Will a strong acid still dissociate "completely" even in the presence of a stronger acid?

For example, nitric acid or sulfuric acid in an equal-molar solution of perchloric acid. Won't perchloric protonate a significant concentration of nitrate ions?




Suppose you have nitric acid (about Ka=20) and perchloric acid (Ka > 100,000). 


$\frac{[A-][H+]}{[HA]} = K\_a$


In 1M nitric acid alone, let x be [$\ce{NO3-}$], that is dissociated nitric acid 


$\frac{x^2}{(1-x)} = 20$


x = 0.954M 


the nitric acid would be about 95% dissociated. 


If the solution is 1M nitric and 1M perchloric, with all the perchloric acid dissociating, the nitric acid equilibrium would be:


$\frac{x(1 + x)}{(1-x)} = 20$


x= 0.913


the nitric acid would be about 91% dissociated.


For 2M nitric acid alone:


$\frac{x^2}{(2-x)} = 20$


x= 1.83M


or 92% dissociated. 


For 2M nitric and 2M perchloric:


$\frac{x(2 + x)}{(2-x)} = 20$


x = 1.69M


or 84% dissociated.


So yes it can make a difference and it is more apparent at higher concentration.


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