assuming that BaSO4 is insoluble.

what ya think?

 

[Bernoull]

If Ag2SO4 and BaSO4 had the same Ksp value, I would think that Ag2SO4 would be LESS soluble than BaSO4, but EK says the opposite.
Ksp = 4x^3 (for Ag2SO4)
vs
Ksp = x^2
Yes?

Here intuition FAILS unfortunately. When you have compounds with different van hoff factors, it can be difficult to judge solubilities qualitatively. So let's play wit some numbers.

Say Ksp = 10^-12
Ag2SO4 = x(2x)^2 = 4x^3
BaSO4 = x^2


4x^3 = 10E-12, x^3= 2.5E-12, x = 2.5E-4 = 250E-6
x^2 = 10E-12, x =10E-6

Ag2SO4 is X25 more SOLUBLE!!!

 

[Beta Cell]

Here intuition FAILS unfortunately. When you have compounds with different van hoff factors, it can be difficult to judge solubilities qualitatively. So let's play wit some numbers.

Say Ksp = 10^-12
Ag2SO4 = x(2x)^2 = 4x^3
BaSO4 = x^2


4x^3 = 10E-12, x^3= 2.5E-12, x = 2.5E-4 = 250E-6
x^2 = 10E-12, x =10E-6

Ag2SO4 is X25 more SOLUBLE!!!

Intuition shouldn't fail, you just have to intuitively know how decimals work 😛 You beat me to it :\

 

[sv3]

Here intuition FAILS unfortunately. When you have compounds with different van hoff factors, it can be difficult to judge solubilities qualitatively. So let's play wit some numbers.

Say Ksp = 10^-12
Ag2SO4 = x(2x)^2 = 4x^3
BaSO4 = x^2


4x^3 = 10E-12, x^3= 2.5E-12, x = 2.5E-4 = 250E-6
x^2 = 10E-12, x =10E-6

Ag2SO4 is X25 more SOLUBLE!!!

that is the key line (the bolded part). However, the second poster was also correct with their qualitative assessment. If you can memorize everthing you're set but I like seeing it this way so you don't have to and quickly work things out

 

[Dr Gerrard]

Note that this only works when the Ksp is small enough.

For example, say Ksp = .1

.1 = 4x^3
.1 = x^2

In this case, BaSO4 would be more soluble than Ag2SO4.

How can you tell when the trend reverses?

 

[Bernoull]

Note that this only works when the Ksp is small enough.

For example, say Ksp = .1

.1 = 4x^3
.1 = x^2

In this case, BaSO4 would be more soluble than Ag2SO4.

How can you tell when the trend reverses?

I thought about da same, i guess it safest to do da math, it's quick anyway.. So intuition is not always intuitive...

 

[kwokkit]

Note that this only works when the Ksp is small enough.

For example, say Ksp = .1

.1 = 4x^3
.1 = x^2

In this case, BaSO4 would be more soluble than Ag2SO4.

How can you tell when the trend reverses?

Wow, that's really tricky!
Thanks for all this, looks like the only way is to do math. - but how do you guys easily approximate cube roots?

 

[loveoforganic]

I think the thing is, if you have a compound that has a ksp of 0.1, you're not going to be given a ksp. ksp is only used for compounds with markedly low solubility. For cases of increased solubility, units are typically grams/ml.

 

[sleepy425]

Note that this only works when the Ksp is small enough.

For example, say Ksp = .1

.1 = 4x^3
.1 = x^2

In this case, BaSO4 would be more soluble than Ag2SO4.

How can you tell when the trend reverses?

For this example, the trend reverses at Ksp=.0625 but obviously, if it were x^2 and 8x^4, it would be different. It's pretty easy to find out. You set 4x^3=x^2 and find the one value of x that will give you the same Ksp with both equations. So that's 4x=1 so x=.25. So now .25^2 equals 0.0625 (if you plug it into 4x^3 instead, you get .0625 as well). Now above Ksp of 0.0625, x^2 dominates. Below 0.0625, 4x^3 dominates. You could do this for any combination you want.