Chemistry

The dissociation equilibrium is 

CH_3? COOH? CH3? COO⁻ + H⁺.
Let α be the degree of dissociation.
The equilibrium concentrations of CH_3? COOH, CH₃COO⁻ and H⁺ are c (1−α), c (α) and c (α) respectively.
The equilibrium constant expression is K_c? = [CH_3? COO⁻] [H⁺]? / [CH₃? COOH].

K_c? = (cα) (cα) / c (1−α)? ≈cα²

α= (K_a? / c)^1/2? = (1.74*10⁻⁵ / 0.05)^1/2?

=1.865*10⁻²
[CH3? CO⁻]= [H⁺]= cα= 0.05*1.865*10⁻²= 9.33*10⁻⁴M
pH= −log [H⁺]= −log (9.33*10⁻⁴)= 3.03

The concentration of acetate ion and its pH are 9.33*10⁻⁴ and 3.03 respectively.

(i) To calculate  [HS⁻] in absence of HCl:
Let,   [HS⁻] = x M.

H_2? S? H⁺ + HS⁻
The initial concentrations of H_2? S, H⁺ and HS⁻ are 0.1 M, 0 M and 0 M respectively.
Their final concentrations are 0.1-x M, x M and x M respectively.

K_a? = [H₂? S] [H⁺] [HS⁻]?
  9.1*10⁻⁸ = x * x / (0.1−x)?
In the denominator, 0.1-x can be approximated to 0.1 as x is very small.
   9.1*10⁻⁸=x*x / (0.1)?

x=9.54*10⁻⁵M= [HS⁻]

(ii) To calculate  [HS⁻] in presence of HCl:
Let  [HS⁻]= y M.

 H₂? S? H⁺+HS⁻
The initial concentrations of H_2? S, H⁺ and HS⁻ are 0.1 M, 0 M and 0 M respectively.
Their final concentrations are 0.1-y M, y M and y M respectively.
Also, HCl? H⁺+Cl⁻
For HCl  [H⁺]= [Cl⁻]=0.1M
K_a? = [HS⁻] [H⁺] / [H_2? S]?
K_a? = y (0.1+y)? / (0.1−y)
In the denominator, 0.1-y can be approximated to 0.1 and in the numerator, 0.1+y can be approximated to 0.1 as y is very small.
9.1*10⁻⁸= (y*0.1) / 0.1?

y= 9.1*10⁻⁸M= [HS⁻]

(iii) To calculate [S²⁻] in absence of 0.1 M HCl:

HS⁻? H⁺+S²⁻
[HS⁻]=9.54*10⁻⁵M
Let  [S²⁻]= x M.
[H⁺]= 9.54*10⁻⁵ M

K_a? = [H⁺] [S²⁻]? / [HS⁻]
= >1.2*10⁻¹³= (9.54*10⁻⁵*X? ) / (9.54*10⁻⁵)
= > x=1.2*10⁻¹³M= [S²⁻]

(iv) To calculate  [S²⁻] in presence of 0.1 M HCl:
Let  [S²⁻]= x′ M.
[HS⁻]= 9.1*10⁻⁸ M
[H⁺]= 0.1 M (from HCl)

K_a? = [HS⁻] [H⁺] [S²⁻]?
1.2*10⁻¹³= (0.1*X′? ) / (9.1*10⁻⁸)

x′= 1.092*10⁻¹⁹= [S²⁻]