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pH of a mixture of two weak acids - Printable Version

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pH of a mixture of two weak acids - Nada - 04-12-2018

Hi!!

I have a problem with  one of the approximate formulas (for a mixture of two weak acids) which (it) derives from the expression:

[H+]= ka_1/(Ka_1+ [H+]) *C_1  +   ka_2/(Ka_2+ [H+])*C_2

At this point my textbook says that there are two main possible approximation:

1) If   [H+]>Ka_1, Ka_2   :
[H+]^2 = Ka_1*C_1 + Ka_2*C_2

2)  If   Ka_1>>Ka_2  and  C_1 >(or equal) C_2 :
[H+]= sqrt (Ka_1*C_1)

My PROBLEM is to understand how i can arrive at the expression  [H+]= sqrt (Ka_1*C_1) , using  the assumptions  Ka_1>>Ka_2  and  C_1 >(or equal) C_2, starting from the expression:
 [H+]= ka_1/(Ka_1+ [H+]) *C_1  +   ka_2/(Ka_2+ [H+])*C_2

Which are the  mathematical-logical steps  that i have to follow in order to get the approximate formula 2)???


Thanks very much!!!! Smile