How to Calculate pH and Molarities in Sulphuric Acid Solutions?

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SUMMARY

This discussion focuses on calculating the pH and molarities of species in sulfuric acid solutions, specifically a 0.1M NaHSO4 and 0.1M H2SO4. The first ionization of sulfuric acid is assumed to be complete, with a second dissociation constant (K_a2) of 0.10M at 25 degrees Celsius. The pH of the 0.1M NaHSO4 solution is calculated to be 1.21, based on a degree of dissociation (a) of 0.0618. The discussion also outlines the necessary steps to calculate the molarities of H^+, HSO4^-, and SO4^{2-} in the 0.1M H2SO4 solution.

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Assuming the first ionization of sulphuric acid is 100% and the K_{a2} of sulphuric acid is 0.10M at 25 degree celsius.(Ka is the acid disocciation constant)
a. Find the pH of a 0.1M NaHSO_4
b. Calculate the molarities of H^+, HSO_4^-, SO_4^{2-} respectively in 0.1M H_2SO_4

Here are my steps:
a. Let a be the degree of dissociation.
K_{a2} = \frac{a^2}{0.1-a} = 0.1
a = 0.0618
pH = - log 0.0618 = 1.21

I have no idea of how to do part b. Please help me with it and tell me whether I have done right in part a.
 
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I've already explained this problem in multiple threads, nevertheless,

a)

Ka_2= \frac{[SO_4^{-2}][H_3O^+]}{[HSO_4^-]}

Ka_2= \frac{[x][x]}{[.1M-x]}

b) The first acid will dissociate completely, thus the initial concentration of both the HSO4- and H3O+ will be .1M. Thus

Ka_2= \frac{[SO_4^{-2}][H_3O^+]}{[HSO_4^-]}

Ka_2= \frac{[x][.1M+x]}{[.1M-x]}
 

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