# pH of a Basic Solution

A weak base with Kb=4.240*10^-7 is added to water to make a 2.00*10^-1 M solution. what is the pH?

Since Kb is small, can assume that the dissociation is small relative to initial concentration of weak base.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

I used this, since formulas were used, and teh equation editor is much nicer than ascii text.

Note that I solve this problem frst disregarding the fact that Kb is very small. This is to show you how to do similar problems when Kb is not that small. In the second page I show that if we use this approximation (small Kb) then we still get the same result.

I encourage you to visit

http://artsci-ccwin.concordia.ca/facstaff/a-c/bird/c206/notes/chapter14.html

For an excellent review of pH calculations for acids and bases.

The initial concentration of the base BOH is and we will denote it as C

If each molecule loses then the concentrations of and B+ in the solution are equal and will be denoted as A.

So after the dissociation the concentration of BOH is C-A

Therefore the equilibrium equation is:

Since this is the concentration of the ions the pOH of the solution is given as:

The pH is therefore:

Now, If we take into account that Kb is extremely small, we can say that the dissociation percentage is very low, and the concentration of the base is pretty much constant.

The equation then becomes:

And to the second significant digit, the concentration of OH is identical to the previous result, and so is the final pH.

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