[sluijten]

Formula for pH of a mixture of acid (3 dissociation steps) & base (1 dissociation step) :

(C_(a ) (K_a1 [H]^2 + 2K_a2 [H] + 3K_a3) / ([H]^3 + K_a1 [H]^2 + K_a2 [H] + K_a3 ) + K_w/[H] =
(C_(b ) (K_b1 [H] ) / (K_w+ [H] K_b1 ) + [H]               

Calculating the pH of a mixture of phosphoric acid (with Ca=0.01,  3 dissociation steps) &
ammonia (with Cb=0.02, 1 dissociation step):
K_a1=10^(-2.148)
K_a2=10^(-7.199)
K_a3=10^(-12.35)
K_w= 10^(-14)
K_b1=10^(-4.75)

Left-hand side works out to be:
(7.11214×10^(-5) [H]^2+1.26482×10^(-9) [H]+1.34005×10^(-14)) / ([H]^3+ 7.11214×10^(-3) [H]^2+6.32412×10^(-8) [H]+4.46684×10^(-13) )+ 10^(-14)/([H])                

Right-hand side works out to be:
(3.55656×10^(-7) [H])/(10^(-14)+1.77828×10^(-5) [H] )+ [H]

When I solve for [H], then I find:
[H] = 7.94328×10^(-6),   with
LHS = RHS = 1.99×10^(-2)

So this would mean that pH = 5.10
However, Chembuddy pH calculator’s solution gives  pH= 8.06

I checked this several ways, over and over again, and can’t find where I go wrong, I would very much appreciate if
someone could indicate what’s going on here, thanks a lot in advance!

[Borek]

Formula for pH of a mixture of acid (3 dissociation steps) & base (1 dissociation step)

I think I know what is going on.

Where did you get this formula from? Have you read everything on the page?

[sluijten]

The formula is from
http://www.chembuddy.com/?left=BATE&right=pH_calculation

and yes I read everything (I think...)

[Borek]

Oops, you found an error on the page 

These are overall dissociation constants, not stepwise ones. This was correctly explained on the page where this equation is derived (http://www.chembuddy.com/?left=pH-calculation&right=pH-salt-solution), obviously I wasn't precise when copying the information to BATE pages.

Corrected now, thank you for spotting, sorry you have lost time because of that.

[sluijten]

Thanks!!

[sluijten]

Although it's explained in the text, using the same symbols for overall and stepwise dissociation constants can be somewhat confusing....
The website overall is great though !!

[Borek]

Although it's explained in the text, using the same symbols for overall and stepwise dissociation constants can be somewhat confusing....
The website overall is great though !!

Good point. And thanks.