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### Course: MCAT > Unit 10

Lesson 3: Solubility equilibria# The common-ion effect

The solubility of an ionic compound is decreased by the presence of a common ion (an ion that is also present in the compound); this is known as the common-ion effect. Created by Jay.

## Want to join the conversation?

- how do you know if it is exceptable to treat x as zero?(15 votes)
- in this example, .1 is so big compared to the ksp that x will not make a big difference to .1 and .1-2x will pretty much just be .1 so now you dont have to solve with weird quadratic stuff and it's just way simpler and you have less of a chance of making a mistake this way(20 votes)

- What will change the Ksp value, if common ions do not?(5 votes)
- The Ksp is temperature dependent, so heating or cooling the solution can affect the Ksp. For some substances, Ksp is higher at higher temperatures, for other substances Ksp is higher at lower temperatures, for some substances there isn't a great deal of temperature dependence for the Ksp, for some substances there is a very complicated relationship between temperature and Ksp.(26 votes)

- Oh! So is this how those Grow A Crystal kits work? They put a powdered form of the ionic compound of the crystal into water, and then add a much more soluble salt with a common ion, which will force the crystal to grow. Is that correct? It's really cool!

Can you grow any ionic network crystal this way? It would be really great to grow a ruby or an emerald by mixing my own solutions.(6 votes)- It's possible to create gemstones using the common-ion effect I would think. My biggest concern with this method is that, would it create large enough crystals and how many defects would it have? Because with gemstone creation it's not enough just to know their chemical composition, a lot of work goes into how they are made since that effects the quality of the crystals produced.

Hope that helps.(6 votes)

- He says that due to common ion effect the reaction shifts in the backward direction to form more PbCl2.But why cant it form more KCl?(6 votes)
- This is an example of Le Châtelier's Principle.

If you add more Cl⁻, the position of equilibrium shifts in a direction that gets rid of the excess Cl⁻.

That is, it forms more PbCl₂.(3 votes)

- How does Qsp relate to Kip?(4 votes)
- By analogy to Qeq, Qsp will tell you how 'close' you are to saturating a solution.

see this section: https://www.khanacademy.org/science/chemistry/chemical-equilibrium/factors-that-affect-chemical-equilibrium/(2 votes)

- I'm confused about how 0.016 M was found at9:45. Please correct me if I am wrong but, if there were no common ions in the solution, then the Ksp would equal 1.7*10^-5= [x]*[2x]^2=x*4x^2=4x^3. I ended up with x=1.41666*10^-6, which should be equal to the molar solubility of the salt.(3 votes)
- So you're correct that if there were no chloride common ions in solution and we were solving for the molar solubility the equlibium equation would be:

1.7x10^(-5) = 4x^(3). Solving for x, we'd need to divide both sides by 4 first.

4.25x10^(-6) = x^(3) Then we'd need to take a cube root of both sides.

1.6198x10^(-2) = x, which agrees with Jay's answer when rounded for sig figs. So if I had to guess, I'd say you didn't do the cube root correctly.

Hope that helps.(3 votes)

- Wouldn't the existing concentration of Cl- be 0.200M in the ICE table? I have a very similar example in my equilibrium package in which the solvent, CaCl2, is 0.150M. in the ICE table when PbCl2 is dissociated into its ions (PbCl2 (s) <---------> Pb (aq) + 2Cl (aq)), the 2Cl initial concentration is 0.300M. It was doubled from the common ion's 0.150M to 0.300M due to the coefficient of 2. In this example that is not so. I'm confused.(0 votes)
- In the example in this video, the initial Cl- concentration is only 0.100 M, which comes entirely from the KCl. Initially, you assume no dissociation of the PbCl2 has occurred.

If you were using CaCl2, rather than KCl, then you have double the number of chlorines so then the initial molarity of Cl- would be doubled.(8 votes)

- How is the common ion effect different from simply increasing the concentration of a reactant by manually adding it?(2 votes)
- I mean, that’s still the common ion effect. The common ion effect says the solubility of a salt is decreased by the presence of constituent ions in the solution.

If the constituent ions are already present in the solution, then the salt will dissolve less so than if it were in pure water. If the salt has already dissolved as much as its equilibrium will allow, and then we add some additional constituent ions, this is essentially a stress on equilibrium and it will shift the reaction to the left thereby decreasing the solubility of the salt. What would happen in that case is that a precipitate would begin to form (or increase the size of an already existing solid).

In both cases we reduce the solubility of the salt with the presence of constituent ions. The only difference is what order we add them to the solution.

Hope that helps.(1 vote)

- Could you just find the solubility for PbCl2 as if there is no KCl in the solution and then multiply by the molarity of the common ion (in this case Cl-) to get the new solubility?(1 vote)
- No, because
**all**the concentrations change when you add a common ion.(3 votes)

- Was it just a coincidence that the molarity of the new solvent was also .1, the same factor that the molar solubility differed from the solubility in water? Or is there some sort of connection to the solubility in water and the molarity in another solution like that?(2 votes)

## Video transcript

- [Instructor] The
presence of a common ion can affect a solubility equilibrium. For example, let's say we have a saturated
solution of lead II chloride. Lead II chloride is a white solid, so here's the white solid
on the bottom of the beaker. And the solid's at equilibrium
with the ions in solution. So that would be Pb2+ and Cl-. Notice how the mole ratio is
one-to-two of Pb2+ to 2Cl-. So if we have two Pb2+
ions in our diagram, there should be twice
as many chloride anions. At equilibrium, the rate
of dissolution is equal to the rate of precipitation. Therefore, the concentration
of ions in solution remains constant. So our system is at equilibrium. And let's add some solid
potassium chloride. Potassium chloride is a soluble salt. So it will dissociate and turn
into K+ and Cl- in solution. Adding a source of chloride anion means the system is no longer at equilibrium. So let me write in here, not at equilibrium at that moment in time. So the system was at equilibrium and a stress was added to the system. In this case, the stress was
increased chloride anion. So there's an increase in
the concentration of Cl-. According to Le Chatelier's principle, the system will move in the direction that decreases the stress. So if the stress is increased concentration of chloride anion, the system will move to the left to get rid of some of
that extra chloride anion. When the system moves to the left, Pb2+ ions will combine with
chloride anions to form PbCl2. And we can see that down
here in the diagram. So imagine, say this Pb2+ ion combined
with these two chloride anions to form some more of the white solid. Looking at the third diagram, the amount of white solid has increased from the second diagram, and we've lost this Pb2+ ion
and these two chloride anions. And the amount of our precipitate PbCl2 will keep forming until
equilibrium is reached. Let's just say this third diagram, it does represent the
system at equilibrium. So I'll write on here, at equilibrium. This is an example of
the common ion effect. For this problem, the common
ion is the chloride anion, because there were two sources of it. One was from the disillusion of PbCl2. If we had dissolved some solid
to make a saturated solution, the source of these chloride
anions would be from PbCl2. And the second source
is from the added KCl, which of course dissolved
to form chloride anion. So the chloride anion is the common ion. And we use Le Chatelier's principle to predict the system
will move to the left to get rid of the extra chloride anion. When the system moved to the left, we formed more of the solid PbCl2. And that's why this amount
got bigger over here. So if we compare the first
diagram with the third diagram, the first diagram has more of the lead II chloride in solution. And the third diagram has less of it. Therefore, the addition of the
common ion of chloride anion, that decreased the solubility
of lead II chloride. So the common ion effect says that the solubility of a slightly soluble salt, like lead II chloride, is decreased by the
presence of a common ion. Another way to think about this is using the reaction quotient, Q. For the diagram on the
left, we're at equilibrium. Therefore the reaction
quotient Qsp is equal to the Ksp value for lead II chloride, which means the system is at equilibrium. Adding chloride anion
increases the value for Qsp. So now Qsp is greater than Ksp and the system is not at equilibrium. In order to decrease the value for Q, the system needs to move to the left. And the system will
continue to move to the left until Qsp is equal to Ksp again and the system is at equilibrium. A shift to the left means an
increase in the amount of PbCl2 which therefore decreases
the solubility of PbCl2. But it doesn't change the value for Ksp. Ksp for PbCl2 stays the same
at the same temperature. Next, let's see how the
presence of a common ion affects the molar solubility of lead II chloride. And to do that, let's calculate the molar
solubility of lead II chloride at 25 degrees Celsius in a solution that is 0.10
molar in potassium chloride. The Ksp value for lead II
chloride at 25 degrees Celsius is 1.7 times 10 to the negative fifth. To help us calculate the molar solubility, we're going to use an ICE table, where I stands for the
initial concentration, C is the change in concentration, and E is the equilibrium concentration. First, let's say that none of the lead II
chloride has dissolved yet. And if that's true, the concentration of lead
II plus ions would be zero, and the concentration of chloride anions from the lead II chloride
would also be zero. However, there's another
source of chloride anions, and that's because our
solution is 0.10 molar in KCl. KCl is a soluble salt. So KCl associates completely
to turn to K+ and Cl-. Therefore, if the concentration
of KCl is 0.10 molar, that's also the concentration
of Cl- from the KCl. So we can add here plus 0.10 molar. And think about that
as being from our KCl. So there are two sources. There's going to be two sources
of chloride anions here. And so the Cl anion and is our common ion. The other source of
chloride anion is PbCl2 when it dissolves. So some of the PbCl2 will dissolve, we don't know how much, so
I like to write -X in here. And if some of that dissolves, the mole ratio of PbCl2 to Pb2+
is a one-to-one mole ratio. So if we're losing X for PbCl2,
we're gaining X for Pb2+. And looking at our mole ratios, if we're gaining X for Pb2+ and it's a one-to-two mole ratio, we would write in here +2X
for the chloride anion. So for the equilibrium
concentration of Pb2+, it would be zero plus X, or just X. And for the equilibrium
concentration of the chloride anion, it would be 0.10 plus 2X. So the 0.10 came from
the potassium chloride, and the 2X came from the
dissolution of lead II chloride. Next, we need to write a Ksp expression, which we can get from
the disillusion equation. So, Ksp is equal to the
concentration of lead II plus ions raised to the first power times the concentration
of chloride anions. And since there's a two as a coefficient in the balanced equation, we need to raise that
concentration to the second power. Pure solids are left out of equilibrium constant expressions. So we don't write anything for PbCl2. Next, we plug in our
equilibrium concentrations. So for lead II plus, the
equilibrium concentration is X. And for the chloride anion, the equilibrium concentration
is 0.10 plus 2X. We also need to plug in the
Ksp value for lead II chloride. Here we have the Ksp value plugged in. X and 0.10 plus 2X. And let's think about 0.10
plus 2X for a second here. With a very low value for Ksp, 1.7 times 10 to the negative fifth, that means that not very much
of the PbCl2 will dissolve. And if that's true, X is
a pretty small number. And if X is a small number,
2X is also pretty small. So we're going to make an approximation and say that 0.10 plus
a pretty small number is approximately equal to just 0.10. And that's going to make
the math easier on us. So instead of writing
0.10 plus 2X squared, we just have 0.10 squared. Solving for X, we find
that X is equal to 0.0017, which we could just write as 1.7 times 10 to the negative third molar. It's okay to write molar here because this X value represents the equilibrium concentration of Pb2+. And if that's the equilibrium
concentration of Pb2+, that's also the concentration
of lead to chloride that dissolved. So this number, this concentration, is the molar solubility
of lead II chloride in a solution at 25 degrees where the solution is 0.10 molar in KCl. Most textbooks leave this
-X out of their ICE tables because the concentration
of a solid doesn't change. I like to just leave it in here though to remind me that X represents the molar solubility of
the slightly soluble salt. Finally, if we'd calculate the molar solubility of lead II chloride without the presence of a common ion, this 0.10 would have been
gone from everything. And doing the math that way,
we would have found that the molar solubility at 25 degrees Celsius and using this value for the Ksp, the molar solubility
comes out to 0.016 molar. So comparing these two
smaller solubilities, 0.016 molar versus 0.0017, that's approximately a factor of 10. Therefore the addition of a common ion decreased the solubility by
approximately a factor of 10. So doing the common ion
effect in a quantitative way also shows a decrease in the solubility of a slightly soluble salt because of the presence of a common ion.