Chemistry - Partition Law

Problem Set


What will the scientists do if they want to extract and help purify a desired product from a reaction mixture? This is when the Partition Law(or Distribution Law) saves the day!

First, we set some variables:

Let AA and BB be two immiscible liquids(cannot dissolve or react with each other), such as water and oil.

Let the solubility of XX in liquid AA be sAs_A.

Let the solubility of XX in liquid BB be sBs_B.

Now, we do the following steps:

1) Mix solute XX into the mixture of liquid AA and BB.

2) Stir them constantly and wait till liquid AA and liquid BB are divided into two layers(they will as they cannot dissolve each other).

3) Now, solute XX is dissolved in both solvent AA and solvent BB but the concentration is different.

This is what Partition Law wants to deliver to us.

Definition: At a fixed temperature, when a solute is added to a system consisting of two solvent, it will distribute itself between the two solvent in proportion to its solubility in each of the two solvent separately.

If we express the definition in formula, it will be

K=sAsBK=\frac{s_A}{s_B}

where KK is the partition coefficient.

If at 40C40^\circ C, the solubility of XX is 50g/100g50g/100g water and 100g/100g100g/100g ether, then the partition coefficient

K=swatersether=50g/100g100g/100g=12K=\frac{s_{water}}{s_{ether}}=\frac{50g/100g}{100g/100g}=\frac{1}{2}.

Now there is an example:

If 1L1L water can dissolve 100g100g organic compound XX and I use 1L1L ether to extract it, what is the mass in grams of XX are left in the ether layer?

Details:

K=sH2Osether=12K=\frac{s_{H_2O}}{s_{ether}}=\frac{1}{2}

Solution:

Let the amount extracted be xx gg.

The solubility of XX in water is sH2O=(100x)g1Ls_{H_2O}=\frac{(100-x)g}{1L}

The solubility of XX in ether is sether=xg1Ls_{ether}=\frac{xg}{1L}

Then,

K=sH2OsetherK=\frac{s_{H_2O}}{s_{ether}}

12=(100x)g1L(x)g1L\frac{1}{2}=\frac{\frac{(100-x)g}{1L}}{\frac{(x)g}{1L}}

x=66.7x=66.7 gg

So, the mass of XX that left in the ether layer is 66.766.7 gg.

**Note that I use g/Lg/L as the unit of solubility instead of g/gg/g in my note before.

Solubility of 5g/1L5g/1L water means 1L1L water can dissolve a maximum of 5g5g of that solute.

Solubility of 5g/100g5g/100g water means 100g100g water can dissolve a maximum of 5g5g of that solute.

So, the unit does not make any changes to the answer as long as we use the same unit. As the example above, we cannot use a unit of solubility written as g/Lg/L while the other written as g/gg/g.

Note by Christopher Boo
5 years, 5 months ago

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Comments

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Top Newest

Why is x=66.7gx = 66.7g?

Daniel Lim - 5 years, 4 months ago

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12=100xx\frac{1}{2}=\frac{100-x}{x}

x=2002xx=200-2x

3x=2003x=200

x=66.7x=66.7

Christopher Boo - 5 years, 4 months ago

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Oh... Thanks

Daniel Lim - 5 years, 4 months ago

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Good Post...

Anish Puthuraya - 5 years, 5 months ago

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good post

Fauline ST - 5 years, 5 months ago

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nice.. :)

joyan florenz delos verges - 5 years, 5 months ago

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Peter Taylor-

I like the way you added the problems into the notes. However, I don't know how to add a line between the problem and the note. Can you teach me, please?

Christopher Boo - 5 years, 5 months ago

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To make a line between things use 3 dashes in a row at the beginning of the line. For instance, this is a picture of the markdown on your problem set in the first note.

Imgur Imgur

Peter Taylor Staff - 5 years, 5 months ago

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Thanks!

Christopher Boo - 5 years, 5 months ago

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I also took the liberty of making you a picture. It's not the best, and it is a little bit of stretch, seeing as the post is mostly about partitioning and not about miscibility. If you don't like it, I can take the picture away.

Peter Taylor Staff - 5 years, 5 months ago

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The picture is very nice, thanks!

Christopher Boo - 5 years, 5 months ago

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Thanks Christopher for this post which is completely new to me.

Soham Dibyachintan - 5 years, 5 months ago

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Thanks for the post! Never learned this back in secondary school.

Marissa Chong - 5 years, 4 months ago

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What does "extract" mean?

Daniel Lim - 5 years, 4 months ago

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Literal Definition: to remove/separate a certain substance(useful) from another substance through various Physical and Chemical methods.

Anish Puthuraya - 5 years, 4 months ago

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To obtain a substance by chemical or mechanical action, as by pressure, distillation, or evaporation. (Google)

Christopher Boo - 5 years, 4 months ago

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Thanks

Daniel Lim - 5 years, 4 months ago

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Thx for the information

Benjamin Setiawan - 3 years, 2 months ago

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